applied
sciences
Article
Safety Issues Referred to Induced Sheath Voltages in
High-Voltage Power Cables—Case Study
Stanislaw Czapp *
and Krzysztof Dobrzynski
Faculty of Electrical and Control Engineering, Gdańsk University of Technology, Narutowicza 11/12,
PL-80-233 Gdańsk, Poland; krzysztof.dobrzynski@pg.edu.pl
* Correspondence: stanislaw.czapp@pg.edu.pl
Received: 20 August 2020; Accepted: 23 September 2020; Published: 25 September 2020
Abstract: Load currents and short-circuit currents in high-voltage power cable lines are sources of
the induced voltages in the power cables’ concentric metallic sheaths. When power cables operate
with single-point bonding, which is the simplest bonding arrangement, these induced voltages may
introduce an electric shock hazard or may lead to damage of the cables’ outer non-metallic sheaths
at the unearthed end of the power cable line. To avoid these aforementioned hazards, both-ends
bonding of metallic sheaths is implemented but, unfortunately, it leads to increased power losses in
the power cable line, due to the currents circulating through the sheaths. A remedy for the circulating
currents is cross bonding—the most advanced bonding solution. Each solution has advantages and
disadvantages. In practice, the decision referred to its selection should be preceded by a wide analysis.
This paper presents a case study of the induced sheath voltages in a specific 110 kV power cable line.
This power cable line is a specific one, due to the relatively low level of transferred power, much lower
than the one resulting from the current-carrying capacity of the cables. In such a line, the induced
voltages in normal operating conditions are on a very low level. Thus, no electric shock hazard exists
and for this reason, the simplest arrangement—single-point bonding—was initially recommended at
the project stage. However, a more advanced computer-based investigation has shown that in the
case of the short-circuit conditions, induced voltages for this arrangement are at an unacceptably
high level and risk of the outer non-metallic sheaths damage occurs. Moreover, the induced voltages
during short circuits are unacceptable in some sections of the cable line even for both-ends bonding
and cross bonding. The computer simulations enable to propose a simple practical solution for
limiting these voltages. Recommended configurations of this power cable line—from the point of
view of the induced sheath voltages and power losses—are indicated.
Keywords: power cables; high-voltage; induced sheath voltages; electric shock hazard; overvoltages;
power losses
1. Introduction
High-voltage transmission and distribution power lines are usually used overhead with bare
conductors. The main reason for the widespread use of overhead power lines, instead of cable lines,
is their lower investment cost. However, there are cases in which the application of overhead lines is
precluded. These refer mainly to urban areas but also to rural areas when an increased risk of electric
shock hazard or exposure to electromagnetic fields exists [1]. With many undoubtable advantages,
the utilization of high-voltage cable lines is associated with some problems. One of the main problems
is the induced voltage generated in the power cable’s metallic concentric sheath. With reference to
this voltage, power cables may operate as single-point bonded, both-ends bonded or cross-bonded.
Recommendations for the performance of power cables bonding and earthing are mainly included
Appl. Sci. 2020, 10, 6706; doi:10.3390/app10196706
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Appl. Sci. 2020, 10, 6706
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Appl. Sci. 2020, 10, x
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in the standards [2,3] as well as the report [4]. Figure 1 presents the three aforementioned cable
mainly included in the standards [2,3] as well as the report [4]. Figure 1 presents the three
bonding arrangements.
aforementioned cable bonding arrangements.
aluminium conductor
copper sheath
XLPE insulation
PE outer sheath
L1
L1
L2
L2
L3
L3
(a)
(b)
L1
L2
L3
(c)
Figure 1.
1. High-voltage
High-voltage power
power cables
cables arrangements:
arrangements: (a)
(a) single-point
single-point bonding;
bonding; (b)
(b) both-ends
both-ends bonding;
bonding;
Figure
(c)
cross
bonding.
(c) cross bonding.
The simplest cable sheath bonding arrangement is single-point bonding. In such a solution
The simplest cable sheath bonding arrangement is single-point bonding. In such a solution
(Figure 1a) the load current in the cable conductor (core) induces a voltage in the sheath, which value
(Figure 1a) the load current in the cable conductor (core) induces a voltage in the sheath, which value
is the highest at the unearthed end of the power cable line. The induced sheath voltages for any cables’
is the highest at the unearthed end of the power cable line. The induced sheath voltages for any
formation in a single-circuit system can be calculated (in simplified form) as follows [2]:
cables’ formation in a single-circuit system can be calculated (in simplified form) as follows [2]:



√
!
2
  1 1  2D

2L1−L2  

2D
3

L1−L3
−7−


DL1-L3 
7− ln 2 DL1-L2   + 3j  2ln
VL1−sh
jωI
2
·
10
(1)


L1

VL1=
j
I
j
2
10
+
ln
ln
ω
=
⋅
−



(1)
-sh
L1
DL1−L3

2 2 D DCu
 2 2 D

DCu ⋅· D


Cu
L1- L3 

Cu

√
!
!#
"
·
D
3 D DL2−L3
 1 4D

L1−L2
L2−L3

−7 1

D
D
⋅
4
3
VL2−sh
=
jωI
2
·
10
ln
+
j
ln
−
7
L1
L2
L2
L3
L2
L3
+ j

VL2-sh = jωL2I L2 2 ⋅ 10 2 ln
ln
DCu22
L1−L2

2 2  DL1D
 2 
DCu
-L2 





√
!

 1  2D2L2−L3 
2D
3
L1−L3
−7 
VL3−sh = jωIL3 2 · 10 − ln
ln
 − j
 
2



21 D 2 D· DL1−L3 − j 32ln  2 D L1D
- L3
Cu 
= jωI 2 ⋅ 10 −7  − ln  Cu L2-L3
V
(2)
(2)
(3)
(3)
L3-sh
L3

 2  D ⋅ D
2  D Cu  
L1-L3(V/m)
 Cu

 sheath
 and L3, respectively;
where: V L1-sh , V L2-sh , V L3-sh are the induced
voltages
in phases L1, L2
IL1 , IL2 , IL3 , are the load currents in the cable conductor (core) of phases L1, L2 and L3, respectively;
where: VL1-sh, VL2-sh, VL3-sh are the induced sheath voltages (V/m) in phases L1, L2 and L3, respectively;
D is the geometric mean sheath diameter; DL1-L2 is the axial spacing of phases L1 and L2; DL2-L3 is
IL1cu
, IL2, IL3, are the load currents in the cable conductor (core) of phases L1, L2 and L3, respectively;
the axial spacing of phases L2 and L3; DL1-L3 is the axial spacing of phases L1 and L3.
Dcu is the geometric mean sheath diameter;
DL1-L2 is the axial spacing of phases L1 and L2; DL2-L3 is the
For more accurate calculation of the voltages, especially taking into account the electromagnetic
axial spacing of phases L2 and L3; DL1-L3 is the axial spacing of phases L1 and L3.
couplings, computer-based tools should be employed. The computer-aided modelling of the induced
For more accurate calculation of the voltages, especially taking into account the electromagnetic
sheath voltages with the use of the PSCAD/EMTDC software is presented in [5], whereas [6] presented
couplings, computer-based tools should be employed. The computer-aided modelling of the
the calculation by the Pearson Correlation. Multiple-circuit systems require the application of
induced sheath voltages with the use of the PSCAD/EMTDC software is presented in [5], whereas [6]
advanced computer-based tools to calculate these voltages, as presented by the authors in [7] or
presented the calculation by the Pearson Correlation. Multiple-circuit systems require the
other researchers in [8,9].
application of advanced computer-based tools to calculate these voltages, as presented by the
To avoid electric shock, the induced voltage-to-earth at the unearthed end should not exceed
authors in [7] or other researchers in [8,9].
permissible values determined by the standard [10]. For a long-time of touch voltage duration,
To avoid electric shock, the induced voltage-to-earth at the unearthed end should not exceed
permissible values determined by the standard [10]. For a long-time of touch voltage duration, the
permissible value is equal to 80 V. When the load current is relatively low or a cable line is not long,
Appl. Sci. 2020, 10, 6706
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the permissible value is equal to 80 V. When the load current is relatively low or a cable line is not
long, values of the induced voltages are usually below the permissible limit. A more serious problem
occurs in the case of a line-to-earth fault at the unearthed end. If the value of the short-circuit current is
high, this current produces a high-value induced voltage, which may damage the cables’ non-metallic
polyethylene (PE) outer sheath. It is assumed in the engineering practice that during the short-circuit
conditions the induced voltage should not exceed 5 kV. To limit values of the induced voltage, an earth
continuity conductor (ECC) is buried in the ground, parallel to the cables, what was widely studied
in [11]. The extensive analysis conducted in [12] shows that in special cases the ECC may reduce the
induced voltages by even over 60% compared to a system without the ECC. Despite this, the induced
voltages may still exceed the acceptable level. Moreover, the study results presented in [13] indicate
that in the case of the uninsulated ECC, dangerous touch voltages may appear around this parallel
cable. For these reasons or when the voltages are too high in normal operating conditions, both-ends
bonding of cables is used as an alternative (Figure 1b).
When both-ends bonding is used, metallic sheaths are bonded and earthed in the accessible points in
substations and no risk of electric shock occurs in normal operating conditions. Moreover, in the case of
a line-to-earth short circuit, the current distribution through the earthing system is more favourable [14],
especially when a global earthing system exists in the analyzed area [15]. The most unfavourable
effect of the both-ends bonding is the presence of sheath circulating currents. These currents produce
additional power losses in the cables and hence decrease the current-carrying capacity. Such power
losses, due to the induced voltages, may occur even in HVDC power cable systems, as underlined in [16].
Therefore, it is important to evaluate sheath circulating currents with relatively high accuracy [17],
taking into account different geometries of the cables [18], sheath resistance, phase rotation and cable
armouring [19] as well as varied load conditions [20]. High circulating currents and high power
losses resulting from them are required to be reduced [21–24]. The most effective method of sheath
currents suppression, but relatively complicated, is the implementation of the cross-bonded cable
system (Figure 1c). Broad studies of this method are included in [25–30]. Transposition of the cables’
sheaths in particular phases compensates induced voltages and theoretically, no production of the
sheath circulation currents occurs.
The literature study leads to the conclusion that methods of the induced sheath voltages and
sheath circulating currents reduction should be applied very carefully. Any given cable system,
especially a complicated one, should always be analyzed individually. Unfortunately, the selection of the
type of bonding in the particular case of the cable system is not an easy task. In practice, a compromise
between technical and economic aspects should be reached.
This paper presents a comprehensive study of the induced voltages in the 110 kV power cable
line. The power cable line is relatively long (12 km) but the power transferred via this line is very
low (approx. 12% with reference to max permissible power transfer via the cables) due to a specific
type of the industrial consumer at the end of the line. Such a low transferred power suggests the
application of the single-point bonding in the analyzed power cable line because the induced sheath
voltages at the unearthed end are clearly below the permissible limit equal to 80 V, hence no electric
shock hazard exists. However, the short-circuit analysis has shown that the single-point bonding is
excluded—very high values of the induced voltages are dangerous for the non-metallic PE outer sheath.
The results of the calculations suggest to apply both-ends bonding or cross bonding, but detailed
analysis for these arrangements has shown that the risk of outer sheath damage still exists in some
sections of the power cable line. A solution for the elimination of too high induced voltages during
a short circuit is indicated.
As an extension of the analysis related to induced voltages, power losses in the cable system,
including in cables’ sheaths, have been calculated for all types of bonding. In some cases, values of the
power losses may be a decisive factor in selecting the type of the bonding system.
The presented results of the analysis of the induced voltages and power losses in the example
high-voltage power cable line can be useful for practical applications, especially for the designers of
parameters of the cable/cable line are as follows [31]:
•
•
nominal voltage of the cable: 110 kV (line-to-line), 64 kV (line-to-earth);
nominal cross-sectional area of the aluminium conductor (core): 240 mm2; (external diameter
DAl2020,
= 17.9
Appl. Sci.
10, mm);
6706
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•
resistance of the aluminum conductor (core): 0.125 Ω/km (DC in 20 °C), 0.161 Ω/km (AC in max
temp. 90 °C);
the
cable
lines.cross-sectional
The analysis has
the possible
points
in such
lines,
which
•
nominal
areaindicated
of the copper
sheath:critical/weak
95 mm2 (mean
diameter
DCu
= 58.5
mm);could
be
overlooked
at
the
design
stage.
•
resistance of the copper sheath: 0.192 Ω/km (DC in 20 °C);
•
inductive reactance of the cable line in the trefoil formation: 0.143 Ω/km;
2. Description of the Analyzed 110 kV Cable Line
•
XLPE insulation external diameter: DXLPE = 52.9 mm;
The
power
cable external
system under
analysis
connects
a 110 kV
power
substation
(supply
•
PE outer
sheath
diameter
(the outer
diameter
of the
cable):
DPE = 66.6
mm; service) and
a• dedicated
consumer/load (Figure
2). in
Thethe
total
lengthformation:
of the single-circuit
three-phase cable
line is approx.
the current-carrying
capacity
trefoil
421 A (single-point
bonding),
409 A
12 km.
The manufacturer’s
(both-ends
bonding); length of the cable (minor section) is equal to approx. 1 km and the points
with
connections of
the consecutive
sections
are
marked
•
short-circuit
power
at the supply
service
point:
1120p.0–p.12
MVA. in Figure 2. In some of these points,
earthing and bonding (including cross bonding) of the cables’ sheaths are possible. Generally, cables are
On the base of the nominal parameters of the cable/cable line, it can be stated that the maximum
laid in trefoil formation without spacing. Some spacing, as well as short sections with flat formation,
permissible power transmitted via this line is approx. 80 MW. However, the consumer’s demand is
are applied in the cable ducts, what is included in the computer model.
only 10 MW and the connection of other loads to this 110 kV cable line is not planned.
Power
system
110 kV
Supply service
Load
10 MW
tgφ = 0.4
Consumer
p.0
p.12
p.1
p.11
~3 km
~3 km
p.2
~1 km
p.10
p.5
p.4
p.6
p.7
p.8
p.3
~3 km
p.9
~3 km
Figure 2. General data of the analyzed power cable system; p.0–p.12—possible points for earthing
Figure 2. General data of the analyzed power cable system; p.0–p.12—possible points for earthing
and bonding.
and bonding.
The type of cable used in this line is presented in Figure 3 (a simplified view). The nominal
parameters of the cable/cable line are as follows [31]:
•
•
•
•
•
•
•
•
•
•
nominal voltage of the cable: 110 kV (line-to-line), 64 kV (line-to-earth);
nominal cross-sectional area of the aluminium conductor (core): 240 mm2 ; (external diameter
DAl = 17.9 mm);
resistance of the aluminum conductor (core): 0.125 Ω/km (DC in 20 ◦ C), 0.161 Ω/km (AC in max
temp. 90 ◦ C);
nominal cross-sectional area of the copper sheath: 95 mm2 (mean diameter DCu = 58.5 mm);
resistance of the copper sheath: 0.192 Ω/km (DC in 20 ◦ C);
inductive reactance of the cable line in the trefoil formation: 0.143 Ω/km;
XLPE insulation external diameter: DXLPE = 52.9 mm;
PE outer sheath external diameter (the outer diameter of the cable): DPE = 66.6 mm;
the current-carrying capacity in the trefoil formation: 421 A (single-point bonding), 409 A
(both-ends bonding);
short-circuit power at the supply service point: 1120 MVA.
Appl. Sci. 2020, 10, 6706
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Appl. Sci. 2020, 10, x
5 of 16
Figure
3. A
view
ofofthe
analyzedcase.
case.
Figure
3. simplified
A simplified
view
thepower
powercable
cableused
used in
in the
the analyzed
On the
of the
nominal
of the
line, with
it canthe
be use
stated
thatPowerFactory
the maximum
Thebase
power
cable
system parameters
under analysis
hascable/cable
been modelled
of the
permissible
transmitted
this takes
line isinto
approx.
80 MW.
However,
thebyconsumer’s
demand
softwarepower
[32]. The
computervia
model
account
all data
delivered
the investor,
among is
onlyother:
10 MW
and
the
connection
of
other
loads
to
this
110
kV
cable
line
is
not
planned.
cable technical parameters, cable line layout (including the arrangement with cable ducts),
The power
cable
system
under
analysis The
has entire
been modelled
with
the
use ofofthe
possible
points
of the
bonding
or earthing.
model of the
line
consists
161PowerFactory
sections, of
software
Thecable
computer
model
takes into
account
all data delivered
investor,
among
which[32].
61 are
ducts with
different
cable
arrangements.
Two typesby
of the
cable
ducts are
used:other:
the
cableflat
technical
parameters,
cable line
layout The
(including
the arrangement
with cableducts
ducts),
points
formation
and the trefoil
formation.
participation
of the flat formation
in possible
the length
of
the
line
is
1.7%,
and
the
participation
of
the
trefoil
formation
ducts
is
8.2%.
Thus,
90%
of
the
cable
of the bonding or earthing. The entire model of the line consists of 161 sections, of which 61 are cable
line
length
is the cable
trefoilarrangements.
formation without
without
rough
of the
ducts
with
different
Twospacing
types ofand
cable
ductsducts—for
are used: the
flatcalculations
formation and
the
induced
voltages,
is acceptableof
to the
assume
such a formation
along
the entire
length
line.and the
trefoil
formation.
Theitparticipation
flat formation
ducts in
the length
of the
lineofisthe
1.7%,
Figure
4a trefoil
presents
a cable ducts
route,iswhich
is reflected
the
computer
model—small
dots
participation
of the
formation
8.2%. Thus,
90% ofinthe
cable
line length
is the trefoilblue
formation
indicate
a
change
in
cable
spacing
(due
to
ducts
application).
The
cables’
joints
are
marked
as
big
redto
without spacing and without ducts—for rough calculations of the induced voltages, it is acceptable
dots.
assume such a formation along the entire length of the line.
The PowerFactory software allows for modelling cable lines, including cable spacing, which
Figure 4a presents a cable route, which is reflected in the computer model—small blue dots indicate
means that the software automatically determines the selected power line electrical parameters.
a change in cable spacing (due to ducts application). The cables’ joints are marked as big red dots.
Impedance Z and admittance Y of cables are defined in two matrix equations presented in [33] and
The PowerFactory software allows for modelling cable lines, including cable spacing, which means
implemented in the software as well as described in its guide [34]:
that the software automatically determines the selected power line electrical parameters. Impedance Z
and admittance Y of cables are defined in two ∂matrix
presented in [33] and implemented
V = −equations
Z⋅I
(4) in
x
∂
the software as well as described in its guide [34]:
∂
(5)
∂ ∂x I = − Y ⋅ V
V =−Z · I
(4)
∂x
where: |V| and |I| are the voltage and current vectors respectively, at distance x along the cable line;
∂
|Z| and |Y| are square matrices of the impedance
and admittance respectively.
I =−Y · V
(5)
∂x
The complexity of |Z| and |Y| matrices
depends on the number of cables and the number of
layers
The impedance
and vectors
admittance
matrices can
be described
in the
where:
|V| per
andsingle
|I| arecable.
the voltage
and current
respectively,
at distance
x along
thefollowing
cable line;
way:
|Z| and
|Y| are square matrices of the impedance and admittance respectively.
The complexity of |Z| and |Y| matrices
the number of cables and the number of layers
[ Z ] = depends
[ Z i ] +  Z on
(6)
p
 + [Z c ] + [Z 0 ]
per single cable. The impedance and admittance matrices can be described in the following way:
h i [Y h] = is ⋅ [Ch ] i h i
(7)
[Z] = Zi + Zp + Zc + Z0
(6)


[C ] = [Ci ] + C p  + [Cc ] + [C0 ]
(8)
[Y] = s · [C]−1
(7)
where: the matrices with subscript i include cable
(core, sheath and armour); the matrices
h parameters
i
with subscript 0 include parameters
outer
[C]of=the
[Ccable
[Cc ] +(air,
[C0 ]earth); the matrices with subscripts p(8)
p +media
i] + C
and c include parameters of a pipe (an enclosure—if applied); C is a potential coefficient matrix; s = jω.
where: the
matrices with subscript i include cable parameters (core, sheath and armour); the matrices
Detailed information on the calculation of individual components of the impedance and
withadmittance
subscript 0matrices
includecan
parameters
cable outer media (air, earth); the matrices with subscripts
be found of
in the
[33,34].
p and c include parameters of a pipe (an enclosure—if applied); C is a potential coefficient matrix; s = jω.
Detailed information on the calculation of individual components of the impedance and admittance
matrices can be found in [33,34].
−1
Appl.
Appl.Sci.
Sci.2020,
2020,10,
10,6706
x
6 6ofof1616
(a)
point
p.0
p.0(c)
point
p.1
~1 km
...
Core L2
...
Core L3
Electric
circuit of cores (c)
...
9m
68 m
p.0(sh)
p.1(c)
p.0.3(c) p.0.4(c)
p.0.2(c)
p.0.1(c)
Core L1
Sheath L1
p.0.1(sh)
22 m
p.0.2(sh)
3m
p.0.3(sh) p.0.4(sh)
p.1(sh)
...
Sheath L2
...
Sheath L3
...
Electric
circuit of sheaths (sh)
Cable arrangement
Cables directly
buried in the ground
(trefoil formation)
160 mm
Cables in ducts
(flat formation)
in consecutive sections
Cables in ducts
(trefoil formation)
(b)
Figure
cable
route
of the
cablecable
system
reflected
in the PowerFactory
software software
(a); an example
Figure4.4.Real
Real
cable
route
of analyzed
the analyzed
system
reflected
in the PowerFactory
(a); an
part
of
the
computer
model
of
the
cable
system
(minor
section
between
point
p.0
and
point
p.1)
(b).
example part of the computer model of the cable system (minor section between point p.0 and point
p.1) (b).
Appl. Sci. 2020, 10, x
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Appl. Sci. 2020, 10, 6706
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In the considered case, the cable line model consists of two electromagnetically coupled circuits:
cores electric circuit (c) and sheaths electric circuit (sh) (Figure 4b). The results of the multi-variant
computer
analysis included
the next
show theoflevels
of voltages induced incoupled
the cables’
In the considered
case, theincable
line sections
model consists
two electromagnetically
circuits:
risks(c)
referred
to them,
as wellcircuit
as the(sh)
power
losses4b).
influencing
the current-carrying
coressheaths
electricand
circuit
and sheaths
electric
(Figure
The results
of the multi-variant
capacity
of the cables.
computer
analysis
included in the next sections show the levels of voltages induced in the cables’
sheaths and risks referred to them, as well as the power losses influencing the current-carrying capacity
3. Results of the Induced Voltages Computer Simulations
of the cables.
3.1. Induced Voltages for Single-Point Bonding
3. Results of the Induced Voltages Computer Simulations
In the first stage of the analysis, the induced sheath voltages in normal operating conditions, in
case of the
single-point
bonding, Bonding
have been analyzed. The load current flow in the cable cores, as
3.1. Induced
Voltages
for Single-Point
well as the induced voltages, are calculated by the software taking into account the electromagnetic
In the firstAll
stage
ofpresenting
the analysis,
the induced
sheath
voltages
in normal
operating
conditions,
couplings.
charts
the induced
voltages
include
the highest
rms values
among phases
in case
of
the
single-point
bonding,
have
been
analyzed.
The
load
current
flow
in
the
cable
cores,
L1, L2, L3.
as well asThe
theanalyses
inducedhave
voltages,
are calculated
the software
taking into account the electromagnetic
been conducted
for thebyfollowing
variables:
couplings.
All charts presenting the induced voltages include the highest rms values among phases L1,
•
the transferred power equal to 1 MW (an example very low power), 10 MW
L2, L3. (contracted/declared consumed power), 80 MW (maximal permissible power in terms of the
The current-carrying
analyses have been
conducted
for the
followingvalue,
variables:
capacity
of the cables;
a theoretical
used for the comparison purposes);
•
•
•
•
the single-point-bonding at the 110 kV supply service substation (p.0 in Figure 2) or at the
the transferred
power equal to 1 MW (an example very low power), 10 MW (contracted/declared
consumer substation (p.12 in Figure 2);
consumed
power), 80 MW
(maximal
in terms
of the current-carrying capacity
•
the reactive-to-active
power
ratio: tgpermissible
φ = Q/P = 0 orpower
tgφ = Q/P
= 0.4 (contracted).
of the cables; a theoretical value, used for the comparison purposes);
Figure 5 presents the induced sheath voltages for the case with the tgφ = 0. When the
the single-point-bonding at the 110 kV supply service substation (p.0 in Figure 2) or at the
single-point bonding is performed at the 110 kV supply service substation (Figure 5a), the induced
consumer
(p.12
in Figure
2); limit 80 V indicated in the standard [10], both for the
voltages aresubstation
significantly
below
the assumed
the
reactive-to-active
power ratio:
= Q/P
= 0value
or tgφ
=isQ/P
= 0.4
(contracted).
power
1 MW and the contracted
powertgφ
10 MW.
The
80 V
many
times
exceeded in the case of
the 80 MW (approx. 330 V), but it is presented only for the comparison purposes. When the
Figure 5 presents
theisinduced
sheath
forsubstation
the case with
the5b),
tgφthe
= 0.
Whenvoltages
the single-point
single-point
bonding
performed
at thevoltages
consumer
(Figure
induced
are
bonding
is
performed
at
the
110
kV
supply
service
substation
(Figure
5a),
the
induced
voltages
generally higher than for the case presented in Figure 5a. For the transferred power 10 MW,
it is are
significantly
below
the assumed
80 unearthed
V indicated
close to the
permissible
limit 80 limit
V at the
endinofthe
the standard
line (point[10],
p.0). both for the power 1 MW
and the contracted
power
10 MW.
Thevoltages
value 80
V is many
the case
ofnatural
the 80 MW
The differences
in the
induced
(Figure
5a vs. times
Figureexceeded
5b) are theineffect
of the
load 330
of the
line
(capacitive),only
which
a capacitive purposes.
current flow
of a changing
value along
(approx.
V),cable
but it
is presented
forforces
the comparison
When
the single-point
bonding
the
length
of
the
cable
line.
It
indicates
that
the
location
of
the
point
of
the
earthing
(reference
point)
is performed at the consumer substation (Figure 5b), the induced voltages are generally higher than for
is important.
Note,
that for5a.
theFor
case
presented
in Figure
5a,10
the
induced
voltages
at the
unearthed limit
the case
presented
in Figure
the
transferred
power
MW,
it is close
to the
permissible
end are practically the same for the power 1 MW and 10 MW. In the case of Figure 5b, the respective
80 V at the unearthed end of the line (point p.0).
voltages at the unearthed end differ about two times.
80 V
400
350
80 MW
300
250
200
induced voltage (V)
induced voltage (V)
400
150
100
80 V
50
0
2
4
6
length (km)
(a)
300
250
200
150
100
10 MW
50
1 MW
0
80 MW
350
8
10
10 MW
12
0
1 MW
0
2
4
6
8
10
12
length (km)
(b)
Figure 5. Induced sheath voltages as a function of the cable line length, for three values of the
Figure 5. Induced sheath voltages as a function of the cable line length, for three values of the
transferred
power
(1 MW,
10 10
MW,
8080MW),
0:(a)
(a)single-point
single-point
bonding
at point
in Figure
2;
transferred
power
(1 MW,
MW,
MW),tgφ
tgφ =
= 0:
bonding
at point
p.0 inp.0
Figure
2;
(b) single-point
bonding
at
point
p.12
in
Figure
2.
(b) single-point bonding at point p.12 in Figure 2.
The differences in the induced voltages (Figure 5a vs. Figure 5b) are the effect of the natural load
of the cable line (capacitive), which forces a capacitive current flow of a changing value along the
length of the cable line. It indicates that the location of the point of the earthing (reference point) is
important. Note, that for the case presented in Figure 5a, the induced voltages at the unearthed end are
Appl. Sci. 2020, 10, 6706
8 of 16
practically the same for the power 1 MW and 10 MW. In the case of Figure 5b, the respective voltages
at the unearthed end differ about two times.
Appl.
88 of
Appl. Sci.
Sci. 2020,
2020, 10,
10, xx
of 16
16
Similar general conclusions flow from the analysis of the results presented in Figure 6 (tgφ = 0.4).
However,Similar
the variations
of the induced
voltages
along the
length
ofpresented
the cablein
line
are slightly
different
general
flow
the
of
results
Figure
66 (tg
Similar
general conclusions
conclusions
flow from
from
the analysis
analysis
of the
the
results
presented
in
Figure
(tgφφ == 0.4).
0.4).
thanHowever,
for
the
tgφ
=
0,
especially
if
one
compares
Figure
5a
vs.
Figure
6a
for
1
MW
and
10 MW.
However, the
the variations
variations of
of the
the induced
induced voltages
voltages along
along the
the length
length of
of the
the cable
cable line
line are
are slightly
slightly
than
one
Figure
MW
MW.
different
than for
for the
the tg
tgφφ == 0,
0, especially
especially
one compares
compares
Figure 5a
5a vs.
vs.power
Figure 6a
6a
for
MW and
and
10well
MW.as the
Thus,different
the reactive-to-active
power
ratioifif tgφ,
natural Figure
capacitive
of for
the11 cables
as10
Thus,
power
tg
capacitive
power
the
as
as
the
Thus,
the
reactive-to-active
power ratio
ratio
tgφφ,, natural
natural
capacitive
power
of
the cables
cables
as well
wellin
asthe
thesafety
location
ofthe
thereactive-to-active
point of the single-point
bonding
and earthing
should
beof
taken
into account
location
of
the
point
of
the
single-point
bonding
and
earthing
should
be
taken
into
account
in
the
location
of
the
point
of
the
single-point
bonding
and
earthing
should
be
taken
into
account
in
the
analysis. In the light of the aforementioned investigation, it can be concluded that for the contracted
safety
In
the
of
the
investigation, itit can
that
for the
safety analysis.
analysis.
In MW,
the light
light
of 0.4),
the aforementioned
aforementioned
can be
be concluded
concluded
that
the
transferred
power (10
tgφ =
the single-pointinvestigation,
bonding is acceptable,
whether in
p.0for
(preferred)
contracted
contracted transferred
transferred power
power (10
(10 MW,
MW, tg
tgφφ == 0.4),
0.4), the
the single-point
single-point bonding
bonding is
is acceptable,
acceptable, whether
whether in
in
or in p.12.
p.0
p.0 (preferred)
(preferred) or
or in
in p.12.
p.12.
80
80 VV
400
400
80
80 MW
MW
350
350
300
300
250
250
200
200
150
150
100
100
80
80 VV
50
50
00
induced voltage
voltage (V)
(V)
induced
induced voltage
voltage (V)
(V)
induced
400
400
00
22
44
66
length
length (km)
(km)
88
10
10
300
300
250
250
200
200
150
150
100
100
10
10 MW
MW
50
50
10
10 MW
MW
11 MW
MW
80
80 MW
MW
350
350
00
12
12
11 MW
MW
22
00
44
(a)
(a)
66
length
length (km)
(km)
88
10
10
12
12
(b)
(b)
Figure
6. Induced
sheath
function
thecable
cable
line
length
three
values
Figure
6.
sheath
voltages
as
line
length
for
three
values
of
Figure
6. Induced
Induced
sheathvoltages
voltages as
as aaa function
function of
ofofthe
the
cable
line
length
for for
three
values
of the
theof the
transferred
power
(1 MW,
1010
MW,
8080
MW),
0.4:(a)
(a)single-point
single-point
bonding
at point
in Figure
2;
bonding
at
p.0
Figure
2;
transferred
power
(1
MW,
MW),
tg
= 0.4:
0.4:
(a)
single-point
bonding
at point
point
p.0 in
inp.0
Figure
2;
transferred
power
(1 MW,
MW,
10
MW,
80
MW),tgφ
tgφφ ==
(b) single-point
bonding
at at
point
p.12
(b)
bonding
p.12
in
Figure
(b) single-point
single-point
bonding
at point
point
p.12in
inFigure
Figure 2.
2.
The The
next
step step
of
theof
is to evaluate
the induced
sheathsheath
voltages
in casein
of case
the line-to-earth
the
is
the
voltages
of
The next
next
step
ofanalysis
the analysis
analysis
is to
to evaluate
evaluate
the induced
induced
sheath
voltages
in
case
of the
the
fault
the
Like
previous
the
bonding
faultline-to-earth
at the unearthed
Like in end.
the previous
the single-point
bonding
was was
assumed
line-to-earth
fault at
at end.
the unearthed
unearthed
end.
Like in
in the
thescenarios,
previous scenarios,
scenarios,
the single-point
single-point
bonding
was
assumed
at
supply
substation
7a)
at
assumedatalternatively
alternatively
at the
the 110
110 kV
kV substation
supply service
service
substation
(Figure
7a) or
or substation
at the
the consumer
consumer
alternatively
the 110 kV supply
service
(Figure
7a) or at(Figure
the consumer
(Figure 7b).
substation
(Figure
7b).
In
the
short-circuit
analysis,
the
induced
voltages
have
been
calculated
for
substation
(Figure
7b).
In
the
short-circuit
analysis,
the
induced
voltages
have
been
calculated
for
the earth
In the short-circuit analysis, the induced voltages have been calculated for the cases without the
an
cases
without
an
earth
continuity
conductor
(ECC)
or
with
this
conductor.
The
ECC
was
laid
parallel
cases
without
an
earth
continuity
conductor
(ECC)
or
with
this
conductor.
The
ECC
was
laid
parallel
continuity conductor (ECC) or with this conductor. The ECC was laid parallel to the cable line at
to
at
20
of
to the
the cable
cable line
at aa distance
distance of
20 cm
cm (Figure
(Figure 8a).
8a). An
An insulated
insulated cable
cable with
with aa copper
copper conductor
of the
the
a distance
of
20 line
cm (Figure
8a). of
An
insulated
cable
with
a copper
conductor
of theconductor
cross-sectional
area
22 was assumed as the ECC. Halfway along the cable line (in p.6), the
cross-sectional
area
of
120
mm
cross-sectional
area
of
120
mm
was
assumed
as
the
ECC.
Halfway
along
the
cable
line
(in
p.6),
the
2
of 120 mm was assumed as the ECC. Halfway along the cable line (in p.6), the ECC was transposed to
ECC
ECC was
was transposed
transposed to
to the
the other
other side
side of
of the
the line
line (Figure
(Figure 8b),
8b), according
according to
to the
the recommendations
recommendations
the other
sideinofthe
theguide
line [2].
(Figure
8b), according to the recommendations included in the guide [2].
included
included in
the guide
[2].
25
25
without
without
ECC
ECC
20
20
15
15
with
with
ECC
ECC
10
10
55
00
without
without
ECC
ECC
20
20
induced voltage
voltage (kV)
(kV)
induced
induced voltage
voltage (kV)
(kV)
induced
25
25
00
22
44
66
length
length (km)
(km)
(a)
(a)
88
10
10
12
12
15
15
with
with
ECC
ECC
10
10
55
00
00
22
44
66
length
length (km)
(km)
88
10
10
12
12
(b)
(b)
Figure
7. Induced
sheath
voltages
as as
aasfunction
ofof
the
cable
line
Figure
7.
sheath
voltages
aa function
the
cable
line
length,
in
case
of
the
line-to-earth
Figure
7. Induced
Induced
sheath
voltages
function
of
the
cable
linelength,
length,in
incase
caseof
ofthe
theline-to-earth
line-to-earth fault
fault
at
end;
bonding
supply
service
(point
p.0
Figure
2);
fault
at the
the unearthed
unearthed
end; single-point
single-point
bonding
at:
(a)
supplyservice
service substation
substation
(point
p.0 in
in
Figure
2); 2);
at the
unearthed
end; single-point
bonding
at: at:
(a)(a)
supply
substation
(point
p.0
in Figure
(b)
substation
(point
p.12
in
(b) consumer
consumer
substation
(pointp.12
p.12in
in Figure
Figure 2).
2).
(b) consumer
substation
(point
Figure
2).
Appl. Sci. 2020, 10, 6706
Appl. Sci. 2020, 10, x
Appl. Sci. 2020, 10, x
9 of 16
9 of 16
9 of 16
p.6
p.6
p.0
p.0
20 cm
20 cm
ECC
ECC
p.12
p.12
ECC
ECC
ECC
ECC
(a)
(a)
(b)
(b)
Figure 8.
8. Arrangement
Arrangementofof
earth
continuity
conductor
(ECC):
a distance
the line;
cable(b)
line;
Figure
thethe
earth
continuity
conductor
(ECC):
(a) a(a)
distance
to theto
cable
its
Figure
8.
Arrangement
of
the
earth
continuity
conductor
(ECC):
(a)
a
distance
to
the
cable
line;
(b)
its
(b)
its transposition.
transposition.
transposition.
Induced sheath
end
of of
thethe
lineline
reach
values
overover
22 kV
the ECC
Induced
sheathvoltages
voltagesatatthe
theunearthed
unearthed
end
reach
values
22without
kV without
the
Induced
sheath
voltages
at the
unearthed
end ofare
thesimilar,
line
values
oversingle-point
22 the
kV without
the
and approx.
12
kV12
with
ECC.
All
respective
values
regardless,
the
bonding
ECC
and approx.
kVthe
with
the
ECC.
All respective
values
arereach
similar,
regardless,
single-point
ECC
and and
approx.
12 kVare
with
the
All
respective
values
arehigh
similar,
regardless,
the between
single-point
and earthing
are
performed
in
p.0ECC.
or inin
p.12.
Such
values
of
thevalues
induced
voltages
the
bonding
earthing
performed
p.0
or
in high
p.12.
Such
of the
induced
voltages
bonding
and
earthing
are
performed
in
p.0
or
in
p.12.
Such
high
values
of
the
induced
voltages
copper
sheath
and
the
earth
may
be
a
source
of
the
damage
of
the
non-metallic
outer
sheath
of
the
between the copper sheath and the earth may be a source of the damage of the non-metallic outer
between
copper
sheath
and
the
be Ita is
source
of thedesign
damage
of the
non-metallic
outer
cable (PE
outer
sheath
in
Figure
3). earth
ItinisFigure
a may
common
design
practice
to assume
that
this
non-metallic
sheath
ofthe
the
cable
(PE
outer
sheath
3).
a common
practice
to
assume
that
this
sheath
of
the
cable
(PE
outer
sheath
in
Figure
3).
It
is
a
common
design
practice
to
assume
that
outer
sheath
will
not
be
damaged
if
the
induced
voltage
does
not
exceed
5
kV.
As
it
is
seen
in
Figure
7,
non-metallic outer sheath will not be damaged if the induced voltage does not exceed 5 kV. As this
it is
non-metallic
outer
sheath
will5 not
be
damaged
if the
induced
voltage
does
not
exceed
5 kV.
As itthe
is
the value
5 kV
is7,not
exceeded
only
the
length
ofonly
the
cable
linelength
(from
thethe
earthing
point)
approx.
seen
in Figure
the
value
kV
isfor
not
exceeded
for the
of
cable line
(from
seen
in
Figure
7,
the
value
5
kV
is
not
exceeded
only
for
the
length
of
the
cable
line
(from
the
2.5
km
without
the
ECC
and
approx.
5
km
with
the
ECC.
Thus,
in
the
considered
power
line
of
the
earthing point) approx. 2.5 km without the ECC and approx. 5 km with the ECC. Thus, in the
earthing
approx.
km
without
the acceptable—too
ECCsingle-point
and approx.
5 km
with
ECC. Thus,
inhigh
the
length 12point)
km,
the
single-point
bonding
not
high
values
induced
voltages
in
considered
power
line of2.5the
length
12iskm,
the
bonding
is of
nottheacceptable—too
considered
power
line of
the length
12 (despite
km,
theshort-circuit
single-point
bonding isexist
not
acceptable—too
high
case of of
thethe
short-circuit
conditions
the
possibleconditions
application
of sheath
voltage
limiters
values
induced
voltages
in exist
case
of the
(despite
the possible
values
of
the
induced
voltages
in
case
of
the
short-circuit
conditions
exist
(despite
the
possible
(SVL);
a
high-level
margin
of
reliability
and
safety
is
required).
application of sheath voltage limiters (SVL); a high-level margin of reliability and safety is required).
application of sheath voltage limiters (SVL); a high-level margin of reliability and safety is required).
3.2. Induced Voltages for Both-Ends Bonding or Cross Bonding
3.2. Induced Voltages for Both-Ends Bonding or Cross Bonding
3.2. Induced
Voltages for Both-Ends
Bonding
or Cross cable
Bonding
Since single-point
bonding in
the analyzed
line is not acceptable, both-ends bonding is
Since single-point bonding in the analyzed cable line is not acceptable, both-ends bonding is
considered
as
an
alternative
solution.
For
the
both-ends
bonding,
the
induced sheath voltages
in the
Since single-point
bonding
in theFor
analyzed
cable line
is not the
acceptable,
bonding
is
considered
as an alternative
solution.
the both-ends
bonding,
induced both-ends
sheath voltages
in the
normal operating
conditions solution.
(10 MW) For
are close
to 0 V. Therefore,
they
are
not presented
in the form
of
considered
as
an
alternative
the
both-ends
bonding,
the
induced
sheath
voltages
in
the
normal operating conditions (10 MW) are close to 0 V. Therefore, they are not presented in the form
the chartoperating
in this paper.
However,
the induced
voltages
areare
very interesting
inincase
of
the
normal
(10 MW)
close
tovoltages
0 V. distributions
Therefore,
they
thecase
form
of the chart
in thisconditions
paper. However,
theare
induced
distributions
are not
verypresented
interesting
in
of
line-to-earth
fault.
The
cable
line
comprises
straight-joints
approx.
every
1
km.
After
discussion
with
of
chart in thisfault.
paper.
However,
induced straight-joints
voltages distributions
very
interesting
in case of
thethe
line-to-earth
The
cable linethe
comprises
approx. are
every
1 km.
After discussion
the industrial partner
involved
inline
the cable
line project, it was decided
toevery
analyze
the induced
voltages
the
fault.
The cable
comprises
1 km.
Afterthe
discussion
withline-to-earth
the industrial
partner
involved
in
the cablestraight-joints
line project, itapprox.
was decided
to
analyze
induced
distribution
in
case
of
the
earth
fault
in
the
selected
joints.
The
line-to-earth
fault
was
consecutively
with
the industrial
partner
involved
the cable
project,
it was
decided
analyze thefault
induced
voltages
distribution
in case
of the in
earth
fault line
in the
selected
joints.
The to
line-to-earth
was
assumed distribution
in the following
points
(Figure
9): fault in the selected joints. The line-to-earth fault was
voltages
in
case
of
the
earth
consecutively assumed in the following points (Figure 9):
consecutively assumed in the following points (Figure 9):
p.3:
quarter of
of the
the line
line length;
length;
••
p.3: aa quarter
••• p.3:
a
quarter
of
the
line
length;
p.6:
half
of
the
line
length;
p.6: half of the line length;
••• p.6:
of the line length;
p.9:
three-quarters
of the
p.9: half
three-quarters
of
the line
line length;
length;
••• p.9:
three-quarters
of
the
line
p.12: the consumer substation.length;
•
p.12: the consumer substation.
Power system
Power
110system
kV
110service)
kV
(supply
(supply service)
p.0
p.1
p.0
p.1
p.2
p.2
p.3
p.3
p.4
p.4
p.5
p.5
p.6
p.6
p.7
p.7
p.8
p.8
p.9
p.9
p.10
p.10
p.11
p.11
p.12
p.12
Figure 9. Simplified diagram of the cable system presenting points of the assumed consecutive
line-to-earth
faults. diagram of the cable system presenting points of the assumed consecutive
Figure 9. Simplified
Figure
9. Simplified
line-to-earth
faults. diagram of the cable system presenting points of the assumed consecutive
line-to-earth
faults. of the induced voltages for the aforementioned points of the fault are presented
The distributions
in Figure
For the both-ends
10a)for
thethe
line-to-earth-fault
at point
induced
The 10.
distributions
of the bonding
induced(Figure
voltages
aforementioned
pointsp.12
of gives
the fault
are
The
distributions
of
the
induced
voltages
for
the
aforementioned
points
of
the
fault
are
voltage
practically
to 0the
V. Itboth-ends
is obviousbonding
because(Figure
this point
is the
located
at the consumer
presented
in Figureequal
10. For
10a)
line-to-earth-fault
at substation,
point p.12
presented
in Figure
10. practically
For the both-ends
10a)because
the line-to-earth-fault
at pointatp.12
gives induced
voltage
equal tobonding
0 V. It (Figure
is obvious
this point is located
the
gives induced voltage practically equal to 0 V. It is obvious because this point is located at the
induced voltage (kV)
induced voltage (kV)
sheaths are performed in p.4 and p.8; see Figure 10b), the induced voltages in the characteristic
points are only slightly lower compared to the both-ends bonding. Unfortunately, the voltages still
exceed the assumed permissible level of 5 kV.
To decrease the induced voltages below the permissible 5 kV, an additional earthing in point
p.6 has been proposed. The earthing is relatively easy to perform in this place—the cables’ metallic
Appl. Sci. 2020, 10, 6706
of 16
sheaths are accessible. With this additional earthing, the power cable system is composed of10three
earthing
points
it
Appl. Sci. 2020,
10, x (p.0, p.6 and p.12) and the induced voltages distributions are as in Figure 11.10As
of 16
was
expected,
in
the
case
of
the
line-to
earth
fault
in
p.6,
for
the
both-ends
bonding
(Figure
11a),
the
which contains an earthing system. An earth fault in points p.3, p.6 or p.9 gives the induced voltages
consumervoltage
substation,
which
contains
an earthing
system. An
earth
fault in points
p.3,see
p.6that
or p.9 gives
induced
in this
point
is reduced
0 V.
the
higher
than the assumed
permissible
limit 5practically
kV (at theto
point
ofHowever,
the fault). one
Thecan
highest
valuefor
of the
the
induced
voltages
higher
than
the
assumed
permissible
limit
5
kV
(at
the
point
of
the
fault).
The
arrangement
with
the
cross
bonding
(Figure
11b),
in
the
case
of
the
line-to
earth
fault
in
p.6,
the
voltage is in p.6 (over 7 kV) mainly because it is located at the farthest distance from the earthed points
highest value
of between
the voltage isand
in p.6
7 kV)
mainly
it is locateddistribution
at the farthest
distance
induced
voltage
p.6 (over
reaches
approx.
250because
V. Similar
is observed
(p.0
and p.12).
In the case p.0
of the cross
bonding
(transpositions
of thevoltage
cable sheaths are performed
in
from
the
earthed
points
(p.0
and
p.12).
In
the
case
of
the
cross
bonding
(transpositions
of
the
cable
between
p.6see
and
p.12, 10b),
in the
of thevoltages
line-to in
earth
p.12. For both
arrangements
(both-ends
p.4
and p.8;
Figure
thecase
induced
the in
characteristic
points
are only slightly
lower
sheaths are
performed
in p.4the
andhighest
p.8; see
Figure
10b), the induced
voltages
in the characteristic
bonding
and
cross
bonding),
value
of the
around
4 kV
in p.3),
compared
to the
both-ends
bonding.
Unfortunately,
the voltage
voltagesisstill
exceed
the (line-to-earth
assumed permissible
pointsisare
onlybelow
slightly
lower
compared
to (5
thekV).
both-ends bonding. Unfortunately, the voltages still
what
clearly
the
permissible
value
level of 5 kV.
exceed the assumed permissible level of 5 kV.
To decrease the induced
voltages below the permissible 5 kV, an additional earthing in point
p.6
p.6
p.6 has
The
earthing
is relatively easy to8 perform in this place—the cables’ metallic
8 been proposed.
p.3
p.9
p.9
p.3
7 power cable system is composed of three
7 are accessible. With this additional earthing, the
sheaths
6
6
earthing
points (p.0, p.6 and p.12) and the induced voltages
distributions are as in Figure 11. As it
5
was expected, in the case of the line-to earth fault in p.6,5for the both-ends bonding (Figure 11a), the
4
4
induced voltage in this point is reduced practically to 0 V. However, one can see that for the
3
3
p.12
arrangement
with the cross bonding (Figure
p.1211b), in the
2 case of the line-to earth fault in p.6, the
2
induced
voltage
between
p.0
and
p.6
reaches
approx.
250
V.
Similar
voltage
distribution
is
observed
1
1
between
p.6 and p.12, in the case of the line-to earth 0in0 p.12.2 For both
arrangements10(both-ends
0
4
6
8
12
0
2
4
10
8
6
12
c-b 4 kV (line-to-earth
c-b
bonding and cross bonding),
the
highest
value
of
the
voltage
is
around
in p.3),
length (km)
length (km)
what is clearly below the(a)permissible value (5 kV).
(b)
induced voltageinduced
(kV) voltage (kV)
induced voltageinduced
(kV)
voltage (kV)
Figure 10. Induced sheath voltages as a function of the cable line length, in case of the line-to-earth
line-to-earth
p.6
p.6
in the
the characteristic
characteristicpoints
points(p.3,
(p.3,p.6,
p.6,p.9
p.9ororp.12):
p.12):(a)
(a)both-ends
bonding;
cross
bonding
(c-b)
fault
in
bonding;
(b)(b)
cross
bonding
(c-b)
in
8both-ends
8
p.3
p.9
p.9
p.3
in7 p.4
and
p.4
and
p.8.p.8.
7
6
6
p.3 in case of the line-to-earth
Figure 11. Induced
sheath voltages as a function of the cable
line length,
p.3
4.5
4.5
p.9
fault
in characteristic points (p.3, p.6, p.9 or p.12); additional
earthing in p.6: (a) both-endsp.9
bonding;
4.0
4.0
3.5
(b)
cross
bonding
(c-b)
in
p.2,
p.4
as
well
as
in
p.8,
p.10.
3.5
3.0
induced voltage (kV)
induced voltage (kV)
To
the induced voltages below the permissible
5 kV, anp.3additional earthing in point p.6
5
5 decreasep.3
4.5
4.5
p.9
4
p.9
4 proposed. The earthing is relatively
has been
easy to perform
in
this place—the cables’ metallic
sheaths
4.0
4.0
3
3
are accessible.
With this additional earthing, the power3.5
cable system is composed of three earthing
3.5
p.12
p.12
2
2
3.0
points3.0
(p.0, p.6 and p.12) and the induced voltages distributions
are as in Figure 11. As it was expected,
1
1
2.5
in the2.5case of the line-to earth fault in p.6, for the both-ends
bonding (Figure 11a), the induced voltage
0
0
2.0
2.0 0
0
2
4
10
6
8
12
2
4
10
8
6
12
in this point is reduced practically to 0 V. However, one can
the
arrangement
1.5 see that for c-b
c-b with the cross
1.5
length (km)
length
(km)
p.12
p.6
p.6case of the line-to
bonding
(Figure 11b), in the
earth fault1.0in p.6, the induced voltage between p.0
and
p.12
1.0
(a)
(b)
0.5
p.6 reaches
approx. 250 V. Similar voltage distribution is observed between p.6 and p.12, in the case of
0.5
0
0
0 bonding
2length,
4 incross
10 highest
the line-to
earth
in p.12.
For
both
arrangements
(both-ends
and
bonding),
the
6 of
8 line-to-earth
12
Figure
10.2 Induced
voltages
as10a function
of the cable
linec-b
case
thec-b
6
0
4 sheath
8
12
c-b
c-b
valuefault
of the
voltage
is
around
4
kV
(line-to-earth
in
p.3),
what
is
clearly
below
the
permissible
value
in the characteristic points (p.3, p.6, p.9 or p.12): (a) both-ends bonding;length
(b) cross
(km) bonding (c-b)
length (km)
(5 kV).
in p.4 and p.8.
(b)
(a)
3.0
2.5
2.5
Thus,
the additional earthing in p.6 eliminates in a simple way the problem of too high induced
2.0
2.0
sheath voltages in case of the short-circuit conditions. The
1.5 both-ends bonding, as well as the cross
1.5
p.6
1.0
p.12
0.5
0.5
0
p.12
p.6
1.0
0
0
2
4
6
length (km)
(a)
8
10
12
0
2
c-b
4
c-b
6
8
c-b
10
c-b
12
length (km)
(b)
Figure 11.
11. Induced
Induced sheath
sheath voltages
voltages as
as aa function
function of
of the
the cable
cable line
line length,
length, in
in case
case of
of the
the line-to-earth
line-to-earth
Figure
fault in
in characteristic
characteristic points
points (p.3,
(p.3, p.6,
p.6, p.9
p.9 or
or p.12);
p.12); additional
additional earthing
earthing in
in p.6:
p.6: (a)
(a) both-ends
both-ends bonding;
bonding;
fault
(b) cross
cross bonding
bonding (c-b)
(c-b) in
in p.2,
p.2, p.4
p.4 as
aswell
wellas
asin
inp.8,
p.8,p.10.
p.10.
(b)
Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced
sheath voltages in case of the short-circuit conditions. The both-ends bonding, as well as the cross
Appl. Sci. 2020, 10, 6706
11 of 16
Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced
sheath voltages in case of the short-circuit conditions. The both-ends bonding, as well as the cross
bonding, can be employed (with additional earthing in p.6) but the latter is a more complicated solution.
4. Power Losses for the Analyzed Types of Bonding
During the selection of the type of bonding, which is to be used in a high-voltage cable system,
an analysis of the power losses in this system is recommended to be performed. In the total power
losses in the cable system, additional losses produced in the cable sheaths should be included.
Generally, power losses ∆P3sh generated in three cables’ sheaths and power losses ∆P3c generated in
three cables’ conductors (cores) can be calculated according to the following expressions:
2
2
2
∆P3sh = Rsh Ish−L1
+ Ish−L2
+ Ish−L3
(9)
2
2
2
∆P3c = Rc IL1
+ IL2
+ IL3
(10)
where: ∆P3sh represents the power losses in three cables’ sheaths; ∆P3c represents the power losses in
three cables’ conductors (cores); Ish-L1 , Ish-L2 , Ish-L3 are the currents flowing through the sheath of the
cable in phases L1, L2 and L3, respectively; IL1 , IL2 , IL3 are the currents flowing through the conductor
(core) of the cable in phases L1, L2 and L3, respectively; Rsh is the resistance of the cable’s sheath; Rc is
the resistance of the cable’s conductor (core).
One of the main problems in the power losses calculation is to evaluate the real current distribution
in each cable sheath (currents Ish-L1 , Ish-L2 , Ish-L3 ). It is relatively difficult to calculate analytically,
especially when the arrangement of the cable line is varied or the cross bonding is applied. In this
investigation, all the parameters have been calculated on the base of the data obtained from the
PowerFactory software, taking into account the arrangement of the cables in every of 161 sections of
the cable line.
Power losses in the cables’ sheaths can be very high in the case of both-ends bonding. Relatively high
circulating currents may give a significant heat flux generation across the sheath’s resistance,
which increases the temperature of the cables. However, in the power cable line under consideration,
the contracted transferred power is relatively low compared to the transmission capacity of the
line, so the selection of the type of the bonding system, from the point of view of the power losses,
is not obvious.
The power losses have been evaluated with the use of the aforementioned computer model of the
cable system. Figure 12a presents power losses in the cable sheaths (all three phases) for the contracted
transferred power (10 MW, tgφ = 0.4) and the cable system arrangements, which are to be implemented
in practice. The both-ends bonding gives, in fact, the highest value of the power losses, but it is only
slightly higher than for the single-point bonding. Generally, for these two aforementioned types of
bonding, the power losses are on the low and acceptable level. This is not a typical phenomenon.
The almost equal power losses for these two arrangements are the effect of the natural capacitive power
of the line. Since the consumer load (active power) in the cable line is at the low level, the natural power
forces a reactive (capacitive) current circulation in the system, which gives observable losses. When the
cross bonding is used, power losses in the copper sheaths are negligible, due to the compensation of
the induced voltages in the consecutive minor sections. The comparison of all the analyzed types of
losses (in cores, in sheaths, total; for 10 MW, tgφ = 0.4) is presented in Figure 12b. The total power
losses (in copper sheaths + aluminium cores) are almost the same, both for the single-point bonding
and both-ends bonding. They are within the range 15.4–15.8 kW, whereas for the cross bonding they
are at the level of 13 kW. Power losses in the cores are the same for every type of bonding.
Appl. Sci. 2020, 10, x
12 of 16
reactive/capacitive current coming from the natural power of the line is not the same along its whole
12 of 16
length—it is a normal phenomenon of the current flowing via capacitance-to-earth of the cables.
Appl. Sci. 2020, 10, 6706
Losses (sheath)
power losses (kW)
3.0
2.5
2.0
1.5
1.0
0.5
0
s-p
in p.12
s-p
in p.0
b-e
c-b
b-e
+earthing
in p.6
c-b
+earthing
in p.6
bonding type
(a)
Losses (core)
Losses (sheath)
Losses (total)
18.0
power losses (kW)
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0
s-p
in p.12
s-p
in p.0
b-e
c-b
b-e
+earthing
in p.6
c-b
+earthing
in p.6
bonding type
(b)
Figure12.
12. Power
Power losses
losses in
in the
the analyzed
analyzed three-phase
three-phase cable
cable system
system for
for the
the transferred
transferred power
power 10 MW,
MW,
Figure
tg
φ
=
0.4:
(a)
losses
in
the
metallic
sheaths;
(b)
comparison
of
the
losses
in
the
metallic
sheaths,
cores
tgφ = 0.4: (a) losses in the metallic sheaths; (b) comparison of the losses in the metallic sheaths, cores and
and losses;
total losses;
s-p: single-point
bonding;
b-e: both-ends
bonding;
c-b: cross
bonding.
total
s-p: single-point
bonding;
b-e: both-ends
bonding;
c-b: cross
bonding.
The
effect
the transfers
natural reactive
power
ofto
the
especially
in Figure
13a when
If the
cableofline
the power
equal
80cable
MW,line
tgφ is
= 0seen
(Figure
13b), giving
practically
the
the
transferred
power
only 1current
MW, tgφ
= 0 (for
theA),
simplicity
of the
analysis,
the is
active
max
permissible
loadis(load
approx.
420
the value
of the
poweronly
losses
two power
orders
transfer
is modelled).
Theresults
natural
reactive
power
of thewas
analyzed
line the
of the
length
12 km
is approx.
higher, compared
to the
from
Figure
13a. What
expected,
highest
value
of the
power
6losses
Mvarisand
exceeds
the In
transferred
(1 MW). In
suchislow-load
conditions
forsignificantly
the both-ends
bonding.
this case,active
when power
the transferred
power
many times
higher
(active
load
current
in thepower,
cable core
is approx.
A; reactive/capacitive
current in the cable core is
than the
natural
reactive
the effect
of the 5latter
power is negligible.
approx.
A), the of
single-point
gives losses
the highest
total power
losses.
It should
be noted
The30analysis
the resultsbonding
of the power
calculations
shows
that all
types ofalso
bonding
are
that
the reactive/capacitive
current
coming
fromtothe
power of thethe
linecross
is notbonding
the same gives
along the
its
acceptable
for the transferred
power
equal
10natural
MW. Admittedly,
whole
length—it
is
a
normal
phenomenon
of
the
current
flowing
via
capacitance-to-earth
of
the
cables.
lowest losses but introduces the most complicated technical solution to the power line.
If the cable line transfers the power equal to 80 MW, tgφ = 0 (Figure 13b), giving practically the
max permissible load (load current approx. 420 A), the value of the power losses is two orders higher,
compared to the results from Figure 13a. What was expected, the highest value of the power losses is
for the both-ends bonding. In this case, when the transferred power is many times higher than the
natural reactive power, the effect of the latter power is negligible.
The analysis of the results of the power losses calculations shows that all types of bonding are
acceptable for the transferred power equal to 10 MW. Admittedly, the cross bonding gives the lowest
losses but introduces the most complicated technical solution to the power line.
Appl. Sci.
Sci.2020,
2020,10,
10,x6706
Appl.
13 of
of 16
16
13
Losses (core)
Losses (sheath)
Losses (total)
power losses (kW)
10.0
8.0
6.0
4.0
2.0
0
s-p
in p.12
s-p
in p.0
b-e
c-b
bonding type
b-e
+earthing
in p.6
c-b
+earthing
in p.6
(a)
Losses (core)
power losses (kW)
1000
Losses (sheath)
Losses (total)
800
600
400
200
0
147
2
2
s-p
in p.12
s-p
in p.0
147
<1
b-e
bonding type
c-b
<1
b-e
+earthing
in p.6
c-b
+earthing
in p.6
(b)
Figure
Figure 13.
13. Power
Power losses
lossesin
inthe
theanalyzed
analyzedthree-phase
three-phasecable
cablesystem:
system:(a)
(a)for
forthe
thetransferred
transferredpower
power11MW,
MW,
tg
φ ==0;0;
(b)(b)
forfor
thethe
transferred
power
80 MW,
tgφ =tgφ
0; s-p:
single-point
bonding;bonding;
b-e: both-ends
bonding;
tgφ
transferred
power
80 MW,
= 0;
s-p: single-point
b-e: both-ends
bonding;
c-b: cross bonding.
c-b:
cross bonding.
5. Conclusions
Conclusions
5.
Most of
of the
the high-voltage
high-voltage power
power cable
cable lines
lines are
are significantly
significantly loaded
loaded in
in practice,
practice, so
so in
in normal
normal
Most
operating
conditions
the
induced
sheath
voltages
or
power
losses
may
be
high.
In
order
to
exclude
the
operating conditions the induced sheath voltages or power losses may be high. In order to exclude
risk
of
the
electric
shock
and
the
negative
effect
of
the
power
losses
in
the
long
cable
lines,
during
such
the risk of the electric shock and the negative effect of the power losses in the long cable lines, during
load load
conditions,
crosscross
bonding
of theofcable
sheaths
is most
oftenoften
indicated
as theasbest
such
conditions,
bonding
the cable
sheaths
is most
indicated
thesolution.
best solution.
However,
if
the
cable
line
carries
a
relatively
low
load,
as
in
the
analyzed
case,
choice
of
However, if the cable line carries a relatively low load, as in the analyzed case, the the
choice
of the
the best
of the
bonding
system
is not
obvious.
For
the
analyzedcable
cableline,
line,aacomparison
comparisonof
of the
the
best
typetype
of the
bonding
system
is not
obvious.
For
the
analyzed
possible
bonding
and
earthing
solutions
is
presented
in
Table
1.
possible bonding and earthing solutions is presented in Table 1.
Table 1. A summary of the properties of the bonding systems in the analyzed cable line.
Table 1. A summary of the properties of the bonding systems in the analyzed cable line.
Criterion
Single-Point
Bonding
Both-Ends Bonding
Cross
Bonding
Single-Point
Cross
Criterion
Both-Ends Bonding
Bonding
Bonding
Induced voltages in normal
(0)
(0)
(0) 1
operating
condition
Induced
voltages
in normal operating
1
(0)
(0)
(0)
Induced voltages
in the case of
(+)
(+)
condition
(-)
short circuit
with earthing
with earthing
Inducedthe
voltages
in the case of the short
(+) in p.6
(+) in p.6
(-)
Power losses
circuit
with earthing
in p.6
with earthing
(0)
(0)
(+) in p.6
in the cable system
Power losses
Simplicity of the solution and
(+)
(0)
(0)
(+)
(+)
(0)
in the aspects
cable system
economic
(0) with ECC
Simplicity of the solution
and
economic
(+)
1 Markings: (+) preferred solution; (0) acceptable solution; (-) (+)
(0)
excluded solution.
aspects
(0) with ECC
1
Markings: (+) preferred solution; (0) acceptable solution; (-) excluded solution.
Appl. Sci. 2020, 10, 6706
14 of 16
When the risk of electric shock in normal operating conditions is considered, the values of the
induced sheath voltages are acceptable in every case—for single point-bonding the highest value is
below the permissible 80 V and for both-ends bonding or cross bonding the voltages are close to 0 V.
In case of the line-to-earth fault, the single point-bonding is excluded in this cable line, due to
very high induced voltages. For the system without ECC, the voltage reaches 22 kV. When the ECC is
installed, it decreases only to 12 kV. In the light of the assumed permissible level being equal to 5 kV,
these high-value voltages are dangerous for the outer non-metallic sheath of the cable. It should also be
noted that, due to the induced voltages in the case of the earth fault, the both-ends bonding, as well as
the cross bonding, requires an additional earthing in the middle of the power cable length (point p.6).
Without this additional earthing, the voltages may exceed 7 kV but with the earthing, they are reduced
to approx. 4 kV.
A comparison of the power losses shows that the best solution is the cross bonding but two other
solutions are acceptable as well—the total losses in the cable system are within the range 15.4–15.8 kW
for the single-point bonding and both-ends bonding, whereas for the cross bonding they are equal to
13 kW. Such low and comparable power losses are the effect of the relatively low transferred power
(10 MW).
Considering the economic aspect and simplicity of the solution, the single-point bonding without
ECC (no additional parallel cable is installed) or both-ends bonding (no equipment for transpositions
of the sheaths is required) are recommended.
Taking into account all the aforementioned aspects, the both-end bonding or cross bonding can
be used in the analyzed cable line. For each of the two solutions, the additional earthing in p.6 is
required. To achieve safe operation of relatively long high-voltage cable lines, which are loaded in
a low percentage, special attention must be given to the study of short-circuit currents. The induced
sheath voltages coming from high-value currents can give unacceptably high-voltage stress, not only in
the case of single-point bonding, but also in the case of both-ends bonding. In the latter case, this stress
applies to points located close to the centre of the cable section between the earthing arrangements.
In such a cable system, shorter distances between the earthing arrangements should be used.
Author Contributions: Conceptualization, S.C.; software, K.D.; validation, S.C. and K.D.; formal analysis, S.C.;
investigation, S.C. and K.D.; resources, S.C.; writing—original draft preparation, S.C. and K.D.; writing—review
and editing, S.C.; supervision, S.C. All authors have read and agreed to the published version of the manuscript.
Funding: This research was supported by Gdańsk University of Technology.
Conflicts of Interest: The authors declare no conflict of interest.
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