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Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
113
CALCULATION OF INDUCED SHEATH VOLTAGES IN
POWER CABLES – SINGLE CIRCUIT SYSTEM VERSUS
DOUBLE CIRCUIT SYSTEM
Stanislaw CZAPP, Krzysztof DOBRZYNSKI, Jacek KLUCZNIK,
Zbigniew LUBOSNY
Gdansk University of Technology, Faculty of Electrical and Control Engineering,
Gdansk, Poland
e-mail: [email protected]
Abstract
This paper presents comparison of values of induced sheath voltages in power
cable metallic sheaths when one or two cables per phase are used. Calculation
of voltages is performed for various phase sequences of the power cables. Three
types of the sheaths bonding and earthing are considered. Shock hazard and
voltage stress of non-metallic outer sheath of cables are evaluated. The
proposed, optimal configuration of the power cable system is indicated.
Keywords: electromagnetic coupling, electrical safety, power engineering,
power system analysis computing
1
INTRODUCTION
In concentric metallic sheaths of single-core high voltage power cables induced
voltages occur. In the steady state, these voltages may reach value of several hundred
volts and electric shock risk exists then. In case of earth fault, induced sheath voltages
are much higher, even several kilovolts, and breakdown of non-metallic outer sheath of
cables may occur [1–7].
For a conductor k lying parallel with a three phase system (three conductors)
a voltage gradient Uk induced along its length can be calculated as follows
1  m  m
U k  j  I  2 10  7  ln Ak Ck
 2  mBk

3  mCk  ,
  j

ln
2  mAk 

(1)
where: I – load current in the reference cable conductor (phase B), mAk – axial spacing
of the parallel k conductor and phase A conductor, mAk – axial spacing of the parallel k
conductor and phase B conductor, mAk – axial spacing of the parallel k conductor and
phase C conductor.
A high voltage cable system can be represented by the structure drawn in Fig. 1 [1].
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Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
U1
I1
R1
Conductor 1
X1
U2
I2
R2
Conductor 2
X2
Un
In
Rn
Conductor n
Xn
Local earth
Local earth
Uepr1
RLE1
IE
RE
Uepr2
RLE2
UE
Earth return path
(remote earth reference)
XE
Fictitious covering cylinder
(free of current)
Figure 1 Equivalent scheme of a high voltage cable system: R1,2,n – resistance of the
conductors, X1,2,n – reactance of the conductors, RLE – resistance to earth, I1,2,n – current
in the conductors, IE – earth current, Uepr – earth potential rise [1]
A cable sheath may be considered as a special parallel concentric conductor.
When in the vicinity of the system is no other current-carrying conductors, voltage
gradients of the sheaths for a group of cables in any formation are given by [8]
2
 1  2mAB

3  2mAC  ,
  j
U As  j  I  2 10 7  ln 
ln 

2  d 
 2  d  mAC 
 1  4m  m
U Bs  j  I  2  10 7  ln AB BC
d2
 2 
(2)

3  mBC  ,

  j
ln
2

 mAB 
(3)


2

1  2mBC
  j 3 ln 2mAC  ,
U Cs  j  I  2  10 7  ln
 2 d m 
2  d 
AC 



(4)
where: UAs, UBs, UCs, – induced sheath voltages in phase A, B and C respectively, I –
load current in the reference cable conductor, d – geometric mean sheath diameter, mAB
– axial spacing of phases A and B, mBC – axial spacing of phases B and C, mAC – axial
spacing of phases A and C.
For trefoil formation in single circuit, induced sheath voltages are calculated
according to the following equations
 1
3  2m
U As  j  I  2  10 7    j
ln
 2
2  d

 2m  ,
U Bs  j  I  2  10 7  ln

 d 
,
(5)
(6)
Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
 1
3  2m ,
U Cs  j  I  2  10 7    j
ln
 2
2  d

115
(7)
where: UAs, UBs, UCs, – induced sheath voltages in phase A, B and C respectively, I –
load current in the reference cable conductor, d – geometric mean sheath diameter, m –
axial spacing of adjacent cables.
When flat formation in single circuit is applied, induced sheath voltages are
calculated according to the following equations
 1 m
3 4m  ,
U As  j  I  2  10 7   ln  j
ln
 2 d
2
d 

(8)
 2m  ,
U Bs  j  I  2  10 7  ln

 d 
(9)
 1 m
3 4m 
.
U Cs  j  I  2  10 7   ln  j
ln
 2 d
2
d 

(10)
Permissible touch voltage (V)
For multiple-circuit system the calculations are more complicated and a computer
model of the power cable system must be designed. The more parallel circuits the more
complicated calculation is.
Induced sheath voltages exist during normal operating condition (long time
duration of induced voltages) and in case of earth fault (short time duration of induced
voltages). These voltages should not exceed values described by the standards.
Figure 2 presents permissible values of touch voltage as a function of fault duration
[9]. For normal operating condition, 80 V is assumed as a permissible value.
800
700
600
500
400
300
200
80 V
100
0
0,05
0,1
0,2
0,5
1
2
5
10
>> 10
Fault duration (s)
Figure 2 Permissible touch voltage as a function of the fault duration
The paper considers induced sheath voltages in the 110 kV power cable system.
The total length of the power line is 1000 m (two sections of 500 m length each, flat
formation). Required power transfer capability is equal to 330 MW. Arrangements of
the power system with one cable per phase (cross-section of conductor is equal to 2000
mm2) and two cables per phase (for equivalent power transfer capability cross-section
of each conductor is equal to 800 mm2) are compared. For the each mentioned case,
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Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
single point bonding or, for sheath voltages limiting purpose, cross-bonding is applied
and analysed. The proposed configuration of the power cable system is indicated.
COMPARED POWER CABLE SYSTEMS
Induced sheath voltages were analyzed with the use of DIgSILENT
PowerFactory® software. The following general arrangements of the power cable
system were considered:
1) One cable per phase (single circuit system) – Distance between adjacent cables
(C1-C2 and C2-C3) inside the section is equal to the outside diameter of the cable
(D in Fig. 3). The number of analysed configurations is equal to 6.
2) Two cables per phase (double circuit system) – Distance between adjacent
cables (C1-C2 and C2-C3) inside the section is equal to the outside diameter of the
cable (D in Fig. 4). Distance to adjacent cables between circuits is equal to twice of the
outside diameter of the cable (2D in Fig. 2). The number of analysed configurations is
equal to 36.
Configurations: W5a, W6a, W6b
2
C1
Sh1
C2
Sh2
C3 Sh3
Cross-bonding
T1 (A), 500 m
T1 (B), 500 m
D
ECC
ECC
D
Ush
E1
E2
A B C
A B C
Figure 3 The power cable system with one cable per phase
C1
Sh1
C2
Sh2
T1 (B), 500 m
D
ECC
C3 Sh3
Configurations: W3a, W4a, W4b
Cross-bonding
T1 (A), 500 m
ECC
D
Ush
2D
E1
C1
Sh1
C2
Sh2
C3 Sh3
E2
Cross-bonding
T2 (A), 500 m
T2 (B), 500 m
D
ECC
ECC
D
Ush
E1
A B C
E2
A B C
Figure 4 The power cable system with two cables per phase
Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
117
The cable systems described above are equipped with an earth continuity
conductor (ECC). Various configurations of earthing and bonding of cables were
assumed (Table 1).
Table 1 List and symbols of the analyzed configurations
Symbol of analysed configuration
One cable per
Two cables per
phase
phase
Type of bonding and earthing
Sheaths bonding and earthing in E1, crossbonding in E2
Single-point bonding; sheaths bonding and
earthing in E1
Single-point bonding; sheaths bonding and
earthing in E2
W5a
W3a
W6a
W4a
W6b
W4b
3
NORMAL OPERATING CONDITION
A first step of the analysis is to find the values of induced sheath voltages Ush, at
the unearthed end, in normal operating condition, when current-carrying capacity of
cables (maximum power transfer for each configuration) is achieved. Figures 5 and 6
present groups of results of the computer calculations – each point represents voltage
for particular configuration of the system.
When two cables per phase are used (configurations W3a, W4a, W4b), total
number of results is 336 = 108, some results overlap themselves and give one point in
particular diagram. The range of power transfer capability varies from about 302 MW
to only 315 MW. Only for configuration W4a (Fig. 5b) the results reach values higher
than 80 V. Configurations W3a (Fig. 5a) and W4b (Fig. 5c) are acceptable.
a)
Induced sheath voltage (V)
75
70
65
60
55
50
45
1
Loa
d cu
315
0.9
rre
nt u
0.8
nifo
rmi
ty (
IIm
in /I
ma )
x
310
305
0.7
300
Powe
sfer c
r tran
ility (M
apab
W)
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Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
b)
Induced sheath voltage (V)
130
120
110
100
90
80
1
Loa
d cu
315
0.9
rre
nt u
nifo
rmi 0.8
ty (
IIm
in /I
ma )
x
310
305
0.7
300
s
r tran
Powe
fer ca
)
W
ity (M
pabil
c)
Induced sheath voltage (V)
65
60
55
50
45
40
1
Loa
d cu
rre 0.9
nt u
nifo
rmi 0.8
ty (
IIm
315
310
305
in /I
ma )
x
0.7
300
y (M
it
pabil
f er c a
s
r tran
Powe
W)
Figure 5 Induced sheath voltages in normal operating conditions as function of power
transfer capability and uniformity (Imin/Imax) of load current – configurations: a) W3a,
b) W4a, c) W4b; two cables per phase; Imin – current in the lowest loaded conductor,
Imax – current in the highest loaded conductor
Unfortunately, for an arrangement of the power system with one cable per phase
(configurations W5a, W6a, W6b – with total number of result 36 = 18; overlapped
too) all results are above the line indicating 80 V (Fig. 6). In some cases the voltage
exceeds even 200 V. The calculation results indicate that the arrangement with two
cables per phase is better than with one cable per phase.
A second step of the analysis is to find such a type of bonding and earthing in two
cable power system which gives maximum power transfer capability, acceptable
induced sheath voltages (not higher than 80 V) and high uniformity of load current in
Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
119
Induced sheath voltage (V)
the cable conductors. Figure 7 presents induced sheath voltages for the most favourable
configurations.
a)
110
105
100
95
90
85
80
0
50
100
150
200
250
300
350
300
350
300
350
Power transfer capability (MW)
b)
Induced sheath voltage (V)
200
180
160
140
120
100
80
0
50
100
150
200
250
Power transfer capability (MW)
c)
Induced sheath voltage (V)
105
100
95
90
85
80
0
50
100
150
200
250
Power transfer capability (MW)
Figure 6 Induced sheath voltages in normal operating conditions as function of power
transfer capability – configurations: a) W5a, b) W6a, c) W6b; one cable per phase
Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
120
These are the configurations: W3a (sheaths bonding and earthing in E1, crossbonding in E2) and W4b (single-point bonding; sheaths bonding and earthing in E2).
Figure 7 also includes detailed information about phase sequence in particular circuit
(e.g. ABC/CBA – phase sequence in circuit T1 is ABC, phase sequence in circuit T2 is
CBA) and induced sheath voltage in particular cable metallic sheath (e.g. W3a(T1C1)
– induced voltages in circuit T1 and conductor C1 for configuration W3a).
a)
Phase sequence in section
Induced sheath voltage (V)
ABC/CBA
ACB/BCA
BAC/CAB
BCA/ACB
CAB/BAC
CBA/ABC
80
70
60
50
40
30
20
10
0
W3a(T1C1)
W3a(T1C2)
W3a(T1C3)
W3a(T2C1)
W3a(T2C2)
W3a(T2C3)
Type of configuration and symbol of section
b)
Phase sequence in section
ABC/CBA
ACB/BCA
BAC/CAB
BCA/ACB
CAB/BAC
CBA/ABC
Induced sheath voltage (V)
80
70
60
50
40
30
20
10
0
W4b(T1C1)
W4b(T1C2)
W4b(T1C3)
W4b(T2C1)
W4b(T2C2)
W4b(T2C3)
Type of configuration and symbol of section
Figure 7 Induced sheath voltages in normal operating conditions for the preferred
configurations of cables: a) configuration W3a – sheaths bonding and earthing in E1,
cross-bonding in E2, b) configuration W4b – single-point bonding; sheaths bonding
and earthing in E2
Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
4
121
PHASE TO EARTH SHORT-CIRCUIT
Induced sheath voltages in case of short-circuit (single phase to earth) were
calculated as well. The value of short-circuit current is assumed to be 50 kA. In order
to avoid installing sheath voltage limiters (SVL), induced voltages should not exceed
5 kV. It is important to find such configurations of power cables that give value of
induced voltages not higher than 5 kV. In the considered cases, earth continuity
conductor (ECC) was implemented (see Fig. 3 and 4). This conductor provides a return
path of fault current and allows limiting induced sheath voltages significantly with
comparison to the arrangement without ECC [1, 10]. Induced sheath voltages are
presented as a function of number of power cables configuration (phase sequence) –
Fig. 8 and 9.
a)
Induced sheath voltage (V)
10000
9500
9000
8500
8000
7500
7000
6500
6000
5500
5000
1
2
3
4
5
6
Variant number of phase sequence
b)
Induced sheath voltage (V)
12000
11000
10000
9000
8000
7000
6000
5000
1
2
3
4
5
Variant number of phase sequence
6
122
Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
c)
Induced sheath voltage (V)
5700
5600
5500
5400
5300
5200
5100
5000
1
2
3
4
5
6
Variant number of phase sequence
Figure 8 Induced sheath voltages in case of short-circuit, as function of variant
number of phase sequence – configurations: a) W5a, b) W6a, c) W6b; one cable per
phase
a)
Induced sheath voltage (V)
6600
6400
6200
6000
5800
5600
5400
5200
5000
0
6
12
18
24
30
36
30
36
Variant number of phase sequence
b)
Induced sheath voltage (V)
8000
7500
7000
6500
6000
5500
5000
0
6
12
18
24
Variant number of phase sequence
Journal of Information, Control and Management Systems, Vol. 12, (2014), No. 2
123
c)
Induced sheath voltage (V)
3950
3900
3850
3800
3750
3700
3650
3600
3550
3500
0
6
12
18
24
30
36
Variant number of phase sequence
Figure 9 Induced sheath voltages in case of short-circuit, as function of variant
number of phase sequence – configurations: a) W3a, b) W4a, c) W4b; two cables per
phase
Comparison of Fig. 8 and Fig. 9 allows to state that the arrangement with one
cable per phase (configurations W5a, W6a, W6b) gives the values of induced sheath
voltages higher than 5 kV. The worst case is for the arrangement W6a (Fig. 8b), where
induced voltages exceed 11 kV. Sheath voltage limiters are necessary then. For the
arrangement with two cables per phase one configuration – W4b (Fig. 9c) – gives
induced voltages not higher than 5 kV. This is the preferred configuration of cables.
Figure 10 includes detailed information about phase sequence in particular circuit and
induced sheath voltage in particular cable metallic sheath.
In case of short-circuit the most favourable configuration is W4b – the same as in
normal operating condition.
Phase sequence in section
ABC/CBA
ACB/BCA
BAC/CAB
BCA/ACB
CAB/BAC
CBA/ABC
Induced sheath voltage (V)
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
W4b(T1C1)
W4b(T1C2)
W4b(T1C3)
W4b(T2C1)
W4b(T2C2)
W4b(T2C3)
Type of configuration and symbol of section
Figure 10 Induced sheath voltages in case of earth fault for the most favourable
configuration of cables: configuration W4b – single-point bonding; sheaths bonding
and earthing in E2
124
Calculation of Induced Sheath Voltages in Power Cables – Single Circuit System…
5
CONCLUSIONS
Computer-aided calculation of the induced sheath voltages in power cable system
allows finding the optimal configuration of the system, with covering technical and
economic aspects. In the considered cases the preferred configuration is the
configuration W4b (two cables per phase, single-point bonding; sheaths bonding and
earthing in E2). This configuration gives acceptable values of induced sheath voltages
and the highest power transfer capability. Power system with two cables per phase,
instead of single cable system with large cross-section of conductor, should be
recommended.
REFERENCES
[1]
CIGRE, Working group B1.18, Special bonding of high voltage power cables,
October 2005.
[2] CZAPP, S.: Principles of protection against electric skock in high voltage power
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wysokiego napiecia). Journal Automatyka Elektryka Zaklocenia, vol. 13, no. 3,
pp. 8–22, 2013, http://epismo-aez.pl/, (in Polish).
[3] CZAPP, S., DOBRZYNSKI, K., KLUCZNIK, J., LUBOSNY, Z.: Computeraided analysis of induced sheath voltages in high voltage power cable system.
The 10th International Conference on Digital Technologies 2014, Zilina,
Slovakia, 9–11.07.2014, pp. 44–50, IEEE Catalog Number CFP14CDT-USB.
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[8] ANSI/IEEE Std 575-1988, IEEE Guide for the application of sheath-bonding
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