Electrical Engineering (2006) 88: 431–439
DOI 10.1007/s00202-005-0299-x
O R I GI N A L P A P E R
E. M. Tag Eldin Æ M. I. Gilany Æ M. M. Abdelaziz
D. K. Ibrahim
An accurate fault location scheme for connected aged cable lines
in double-fed systems
Received: 21 November 2004 / Accepted: 16 February 2005 / Published online: 23 June 2005
Ó Springer-Verlag 2005
Abstract This paper presents an adaptive fault location
scheme for aged power cables using synchronized phasor
measurements from both ends of the cable. The proposed fault location scheme is derived using the twoterminal synchronized measurements incorporated with
distributed line model, modal transformation theory and
Discrete Fourier Transform. The proposed scheme has
the ability to solve the problem of cable changing
parameters, especially the change of the relative permittivity over its age and thus for the operating positive,
negative, and zero-sequence capacitance changes.
Extensive simulation studies are carried out using
Alternative Transients Program ATP/EMTP. The simulation studies show that the proposed scheme provides
a high accuracy in fault location calculations under
various system and fault conditions. The results show
that the proposed scheme responds very well to any fault
insensitive to fault type, fault resistance, fault inception
angle and system configuration. The proposed scheme
solves the problem of aged cables with the change of the
electric parameters. In addition to, it gives an accurate
estimation of the fault resistance.
Keywords Aged power cables Æ Distributed line model Æ
Fault location Æ Modal transformation Æ Phasor
extraction
1 Introduction
Underground cables are very important parts in a power
system and are depended upon for reliable transmission
E. M. T. Eldin (&) Æ M. M. Abdelaziz
Faculty of Engineering, Cairo University, Cairo, Egypt
E-mail: stageldin@ieee.org
M. I. Gilany
College of Technological Studies, Shuwaikh, Kuwait
D. K. Ibrahim
Faculty of Engineering, Cairo University, Giza, Cairo, Egypt
and distribution services. The fault location in complex
cable distribution systems is at present, difficult, time
consuming and labor intensive; consequently the cable
fault location technique with high degree of accuracy
and a high degree of efficiency is increasingly demanded
with the increased use of underground cables. Benefits of
accurate fault location are quick repairs to restore power
system, improvement of system availability and performance, reduction of operating costs, and saving of time
and expense of crew searching in bad weather and tough
terrain.
A variety of fault location techniques are used to
achieve the aim and the above-specified benefits [1].
While numerous techniques are now available to the
fault locator, some techniques can be destructive to the
cable, some may require instruments not readily in
stock, and others may involve detection methods not
familiar to the user. Such challenges led to the need for a
comprehensive fault locator reference manual.
In the field of fault location for underground cables,
off-line and on-line methods are available. Off-line
methods are divided into two main groups: terminal
methods and tracer methods [2–4]. Terminal methods
are applied to the cable from one or two terminals and
are usually used as a preliminary step of fault location:
such as capacitance method, bridge technique and earth
gradient method. After finding the approximate location
of the fault, tracer methods are used to get the exact
location such as: tracing current method and Thumper
Acoustic method. Acoustic method involves a capacitor
discharge through the cables with utility personnel
having headphone sensors listening for the noise associated to the arcing in the cable, the applied voltage and
current in such methods are so large that they may cause
additional damage to the cable. All the above techniques
require the cable to be taken out of service and are not
able to detect incipient faults or partial discharges.
On the other hand, in the on-line methods, fault
location is solved by processing the recorded information of fault current and voltage. Examples of the online methods are A/D techniques [5], fault generated
432
high frequency transient method [6, 7], neural networks
method [8, 9], and global positioning systems [10].
Some parameters of the power cable may change
during its operation. The main parameter is the temperature that leads to a change of the 3-phase positive,
negative, and zero-sequence capacitance. In other
words, the change in relative permittivity r, which occurs over cable age; affects the operating capacitance C,
the capacitive current and the earth leakage current result in significant errors in fault location estimation [11].
The change in r may reach 110% to 200% or more,
leading to an error of about 4.65% to 29.2% in fault
location estimation methods that use the manufacture
parameters of the cables. The proposed method would
present a solution for this problem.
The adaptive fault location scheme proposed uses the
distributed line model, modal transformation theory and
Discrete Fourier Transform. It can be used following the
operation of digital relays or using the data stored in the
digital transient recording apparatus. The method proposed has no predetermined fixed data except for the
cable length. The main advantage of the proposed
scheme is that it has the ability to adopt its response
according to cable line parameter changes over cable
age, which is coincident to the CIGRE definition of
adaptive protection ‘‘a protective philosophy which
permits and seeks to make adjustment to various protection functions in order to make them more attuned to
the prevailing power system conditions’’ [12]. The
method considers the line cable sections to be transposed. No assumptions were made for fault boundary
conditions or fault resistance.
Extensive simulation studies using ATP software are
conducted to investigate the feasibility of the proposed
scheme and to evaluate the performance of the proposed
scheme [13]. The proposed technique is examined under
different fault conditions. The results indicate that the
proposed fault location scheme is able to locate the fault
location correctly. Results also show that the technique
is insensitive to fault type, fault resistance, fault inception angle and system configurations.
As power cables are widely used in the power system
in different voltage levels, it is sometimes used to supply
a large isolated load (in radial system). On the other
hand, it is also used to connect substations, especially
inside cities. The proposed technique solved the fault
location problem in such case. In this paper, an example
of 20 kV double-fed system connected with two different
distribution aged cables is to be presented.
shown in Fig. 1, the voltage and current phasors can be
represented when considering a very small element (d x) in
the line and can be calculated the difference in voltage and
in current between the ends of the element. The voltage
rise over the element in the direction of increasing x is d V.
This rise in voltage is also the product of the current in the
element flowing opposite to the direction of increasing x
and the impedance of the element. Similarly, the current
flowing out the element, the magnitude and phase of the
current vary with distance along the line because of the
distributed shunt admittance along the line.
The differential voltage and current can be expressed
as:
dV
¼zI
dx
dI
¼yV
dx
By differentiating Eq. 1 with respect to d x, the following equations are obtained [14]
d2 V
dI
¼ z ¼ z y V ¼ c2 :V
dx2
dx
d2 I
dV
¼ z y I ¼ c2 : I
¼y
dx
d2 x
ð2Þ
where z is the series impedance of the line in X/km, y is
the shunt admittance of the line in X1/km. The
parameters R, L, G, and C are resistance, inductance,
conductance and capacitance of the cable per unit
length. Solving Eq. 2 using the known boundary conditions shown in Fig. 1 leads to Eqs. 3 and 4.
– With receiving end boundary conditions V0= VR and
I0= IR, the solutions are :
VR þ IR ZC
VR IR ZC
eþcx þ
ecx
2
2
VR =ZC þ IR
VR =ZC IR
eþcx ecx
Ix ¼
2
2
Vx ¼
ð3Þ
– With the sending end boundary conditions, VL=
VSand IL= IS, (L is the total cable line length), the
solutions are:
V S þ I S ZC
VS IS ZC
eþcðxLÞ þ
ecðxLÞ
Vx ¼
2
2
ð4Þ
VS =ZC þ IS
VS =ZC IS
þcðxLÞ
cðxLÞ
e
e
Ix ¼
2
2
2 Fault location for a single-phase cable
To explain the concept used in the proposed scheme, the
paper starts with the fault location solution in a singlephase cable line and then extends to the three phase
solution.
As the voltage and current along a single-phase cable
are functions of the distance from the end of the line as
ð1Þ
Fig. 1 A single-phase power cable line
433
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where ZC ¼ ðR þ jxLÞ=ðG þ jxCÞ;
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c ¼ ðR þ jxLÞ ðG þ jxCÞ
2
Consider a fault occurred at the point F, with D km
away from receiving end. Cable line is thus divided into
two homogeneous parts. One is the cable section SF,
with a length of L – D km; the other cable section is the
line section FR, with a length of D km. These two line
sections can still be regarded as perfect cable power
lines. This means that the voltages at any point on the
two cable sections can be expressed by the voltages and
currents measured at the healthy end of that section.
Moreover, at fault point F, the voltages expressed in
terms of these two data sets (VS,IS) and (VR,IR) are
identical. Then the voltage at the fault location D km
away from the receiving end can be expressed using
Eqs. 3 and 4 as:
VR þ IR ZC
VR IR ZC
ecD þ
ecD
2
2
VS þ IS ZC
VS IS ZC
ecðDLÞ þ
ecðDLÞ
VF ¼
2
2
VF ¼
ð5Þ
Since VF is the voltage at the same point F, solving
Eqs. 5 for the fault location from the receiving end D
yields to [15, 16]:
D¼
lnðN =MÞ
2c
ð6Þ
where
VR IR ZC VS IS ZC
eþcL
2
2
VR þ IR ZC VS þ IS ZC
þ
ecL
M ¼
2
2
N¼
ð7Þ
3 Fault location scheme for three phase cable
3.1 Modal decomposition
In this subsection, the above theory is extended to the
three-phase line. The three phase lines have significant
electromagnetic coupling between conductors. By means
of decomposition, the coupled voltages and currents are
decomposed into a new set of modal voltages and currents; each can be treated independently in a similar
manner to the single-phase line. In this paper, real Clarke
transformation matrix has been used with its two-phase
stationary components (a and b) and a component called
ground or zero sequence component (o) as follows [17]:
2
3
þ1 þ1 þ1
1
5
T ¼ 4 þ2 p
1ffiffiffi 1
pffiffiffi
3
0
3 3
The samples of phase voltage and current at both
ends of the cable have been decoupled into three single
modes as follows: Then
3
2
3
Vo
VA
4 VB 5 ¼ T 4 Va 5;
Vb
VC
2
3
2
3
Io
IA
4 IB 5 ¼ T 4 Ia 5
Ib
IC
Each mode has a different velocity of propagation
and different surge impedance. The ground mode is the
most dependent on ground resistivity and the lowest
velocity of propagation. The other modes (aerial), which
are frequency invariant, are favored for fault location.
3.2 Fault location algorithm
The single-phase solution is extended to the three phase
line using o, a and b modal components of the signals.
Each modal component is represented with its own
propagation constant ci and surge impedance ZCi.
Assuming complete transposition, the surge impedances
of each mode are:sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffi
ZS þ 2Zm
Zo
ZCo ¼
¼
YS 2Ym
Yo
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffi
ZS Zm
Z1
ZCa ¼ ZCb ¼
¼
YS þ Ym
Y1
where ZCi is the i - mode surge impedance (i is for o, a
and b modes), ZS,YS are the average sum of all conductor self impedances and admittances at any frequency. Zm,Ym are the average sum of all conductor
mutual impedances and admittances at any frequency,
Zo, Yo are the zero phase sequence impedance and
admittance and Z1,Y1 are the positive phase sequence
impedance and admittance [18]. The modal propagation
constants are similarly given in terms of phase sequence
impedances and admittances by:pffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffi
co ¼ Zo Yo ; ca ¼ cb ¼ Z1 Y1
Thus, the fault location from the receiving end Di for
the three modal components are:
Di ¼
lnðNi =Mi Þ
2ci
i ¼ o; a and b
ð8Þ
Where Ni, Mi is computed as following:1
1
Ni ¼ ðVRi IRi ZCi Þ ðVSi ISi ZCi Þ eþci L
2
2
1
1
Mi ¼ ðVRi þ IRi ZCi Þ þ ðVSi þ ISi ZCi Þ eci L
2
2
ð9Þ
where S and R are for the sending and receiving end data
respectively, i = o, a, and b for modal components of
signals.
4 Fault location problem in aged cables
The performance of underground cables depends on a
number of parameters that may not remain constant
434
Fig. 2 Change in C and r as a function of temperature for
protodur compounds
over a period, and the contributions of each is added to
the performance in a complex manner. The main
parameter is the temperature that leads to a change of
the 3-phase positive, negative, and zero-sequence
capacitance. The change in the relative permittivity r of
the cable over its age results in significant errors in fault
location estimation. Guiding values for Protodur cables
are shown in Fig. 2 [11], with the basis value at 20 C°
=1. For example at 40 C°, the ratio of C to C20 is equal
to 1.3 at 15–30 kV, leads to an error in fault location
techniques which used the value of C20 of about 12.3%,
Another example at 30 C°, the ratio of C to C20 is equal
to 1.15 thatpleads
ffiffiffiffiffiffiffiffiffi to a change of the velocity of propagation of 1= 1:15 ¼ 0:9325; and also leads to an error in
fault location of 6.75%.
Any change of the 3-phase positive, negative, and
zero-sequence capacitance of the cable line leads to a
change in phase sequence admittances and thus also
brings about for a change in propagation constant of
each mode and its associated surge impedance. Therefore an error occurs in the fault location calculation
when applying the above equations derived in section 3.2
[11].
The power of the proposed technique compared with
the traditional techniques which are dependent on the
line parameters comes from its fault location equations
that are only dependent on cable length. The next section will introduce the main advantage of the proposed
scheme to adopt its response according to cable line
parameter.
5 Estimation of aged cable changed parameters
The adaptive feature of the proposed method presents a
solution for the problem of changing parameters with
age by estimating cable mathematical model with its
parameters. Propagation constants ci, associated surge
impedances ZCi for i = o, a and b modal components of
signals are determined using one cycle of the measured
voltage and current signals from both sides, before the
instance of fault occurrence without using the original
manufacturing parameters data of the cable. The
homogenous line equation is applied from both side over
the total line length as follows:
1. Using Eq. 3 to get the phasor values of the prefault
modal sending end voltages and currents as functions
of the phasor values of the prefault modal receiving
end voltages and currents.
2. Using Eq. 4 to get VRi and IRi as functions of VSi, ISi,
ZCi and ci. All phasors values are calculated using
only one cycle before fault.
3. The mentioned derived four equations are obtained
for each modal then be solved to obtain the propagation constant of each mode and its associated surge
impedance as follows [15, 16]:sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
VSi2 VRi2
ZCi ¼
2
ISi2 IRi
cosh1 ðFi Þ
Cable length
VSi ISi þ VRi IRi
Fi ¼
ISi IRi þ IRi ISi
ci ¼
ð10Þ
where S and R are for the sending and receiving end,
respectively, i = o, a, and b for modal components.
6 Proposed fault location scheme for double-fed system
with different aged cables
The paper describes a fault locator for the combined
aged underground power cables. The response of the
system is evaluated by simulating a typical two-ended
system as shown in Fig. 3. A schematic description of
the proposed fault locator is given in Fig. 4.
6.1 Signals processing
The three phase currents and voltages at both sides of
the cables are collected, sampled, and then fed to a
transformation routine as described in Sect. 3.1 to get
three decoupled modes o, a and b.
The three double-ended modal phasors currents and
voltages are extracted via discrete fourier transform
(DFT). In the proposed scheme, full cycle DFT is used
to identify the power frequency sinusoid with its
amplitude and phase shift. A moderate sampling frequency of 2 kHz is used in the proposed scheme.
Fig. 3 System under study
435
6.3.1 Preliminary fault locations estimation
In the first solution, the fault is assumed to be in the first
cable line (in front of the joint). The changed modal
surge impedances and associated propagation constants
for that cable are calculated, the modal phasors of the
currents and voltages at the two ends of the cable (first
bus and at the joint) are extracted as explained in Sect.
6.1 and are used to calculate Ni and Mi as in Sect. 3.2.
Equation 8 is used to calculate Di1 for i = o, a and b (D
o,D a or D b) using the predetermined fixed cable length.
The same procedure is repeated but with the
assumption of a fault in the side of the second cable line
(behind the joint), a second solution of Di2 is obtained
with only current and voltage signals at its two ends (at
the second bus and at the joint) and the length of the
second cable line.
6.3.2 Correct fault location identification
Fig. 4 Schematic diagram for the fault locator
6.2 Estimating aged cables parameters
Using only one cycle of the measured voltages and
currents signals stored in the digital recording apparatus
at each bus and the joint before the instant of fault
occurrence, the signal processing unit can extract the
power frequency modal voltages and currents phasors.
Thus the locator settled at the first bus can estimate the
changed modal surge impedances and associated propagation constants for each aged cable as given in Sect. 5
without using the manufacturing parameters data of the
aged cables.
6.3 Fault location algorithm
DFT extracts the modal post-fault voltages and currents
phasors within 1.25 cycles after the instant of fault
occurrence, these quantities are used to estimate fault
location using two stages:
1. Preliminary fault locations estimation.
2. Correct fault location identification.
Since the fault location with respect to the joint between the two different cables is not known prior to the
fault occurrence, the proposed algorithm assumes two
preliminary fault locations: a fault in the first cable line
in front of the joint (fault1), and a fault in the second
cable section behind the joint (fault2). Two solutions are
obtained for the fault location in the first stage. The true
location is to be selected using the second stage.
Locating a fault with respect to the joint between the
two different cables in the system of Fig. 3 is a separate
issue. However, the problem is to be narrowed to the
selection of the correct location from two solutions (Di1)
and (Di2). The simple and straightforward algorithm
that works in most cases is similar to that used in the
case of fault location algorithm in series compensated
transmission lines as follows [19]:
If Di1 is within the first cable line length and Di2 is out
the second cable line length then accept (Di1) as a correct
solution otherwise
If Di1 is out of first cable length and D12 is within the
second cable length then accept (D12) as a correct solution.
6.4 Appropriate mode selection according to fault type
It is necessary to choose the accurate fault location by
selecting the appropriate mode. Only the areal modes are
used in the fault location algorithm, because the velocity
of the ground mode is frequency-dependent. For transformation matrix used, mode a is valid to deal with all
type of faults except the fault of B-C. Thus an appropriate solution is in taking fault location of a modal as a
true location for all fault types except for a B-C fault. In
such a case, it is appropriate to take fault location of b
modal. The proposed scheme assumes that the fault type
is known from another diagnostic block. However, using
the voltage and current vectors calculated at the fault in
the next Section, the fault type may also be verified.
6.5 Calculation of the fault resistance
The proposed scheme has the ability to determine the
fault resistance for various fault types in either first aged
cable or second cable line. Using the values of Di (fault
locations from the receiving end in either first or second
436
cable line) for o, a and b, the fault resistance can be
obtained as follows:
1. Calculating the phasor fault voltage VFiand fault
current I FiS supplied from the sending end, the first
homogeneous part of the faulty section of length
(Lcable - Di) by applying Eq. 4 with x = 0, Length =
Lcable – Di .
2. Calculating the fault current I FiR supplied from the
receiving end, the second homogeneous part of the
faulty section of length (DI ) by applying Eq. 3 with x
= Di .
3. The fault current I Fi is calculated by summing both
components I FiSand IFiR,.
4. Then the phase voltages (VFA, VFB,VFC) and currents
(I FA, I FB,I FC) at the fault point are calculated using
Clarke transformation matrix given in Sect. 3.1.
Thus, according to the fault type, the fault resistance
RFis calculated as follows [20]:
VFA
For A to ground fault : RF ¼
IFA
VFB þ VFC
For B to C to ground fault : RF ¼
I þ IFC
VFB VFC FB
For B to C fault : RF ¼
IFB IFC
7 Simulated case stud
Power cables are widely used in the power system at
different voltage levels. They are sometimes used to
supply a large isolated load. On the other hand, they are
also used to connect substations, especially inside cities.
The proposed scheme addressed the latter case and
typical results are presented.
Two different underground cables for 20 kV applications are connected in the system shown in Fig. 3;
each cable is represented by Bergeron model representation which is as a quite suitable for more exact computer simulation. Configuration and installation of the
first and second cables are shown in Fig. 5. The physical
and insulation constants of each phase of the first and
second cables are given in Table 1.
Extensive simulations were carried out using the
Alternative Transients Program, which is considered
one of the widely used universal program system for
digital simulation of transient phenomena of electromagnetic as well as electromechanical nature in electric
Table 1 Cables parameters
R1
R2
R3
R4
R5
qc
lc
r1
lr1
qs
ls
r2
lr2
First cable (5 km)
Second cable (10 km)
0 mm
20 mm
40 mm
43 mm
45 mm
1.724e–8 X.m
1
2.7
1
2.84e–8 X.m
1
2.7
1
0 mm
23 mm
43 mm
47 mm
49 mm
1.724e–8 X.m
1
3.8
1
2.30e–8 X.m
1
3.8
1
power systems. ATP has extensive modeling capabilities and additional important features besides the
computation of transients. The voltage and current
signals from both sides of the cables are determined during different fault conditions, different fault
locations, different fault types and different fault
inception angles. The fault resistance varied from 0 to
100 ohm.
As an example, the simulated results for a single
line B to ground fault at 40 msec through fault resistance of 10 X occurring at 1.5 km from the source
terminal (in the first cable line section, in front of the
joint) is presented. The three phase voltage and current signals collected from the first and second buses
are shown in Fig. 6. Figure 7 shows the three modal
(o, a, b) voltage and current signals at the first and
second the buses. Figure 8 shows the output of the
signal processing unit of the three modal voltages and
currents signals at both buses. It is shown from Fig. 8
that the aged cable parameters using phasors values
are estimated within less than 1.25 cycles after fault
occurrence.
The fault location algorithm gives two solutions for
the case described above (fault at 1.5 km in the first
cable), the first solution of modal fault locations o, a and
b are at 2.0039, 1.4668 and 1.4391 km respectively. The
second estimates of the fault modal locations o, a and b:
at 8.3439, 543.3092 and 536.4067 kms. respectively.
Applying the correct fault location identification subroutine, the algorithm chooses the first estimation of the
location to be the correct solution. Modal a location of
1.4668 km is selected as fault location for the phase to
ground fault tested.
8 Proposed scheme evaluation
Fig. 5 Structure and installation of the first and second three phase
single core cable
The performance of the scheme was tested to check
whether the protection scheme is suitable for accurate
fault location determination, even in different fault
conditions especially when the parameters of the cable
are changed over its age.
437
Fig. 6 Voltages and currents for a phase B to ground fault at
1.5 km in first cable line section (a) At bus1 (b) At bus2
Fig. 7 Modal voltages and currents for a phase B to ground fault
at 1.5 km in first cable line section (a) At bus1 (b) At bus2
The error in the next sections is calculated as follows:
(fault1), 0° inception angle and 10 X fault resistance
were considered. The results in Table 3 show that the
accuracy is hardly affected by fault type.
Percentage of error
jactual fault location calculated faultj
100
¼
faulty cable length
ð11Þ
8.1 Influence of the fault location
To evaluate the influence of the fault location on the
algorithm accuracy, different cases of phase-to-ground
faults with 20 ohm of fault resistance at various locations
within the two aged cables were considered. The results
presented in Table 2 show the effectiveness of the proposed scheme in fault location estimation for different
locations.
8.3 Influence of the fault resistance
To estimate the fault resistance influence, different fault
types were considered with fault location of 7.5 km in the
second cable (measured from the joint), the fault resistance varied from 10 X to 100 X and the results are
shown in Table 4. Table 5 shows the estimated fault
resistance for different fault types. It represents the ability
of the proposed scheme to estimate the fault resistance
under different fault types at different fault locations.
8.4 Influence of the inception angle
8.2 Influence of the fault type
To analyze the influence of the fault type, seven different
faults, with a fault location of 4 km in the first cable
In the analysis of the inception angle influence, cases
corresponding to double phase to ground faults, with
fault location at 8 km in the second cable with inception
angle varied from 0° to 90°. Table 6 shows that the
438
Table 3 Influence of fault type on estimated fault location
Fault
type
Exact location
(km)
Calculated
location (km)
Percentage
of error
AG
BG
CG
ABG
ACG
BCG
ABCG
4
4
4
4
4
4
4
3.9803
3.9584
3.9595
3.9788
3.9681
3.9567
3.9655
0.394
0.832
0.810
0.424
0.638
0.866
0.690
Table 4 Influence of fault resistance on estimated fault location
Fault type
Fault
resistance (X)
Calculated
location (km)
Percentage
of error
single-phase
to ground
10
50
100
10
50
100
10
50
100
7.4396
7.4205
7.4143
7.5069
7.5106
7.5143
7.4813
7.4790
7.4695
0.6040
0.7950
0.8570
0.0690
0.1060
0.1430
0.1870
0.2100
0.3050
Double phase
to ground
Three phase
to ground
Table 5 Estimated fault resistance
Fault
type
Fig. 8 DFT of modal voltages and currents for phase B to ground
fault at 1.5 km in first cable line (a) At bus1 (b) At bus2
accuracy of the proposed scheme is hardly affected by
the fault inception angle.
8.5 Influence of the cable parameters changes with
temperature and age.
The evaluation of influence of the cable parameters
change in the algorithm accuracy is examined by
Table 2 Fault location influence on algorithm accuracy
Faulted cable
Actual fault
location (km)
Calculated fault
location (km)
Percentage
of error
First cable
(5 km)
0.8
1.2
2
3.5
4.1
1
3.5
7
8.5
9.3
0.7460
1.1497
1.9508
3.4471
4.0497
0.8946
3.4448
6.8931
8.4106
9.1872
1.0800
0.8060
0.9840
1.0580
1.0060
1.0540
0.5520
1.0690
0.8940
1.1280
Second cable
(10 km)
SLG
DLG
LL
RF
(X)
10
20
100
10
30
15
Fault at 2 km
(in cable 1)
Fault at 3 km
(in cable 2)
Estimated
RF (X)
Percentage
error
Estimated
RF (X)
Percentage
of error
10.176
19.7905
98.3640
9.9269
29.0513
15.3298
1.7600
1.0475
1.6360
0.7310
3.1623
2.1987
10.3117
20.5378
99.2518
10.3242
30.1617
15.2321
3.117
2.6890
0.7482
3.2420
0.5390
1.5473
changing the positive and zero sequences capacitances of
the first cable to simulate any change on cable temperature as discussed above on Sect. 4.
In this analysis, cases corresponding to single-phase
to ground faults, with fault location at 3 km, varying the
system capacitance from 0.9 to 2.5 times of the nominal
capacitance at 20° (C20) were considered.
The results presented in Table 7 show that the
method accuracy is hardly affected by any change in
Table 6 Influence of the inception angle on the estimated fault
location
Inception (°)
Calculated
location (km)
Percentage
of error
0
30
45
60
90
8.0178
8.0180
8.0146
8.0174
8.0158
0.178
0.180
0.146
0.174
0.158
439
Table 7 Influence of cable parameters changes on estimated fault
location
C/C20
Calculated
location (km)
Percentage
of error
.9
1.2
1.8
2.5
2.9527
2.9528
2.9535
2.9602
0.9460
0.9440
0.9300
0.7960
Table 8 Estimated parameters in comparison with actual modified
parameters
Parameter
Actual Zca (X)
Estimated Zca (X)
Actual Zcb (X)
Estimated Zcb (X)
Actual ccb
Estimated ccb
C/C20
1.2
3
5
10.6085
10.6117
10.6085
10.5998
0.0080
0.0080
6.7094
6.7105
6.7094
6.7021
0.0126
0.0127
5.1971
5.1985
5.1971
5.1986
0.0163
0.0162
cable parameters, that is the most significant advantage
of the algorithm proposed. Additionally, the ability of
the proposed scheme to estimate the modified parameters is verified in Table 8.
9 Conclusions
In this paper, a fault location scheme is proposed for
aged power cables using synchronized phasor measurements from both ends of the cable. The proposed scheme
estimates the changed parameters of aged cables. Using
the post fault phasor measurements, it calculates the
fault location using the two aerial modals of the cable
line.
The proposed scheme showed also its ability for
adaptation by accurate estimation of cable parameters
using only one cycle of pre fault voltages and currents
and the cable length. In other words, the algorithm results are not sensitive to the variations in the parameters
of the cable power lines over its age. So this method can
be applied on any cable with double-ended measurements of voltages and currents without any predetermined cable data except the cable length. The simulation
results show that the proposed method responds very
well, insensitive to fault type, fault location, fault resistance, fault inception angle and system configuration.
Accurate results for all fault conditions were obtained,
as the maximum percentage error in the simulated fault
cases is only 1.1280% of the 10 km cable (about 113 m).
Moreover, the proposed scheme introduced a good
method for estimating the value of fault resistance for all
fault types.
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