POWER CABLE FAULT LOCATION
TECHNIQUE BASED ON PARAMETER
OPTIMIZED VARIATIONAL MODAL
DECOMPOSITION
Yuning-Tao*
• College of Electrical Engineering and New Energy, China Three Gorges
University, Yichang, Hubei, 443000, China
•taoyuning12@163.com
Reception: 11 April 2024 | Acceptance: 6 May 2024 | Publication: 10 June 2024
Suggested citation:
Yuning-Tao (2024). Power cable fault location technique based on
parameter optimized variational modal decomposition. 3C Tecnología.
Glosas de innovación aplicada a la pyme, 13(1), 130-155. https://doi.org/
10.17993/3ctecno.2024.v13n1e45.130-155
https://doi.org/10.17993/3ctecno.2024.v13n1e45.130-155
3C Tecnología. Glosas de innovación aplicadas a la pyme. ISSN: 2254-4143
Ed.45 | Iss.13 | N.1 April - June 2024
130
POWER CABLE FAULT LOCATION
TECHNIQUE BASED ON PARAMETER
OPTIMIZED VARIATIONAL MODAL
DECOMPOSITION
Yuning-Tao*
• College of Electrical Engineering and New Energy, China Three Gorges
University, Yichang, Hubei, 443000, China
•taoyuning12@163.com
Reception: 11 April 2024 | Acceptance: 6 May 2024 | Publication: 10 June 2024
Suggested citation:
Yuning-Tao (2024). Power cable fault location technique based on
parameter optimized variational modal decomposition. 3C Tecnología.
Glosas de innovación aplicada a la pyme, 13(1), 130-155. https://doi.org/
10.17993/3ctecno.2024.v13n1e45.130-155
https://doi.org/10.17993/3ctecno.2024.v13n1e45.130-155
ABSTRACT
With the complexity of power systems and the increase of loads, power cable faults
occur frequently, affecting the safety of power supply. A parameter optimization-based
variational modal decomposition (VMD) technique combined with wavelet transform is
used. Through in-depth analysis of cable fault signals, this study first applies VMD to
decompose the signals, and then further analyzes the processed signals in
combination with wavelet transform. The experimental results show that the method
achieves a significant reduction in the average localization error in the simulated fault
test, with an average error of less than 1%, which improves the localization accuracy
by about 30% compared with the traditional method. In the processing of complex
fault signals, the present method shows better adaptability and robustness. Overall,
this study not only improves the accuracy of fault localization, but also provides a new
technical path for the diagnosis and maintenance of power system faults.
KEYWORDS
Power cable fault location, variational modal decomposition, parameter optimization,
wavelet transform
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INDEX
ABSTRACT .....................................................................................................................2
KEYWORDS ...................................................................................................................2
1. INTRODUCTION .......................................................................................................4
2. POWER CABLE FAULT RELATED ANALYSIS ......................................................5
2.1. Power Cable Failure Related Causes ................................................................6
2.1.1. Causes of power cable failures ...................................................................6
2.1.2. Characteristics of power cable faults ...........................................................6
2.2. Power cable fault detection process ..................................................................7
2.2.1. Fault detection of power cables ...................................................................7
2.2.2. Equivalent modeling of power cables ..........................................................8
2.3. Power cable fault traveling wave process ..........................................................9
2.3.1. Traveling Wave Velocity of Power Cable .....................................................9
2.3.2. Calculate reflected and refracted waves ...................................................10
3. POWER CABLE FAULT LOCATION DIAGNOSIS ................................................11
3.1. Parameter optimized variational modal decomposition ....................................12
3.1.1. variational modal decomposition (VMD) ....................................................12
3.1.2. AOA lgorithmic optimization of VMD parameters ......................................13
3.2. AO-VMD-CWT fault localization model ............................................................14
3.2.1. Continuous Wavelet Transform (CWT) ......................................................14
3.2.2. AO-VMD-CWT Signal Noise Reduction ....................................................15
4. POWER CABLE FAULT LOCATION SIMULATION ..............................................17
4.1. Signal Noise Reduction and Fault Localization Simulation ..............................18
4.1.1. AO-VMD-CWT Signal Noise Reduction ....................................................18
4.1.2. Simulation of power cable fault distance ...................................................19
4.2. Power cable fault location performance comparison .......................................21
4.2.1. Comparison of Double-Ended Traveling Wave Ranging Methods ............21
4.2.2. Compare to other network models ............................................................23
5. CONCLUSION ........................................................................................................24
REFERENCES ..............................................................................................................25
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INDEX
ABSTRACT .....................................................................................................................2
KEYWORDS ...................................................................................................................2
1. INTRODUCTION .......................................................................................................4
2. POWER CABLE FAULT RELATED ANALYSIS ......................................................5
2.1. Power Cable Failure Related Causes ................................................................6
2.1.1. Causes of power cable failures ...................................................................6
2.1.2. Characteristics of power cable faults ...........................................................6
2.2. Power cable fault detection process ..................................................................7
2.2.1. Fault detection of power cables ...................................................................7
2.2.2. Equivalent modeling of power cables ..........................................................8
2.3. Power cable fault traveling wave process ..........................................................9
2.3.1. Traveling Wave Velocity of Power Cable .....................................................9
2.3.2. Calculate reflected and refracted waves ...................................................10
3. POWER CABLE FAULT LOCATION DIAGNOSIS ................................................11
3.1. Parameter optimized variational modal decomposition ....................................12
3.1.1. variational modal decomposition (VMD) ....................................................12
3.1.2. AOA lgorithmic optimization of VMD parameters ......................................13
3.2. AO-VMD-CWT fault localization model ............................................................14
3.2.1. Continuous Wavelet Transform (CWT) ......................................................14
3.2.2. AO-VMD-CWT Signal Noise Reduction ....................................................15
4. POWER CABLE FAULT LOCATION SIMULATION ..............................................17
4.1. Signal Noise Reduction and Fault Localization Simulation ..............................18
4.1.1. AO-VMD-CWT Signal Noise Reduction ....................................................18
4.1.2. Simulation of power cable fault distance ...................................................19
4.2. Power cable fault location performance comparison .......................................21
4.2.1. Comparison of Double-Ended Traveling Wave Ranging Methods ............21
4.2.2. Compare to other network models ............................................................23
5. CONCLUSION ........................................................................................................24
REFERENCES ..............................................................................................................25
https://doi.org/10.17993/3ctecno.2024.v13n1e45.130-155
1. INTRODUCTION
Cables are widely used in power distribution networks and play a significant role in
power supply reliability. Although the power supply reliability of power cables is higher
than that of overhead lines, they are generally buried directly underground and the
line structure is more complex, so it is not easy to locate the fault location and
troubleshoot the fault in time when a fault occurs [1-3]. Therefore, fast and accurate
localization of distribution network cable faults is very important for fault removal,
reducing fault outage time and improving power supply reliability [4-5].
In recent years with the increasing service life of cables, the incidence of cable
faults has begun to rise gradually, and the problem of detecting and diagnosing cable
faults has gradually attracted people's attention [6-8]. Cable fault refers to a series of
faults occurring in cables, including but not limited to insulation aging, insulation
breakdown, joint failure, conductor breakage, etc. The occurrence of these faults will
seriously affect the stable operation of the power system, and may even cause safety
accidents. Therefore, the detection and diagnosis techniques of cable faults are of
great significance in ensuring the stable operation of power systems and extending
the service life of cables [9].
Different techniques have different advantages and disadvantages, and in the
actual signal cable fault screening and localization, the applicability of different
techniques, the reliability is different. Literature [10] introduces a method based on
transient current measurement of cable shield grounding, which can identify the fault
identification and localization of underground cables and hybrid lines, based on which
a new transient grounding fault detection and localization algorithm is proposed, the
new algorithm has the ability of autonomous learning, compared with the traditional
method can be identified under the conditions of transient grounding faults on the
distribution feeder branch, and the feasibility of the algorithm is examined through the
test. Literature [11] aims to realize the precise location of cable faults, and proposes
two hybrid schemes, MT-CT-DFT scheme and ANN-WT, and detects and compares
the two schemes through multi-fault type tests, and finds that the ANN-WT method is
more accurate and shows low sensitivity to parameter changes. Literature [12]
describes the evaluation of a fault localization technique based on the FasTR method
in an airborne portable system, and the results show that the system can achieve on-
line detection of transient faults in complex networks and ensure the accuracy of the
detection. Literature [13] describes Megger's new EZ-THUMP 3 cable fault location
system, which works by combining TDR measurements with a surge generator to
identify high resistances and thus locate faults. It can help users to locate faults easily,
quickly and accurately. Literature [14] designed a hybrid fault location method for
overhead lines containing underground cables, which was proved to be superior to
other traditional methods by simulation techniques, showing high accuracy in both
fault location and identification functions. Literature [15] discusses Megger's new
SMART THUMP ST25-30 portable cable tester, which is based on automated test
sequencing technology and provides fault identification and location, as well as
interpretation and analysis of the test results for non-specialized users to obtain
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reliable fault location results in a safe and fast manner. Literature [16] on the iterative
method and non-iterative method of localization function of the simulation test method
for comparison, the results show that the positioning accuracy of the PD by the
algorithm error, iteration algorithm, the number of iterations and iteration of the initial
value of the impact of the algorithm. Literature [17] describes a strategy to reduce the
occurrence of CCFS currents in cables by using current limiting reactors to shield the
cables and then connect them to the electrodes of the primary substation, which can
effectively reduce the thermal burning of insulation due to CCF in cables. Literature
[18] studied cable joint breakdown faults, and through the analysis of fault waveforms,
simulation model calculations and discussion of finite element methods, it was pointed
out that moisture in the internal joints of cables causes transient ground faults,
damages the grounding wire, and reduces the sensitivity of the protective device.
Literature [19] proposes a Bayesian function based signal type identification method
to identify the signal. A scheme to discriminate pole-to-pole and pole-to-ground short
circuits in VSC cables is also proposed, and the reliability and innovation of the
described method is confirmed by the study of real cases. Literature [20] points out
that in cable-related construction, cross-connection errors often occur resulting in no
effective limitation of the induced voltage in the metal shield, resulting in cable
accidents, in order to solve this status quo, the cross-grounding faults in the metal
shield of the 5kv single-core power cables are investigated, and at the same time
remedial suggestions and measures are given for the cross-grounding faults.
In this paper, we analyze the characteristics of cable faults and select a suitable
signal processing method. Then, VMD is used for the initial processing of the cable
fault signal, followed by the application of wavelet transform for further analysis and
noise reduction. On this basis, the key parameters of VMD and wavelet transform are
adjusted using parameter optimization methods to adapt to different fault signal
characteristics. The effectiveness of the proposed method is evaluated through
comparative analysis and compared with traditional methods to verify its superiority.
2. POWER CABLE FAULT RELATED ANALYSIS
Power cables with its small footprint, high reliability, easy maintenance and other
unique advantages in the distribution network is increasingly widely used, and along
with the social and economic take-off, national consumption level, the reliability and
security of the distribution network operation of high-level quality requirements. Under
the threat of extreme weather, line aging, natural disasters, external damage, man-
made theft of cables and other factors, it is very easy to cause cable operation faults,
resulting in the entire power line blackout accidents, power transmission interruptions
directly lead to the production of life safety hazards and economic property losses.
This chapter mainly discusses the relevant basic knowledge of power cable faults, in
order to realize the precise positioning of power cable faults to provide support.
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reliable fault location results in a safe and fast manner. Literature [16] on the iterative
method and non-iterative method of localization function of the simulation test method
for comparison, the results show that the positioning accuracy of the PD by the
algorithm error, iteration algorithm, the number of iterations and iteration of the initial
value of the impact of the algorithm. Literature [17] describes a strategy to reduce the
occurrence of CCFS currents in cables by using current limiting reactors to shield the
cables and then connect them to the electrodes of the primary substation, which can
effectively reduce the thermal burning of insulation due to CCF in cables. Literature
[18] studied cable joint breakdown faults, and through the analysis of fault waveforms,
simulation model calculations and discussion of finite element methods, it was pointed
out that moisture in the internal joints of cables causes transient ground faults,
damages the grounding wire, and reduces the sensitivity of the protective device.
Literature [19] proposes a Bayesian function based signal type identification method
to identify the signal. A scheme to discriminate pole-to-pole and pole-to-ground short
circuits in VSC cables is also proposed, and the reliability and innovation of the
described method is confirmed by the study of real cases. Literature [20] points out
that in cable-related construction, cross-connection errors often occur resulting in no
effective limitation of the induced voltage in the metal shield, resulting in cable
accidents, in order to solve this status quo, the cross-grounding faults in the metal
shield of the 5kv single-core power cables are investigated, and at the same time
remedial suggestions and measures are given for the cross-grounding faults.
In this paper, we analyze the characteristics of cable faults and select a suitable
signal processing method. Then, VMD is used for the initial processing of the cable
fault signal, followed by the application of wavelet transform for further analysis and
noise reduction. On this basis, the key parameters of VMD and wavelet transform are
adjusted using parameter optimization methods to adapt to different fault signal
characteristics. The effectiveness of the proposed method is evaluated through
comparative analysis and compared with traditional methods to verify its superiority.
2. POWER CABLE FAULT RELATED ANALYSIS
Power cables with its small footprint, high reliability, easy maintenance and other
unique advantages in the distribution network is increasingly widely used, and along
with the social and economic take-off, national consumption level, the reliability and
security of the distribution network operation of high-level quality requirements. Under
the threat of extreme weather, line aging, natural disasters, external damage, man-
made theft of cables and other factors, it is very easy to cause cable operation faults,
resulting in the entire power line blackout accidents, power transmission interruptions
directly lead to the production of life safety hazards and economic property losses.
This chapter mainly discusses the relevant basic knowledge of power cable faults, in
order to realize the precise positioning of power cable faults to provide support.
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2.1. POWER CABLE FAILURE RELATED CAUSES
2.1.1. CAUSES OF POWER CABLE FAILURES
City cables are generally buried in the ground and the pipeline by the cable length
of the impact of the existence of two cables with joints, cable storage is not good there
are old and new cables and cables in the laying of grafting whether in strict
accordance with the requirements of these are for the occurrence of faults buried
hidden dangers. In addition, the actual operation of many other reasons for failure,
power cable line failure causes are mainly the following:
1.
External damage. Cables are mostly laid in the ground, the rise of central
China in recent years, infrastructure construction increased, urbanization
accelerated, rural decentralized building into a centralized, mechanical damage
caused by a lot of cable failures.
2.
Cable joint failure. Cables and cables are connected by the joints, in the cable
joints are prone to failure, the joints have become the entire cable part of the
most "fragile" place.
3.
Chemical corrosion. For the existence of acid and alkali soil laying cable will
inevitably be eroded by acid and alkali, often resulting in damage to the
external protective layer.
4.
External environment. Whether the heat source around the cable exceeds the
standard needs to be taken into account, overheating will cause damage to the
insulation of the cable, reduce the insulation strength of the cable caused by
insulation breakdown resulting in power outages.
5.
Cable long-term overload operation. Due to the cable's own design defects,
three-phase load imbalance, etc., so that the cable in the unprotected
environment for a long time overloading operation will lead to the cable with the
operation of the time to lengthen the temperature is too high, too high a
temperature will make the "fragile" joints part of the first damage.
6. The lack of technology. Cable body in the manufacturing process is not in strict
accordance with the design requirements of the environment and technology,
materials, such as failure to lead to normal aging or in the normal energized
lead to breakdown and so on.
2.1.2. CHARACTERISTICS OF POWER CABLE FAULTS
When power cables have various types of faults, the consequences of which can
lead to regional local power outages, or paralyze the entire power supply system, thus
seriously affecting the productivity of enterprises. In order to quickly determine the
type of cable faults and maintenance strategies, first of all need to classify the power
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cable faults, and then according to the classification results to choose the appropriate
protection measures, in order to quickly restore power supply, minimize the loss of
enterprises. The classification method of cable faults can be classified according to
different criteria, and its specific classification is shown in Figure 1, which mainly
includes three categories of series faults, parallel faults and compound faults.
Figure 1 Power cable fault classification chart
Series fault refers to the internal conductor of the cable at a place where a break or
short circuit occurs, resulting in a cable blackout accident, parallel fault is due to the
loss of insulation medium between the core wires inside the cable and lead to
parallelism between the core wires, resulting in faults, composite faults refers to the
simultaneous existence of the above two types of faults in the cable.
2.2. POWER CABLE FAULT DETECTION PROCESS
2.2.1. FAULT DETECTION OF POWER CABLES
Power cable fault diagnosis process shown in Figure 2, the specific principle is that
the cable core conductor resistance and core distance into a proportional relationship,
as long as the calculation of the beginning of the fault phase of the cable to the fault
point of the core conductor resistance and the fault phase of the proportionality
coefficient of the conductor resistance, then in the case of the full length of the cable
known to be able to calculate the distance from the beginning of the point of failure, to
complete the diagnosis of the cable fault and localization.
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cable faults, and then according to the classification results to choose the appropriate
protection measures, in order to quickly restore power supply, minimize the loss of
enterprises. The classification method of cable faults can be classified according to
different criteria, and its specific classification is shown in Figure 1, which mainly
includes three categories of series faults, parallel faults and compound faults.
Figure 1 Power cable fault classification chart
Series fault refers to the internal conductor of the cable at a place where a break or
short circuit occurs, resulting in a cable blackout accident, parallel fault is due to the
loss of insulation medium between the core wires inside the cable and lead to
parallelism between the core wires, resulting in faults, composite faults refers to the
simultaneous existence of the above two types of faults in the cable.
2.2. POWER CABLE FAULT DETECTION PROCESS
2.2.1. FAULT DETECTION OF POWER CABLES
Power cable fault diagnosis process shown in Figure 2, the specific principle is that
the cable core conductor resistance and core distance into a proportional relationship,
as long as the calculation of the beginning of the fault phase of the cable to the fault
point of the core conductor resistance and the fault phase of the proportionality
coefficient of the conductor resistance, then in the case of the full length of the cable
known to be able to calculate the distance from the beginning of the point of failure, to
complete the diagnosis of the cable fault and localization.
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Figure 2 Fault diagnosis process of power cable
The above method is currently a relatively simple and fast way to diagnose and
locate power cable faults, can effectively, accurately, quickly, conveniently and safely
determine the cable fault category and locate the fault point, is to protect the normal
operation of the power system is the key. Reasonable analysis of the causes of power
cable faults to help solve the source of cable faults, and for the development of
scientific cable fault detection technology to provide a basis.
2.2.2. EQUIVALENT MODELING OF POWER CABLES
Power cable is a power transmission line, when the power cable is considered a
long line, it is no longer a simple conductor - insulation - to ground circuit, but many
more equivalent resistance, conductance, inductance, capacitance composed of
these parameters are uniformly distributed along the entire cable line, so called
distribution parameters. Figure 3 for the cable equivalent long line distribution
parameter circuit. Figure for the cable line unit length of the resistance,
for the cable line unit length of the conductance, for the cable line
unit length of the inductance, for the cable line unit length of the capacitance.
Figure 3 Equivalent long line distribution parameter circuit of cable
R0(Ω/m)
G0(S/m)
L0(H/m)
C0(F/m)
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Signal current after resistance and inductance, through the unit length of the cable
line, are generated voltage drop and through the conductance, capacitance, etc., split
the flow, and in the middle of the flow back. Cable transmission of high-frequency
waves, it will lose a considerable amount of energy into the attenuation, at this time,
conductivity, resistance and other losses can be ignored, and such a circuit is known
as lossless circuit.
2.3. POWER CABLE FAULT TRAVELING WAVE PROCESS
2.3.1. TRAVELING WAVE VELOCITY OF POWER CABLE
Power cable traveling wave speed is expressed in the traveling wave propagation
process fast and slow physical quantities, when the traveling wave propagation in the
cable line, from a point in the cable propagation to another point needs to go through
a certain amount of time, the traveling wave propagation distance and propagation
time ratio is known as the wave speed.
For the purpose of calculating the wave velocity v, assume that the current wave
acting on the wire is an oblique angle current wave. Suppose that the initial condition
is zero, and that an oblique wave current of value ( in units of in units of
s) is applied to the wire at point A at . Suppose that the wave moves along the
wire with some known wave speed v and after an elapsed time t, the wave reaches
point B and the potential at point B is zero. Then the voltage drop across the inductor
LOx point A to point B is the potential at point A. And since and therefore
, the following relation for can be written:
(1)
Assuming that the charge per unit length of wire at point A is q, according to the
definition of capacitance, it can be seen that the charge qdx stored on the capacitance
of the dx section at point A and the potential uA at point A can be expressed as
, i.e., the potential uA at point A
can be expressed in terms of
capacitance:
(2)
According to the definition of current, the current i at point A
is the number of
charges passing per unit time is:
(3)
Thus, the charge per unit length q can be expressed as:
i=αt
α
A/s,t
t= 0
uA
x=vt
L0x=L0vt
uA
u
A=L0vt
di
dt
=L0vt
α
C0d x
C0d x =uAqd x
u
A=
qd x
C0d x
=
q
C0
i
=
qd x
dt
=q
d x
dt
=q
v
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Signal current after resistance and inductance, through the unit length of the cable
line, are generated voltage drop and through the conductance, capacitance, etc., split
the flow, and in the middle of the flow back. Cable transmission of high-frequency
waves, it will lose a considerable amount of energy into the attenuation, at this time,
conductivity, resistance and other losses can be ignored, and such a circuit is known
as lossless circuit.
2.3. POWER CABLE FAULT TRAVELING WAVE PROCESS
2.3.1. TRAVELING WAVE VELOCITY OF POWER CABLE
Power cable traveling wave speed is expressed in the traveling wave propagation
process fast and slow physical quantities, when the traveling wave propagation in the
cable line, from a point in the cable propagation to another point needs to go through
a certain amount of time, the traveling wave propagation distance and propagation
time ratio is known as the wave speed.
For the purpose of calculating the wave velocity v, assume that the current wave
acting on the wire is an oblique angle current wave. Suppose that the initial condition
is zero, and that an oblique wave current of value ( in units of in units of
s) is applied to the wire at point A at . Suppose that the wave moves along the
wire with some known wave speed v and after an elapsed time t, the wave reaches
point B and the potential at point B is zero. Then the voltage drop across the inductor
LOx point A to point B is the potential at point A. And since and therefore
, the following relation for can be written:
(1)
Assuming that the charge per unit length of wire at point A is q, according to the
definition of capacitance, it can be seen that the charge qdx stored on the capacitance
of the dx section at point A and the potential uA at point A can be expressed as
, i.e., the potential uA at point A can be expressed in terms of
capacitance:
(2)
According to the definition of current, the current i at point A is the number of
charges passing per unit time is:
(3)
Thus, the charge per unit length q can be expressed as:
i=αt
α
A/s,t
t= 0
uA
x=vt
L0x=L0vt
uA
uA=L0vt di
dt =L0vtα
C0d x
C0d x =uAqd x
uA=qd x
C0d x =q
C0
i=qd x
dt =qd x
dt =qv
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(4)
Bringing Eq. (4) into Eq. (2) and replacing i with at yields the relation for uA as:
(5)
Up to this point, two expressions (1) and (5) for uA are obtained and this two
equations should be equal, i.e.:
(6)
Organizing the above equation, the expression for the wave velocity v is obtained
as:
(7)
Substituting and into equation (7) we get:
(8)
Since and are both constants, it can be seen according to Eq. (8) that the
wave velocity v of the cable line is only related to the relative permittivity of the
medium around the cable core and the relative permeability coefficient of the
medium around the cable core such as insulation and shielding, while factors such as
the material of the conductor core and the cross-sectional area do not affect the wave
velocity of the cable line.
2.3.2. CALCULATE REFLECTED AND REFRACTED WAVES
Reflected and refracted waves are important concepts in the calculation of traveling
waves. When a voltage is applied to a power cable, a current is generated on the
cable, then if a sudden change occurs in the power a A, then refracted and reflected
waves will be generated at A now. The refraction and reflection of traveling waves is
shown in Figure 4, according to the relationship between circuit current and voltage,
then there is:
(9)
q
=
i
v
u
A=
i
vC0
=
αt
vC0
L
0vtα=
αt
vC0
v
=±
1
L
0
C
0
L
0=
μ
0
μ
r
2π
ln
2h
r
C
0=
2πε
0
ε
r
ln
2h
r
v
=±
1
μ
0
μrε
0
εr
ε0
μ0
ℰ
μr
u
r2
=u
r1
+u
f1
ir2=ir1+if1
}
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(10)
Figure 4 Refraction and reflection of the traveling waves
from Eq. (9) and Eq. (10):
(11)
Where is the voltage refraction coefficient, , is the voltage
reflection coefficient, .
From Eq. (11) and Eq. (10), it can be solved as follows.
(12)
(13)
Where, is the current emission coefficient.
3. POWER CABLE FAULT LOCATION DIAGNOSIS
The development of urbanization needs to build more power cables as a support,
urban power transmission needs to use advanced scientific power transmission
methods, to provide great convenience and safety for people's electricity. nowadays,
the city mainly uses underground cables for power transmission, this way not only can
ensure the stable transmission of electricity, but also can reduce the probability of
power cable line faults. however, underground cable power transmission can also
have faults and need to be repaired. this chapter mainly explores the optimization
based on the skyhawk algorithm variable modal decomposition combined with
wavelet transform in power cable fault location related technology, in order to realize
the power cable faults. This chapter mainly explores the optimized variational modal
u
r1
=i
r1
Z
1
ur2=ir2Z2
u
f1=−if1Z1
u
r2=
2Z
2
Z2+Z1ur1=γuur1
u
f1=Z2−Z1
Z
1
+Z
2
ur1=ρuur1
γu
γ
u=
2Z
2
Z2+Z1
ρu
ρ
u=
2Z
2
Z2+Z1
.
if1=−ρuir1
ρi=−ρu
ρi
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(10)
Figure 4 Refraction and reflection of the traveling waves
from Eq. (9) and Eq. (10):
(11)
Where is the voltage refraction coefficient, , is the voltage
reflection coefficient, .
From Eq. (11) and Eq. (10), it can be solved as follows.
(12)
(13)
Where, is the current emission coefficient.
3. POWER CABLE FAULT LOCATION DIAGNOSIS
The development of urbanization needs to build more power cables as a support,
urban power transmission needs to use advanced scientific power transmission
methods, to provide great convenience and safety for people's electricity. nowadays,
the city mainly uses underground cables for power transmission, this way not only can
ensure the stable transmission of electricity, but also can reduce the probability of
power cable line faults. however, underground cable power transmission can also
have faults and need to be repaired. this chapter mainly explores the optimization
based on the skyhawk algorithm variable modal decomposition combined with
wavelet transform in power cable fault location related technology, in order to realize
the power cable faults. This chapter mainly explores the optimized variational modal
ur1=ir1Z1
ur2=ir2Z2
uf1=−if1Z1
ur2=2Z2
Z2+Z1ur1=γuur1
uf1=Z2−Z1
Z1+Z2ur1=ρuur1
γu
γu=2Z2
Z2+Z1
ρu
ρu=2Z2
Z2+Z1
.
if1=−ρuir1
ρi=−ρu
ρi
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decomposition based on the eagle algorithm combined with the wavelet transform in
the power cable fault localization technology, to provide technical support for the
realization of the accurate positioning of power cable faults.
3.1. PARAMETER OPTIMIZED VARIATIONAL MODAL
DECOMPOSITION
3.1.1. VARIATIONAL MODAL DECOMPOSITION (VMD)
Variational modal decomposition (VMD) algorithm is a non-recursive decomposition
of a set of signals into K quasi-orthogonal and specific sparsity intrinsic modal
functions (IMFs) to achieve effective separation of signals. The VMD algorithm is
based on the concepts of Wiener filtering, the Hilbert transform, and frequency mixing,
etc., and the overall idea is to construct a variational problem. The constraints on the
variational components need to be satisfied that all the sums of the components are
consistent with the original signal, and the constraints on the variational model are as
follows.
(14)
Where, is the K eigenmode components obtained after VMD decomposition,
, are the center frequencies of each of the K eigenmode
components, , are the original signals, is the sign of gradient
computation, is the Dirac Lay function,* is the sign of convolution operation, and
s.t. is the constraint term.
In order to solve the variational constrained problem and complete the
transformation from constrained to unconstrained problem, the Lagrange operator
and the quadratic penalty factor are introduced, and the transformations result in the
augmented and generalized Lagrange formulas, namely:
(15)
In the formula, the value of affects the denoising effect of the algorithm, and the
appropriate value of can reduce the noise interference.
min{uk}wk}
{∑K
k=1 ∥ ∂t[(δ(t) + j
πt)∗uk(t)]e−jwkt∥
2
2
}
s.t. ∑k uk=f(t)
{uk}
{u1,u2,⋯,uk},{wk}
{w1,w2,⋯,wk}
f(t)
∂
δ(t)
α
L
({uk},{wk},λ)=α
K
∑
k=1
∥ ∂t
[(
δ(t) +
j
πt
)
∗uk(t)
]
e−jwkt∥
2
2
+∥f(t)−
K
∑
k=1
uk(t)∥
2
2
+⟨λ(t), f(t)−
K
∑
k=1
uk(t)
⟩
α
α
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Finally, the alternating direction multiplier algorithm is used to iteratively update
, and until the termination condition is satisfied, and the final K IMF
components and the corresponding center frequencies are output.
From the above formula, it can be seen that the values of parameters K and will
have an important impact on the decomposition results of the algorithm. If the K value
is too small, it will lead to insufficient decomposition, if it is too large, it will be prone to
problems such as false components and frequency overlap, if the value is too small,
the signal denoising will not be thorough enough, and if it is too large, the active
components will be removed by mistake. Empirical selection of the above parameter
values does not ensure that they are optimal.
To address this problem, this paper introduces the Skyhawk optimization algorithm
to improve the VMD and get the optimal parameter combination . In this
process, the envelope entropy reflects the sparsity of the signal, the more noise there
is in the signal, the less effective components there are, which is manifested by the
larger envelope entropy value; on the contrary, the more the signal contains effective
components, the smaller the envelope entropy value is, i.e., when the value of
envelope entropy is the smallest, the signal contains the largest number of effective
components, and at this time, the corresponding parameter is the optimal. Therefore,
the author adopts the minimum value of the envelope directrix as the fitness function
of the Skyhawk optimizer to evaluate the decomposition effect of the parameter
combination. The mathematical formula for the envelope entropy is as follows.
(16)
(17)
(18)
Where, m is the number of sampling points, Pq is the normalized form of a(q), a(q) is
the envelope signal after Hilbert transform.
3.1.2. AOA LGORITHMIC OPTIMIZATION OF VMD
PARAMETERS
The VMD is continuously updated in the frequency domain and transformed to the
time domain by Fourier inverse transform, and the final results will be different when
different decomposition layers K and quadratic penalties are inputted, so finding the
optimal combinations of decomposition layers K and quadratic penalties is the key to
the VMD. In this paper, we propose to optimize the parameters of the VMD based on
the AO algorithm, and the optimized parameters can be obtained quickly and
accurately. The AO algorithm is a new population-based optimization method, which
{uk},{wk}
λ
α
α
[K,α]
Ep
E
p=−
m
∑
q=1
pqlgp
q
pq=a(q)/
m
∑
q=1
a(q
)
a
(q) = [x(q)]2+ {H[x(q)]}
2
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Finally, the alternating direction multiplier algorithm is used to iteratively update
, and until the termination condition is satisfied, and the final K IMF
components and the corresponding center frequencies are output.
From the above formula, it can be seen that the values of parameters K and will
have an important impact on the decomposition results of the algorithm. If the K value
is too small, it will lead to insufficient decomposition, if it is too large, it will be prone to
problems such as false components and frequency overlap, if the value is too small,
the signal denoising will not be thorough enough, and if it is too large, the active
components will be removed by mistake. Empirical selection of the above parameter
values does not ensure that they are optimal.
To address this problem, this paper introduces the Skyhawk optimization algorithm
to improve the VMD and get the optimal parameter combination . In this
process, the envelope entropy reflects the sparsity of the signal, the more noise there
is in the signal, the less effective components there are, which is manifested by the
larger envelope entropy value; on the contrary, the more the signal contains effective
components, the smaller the envelope entropy value is, i.e., when the value of
envelope entropy is the smallest, the signal contains the largest number of effective
components, and at this time, the corresponding parameter is the optimal. Therefore,
the author adopts the minimum value of the envelope directrix as the fitness function
of the Skyhawk optimizer to evaluate the decomposition effect of the parameter
combination. The mathematical formula for the envelope entropy is as follows.
(16)
(17)
(18)
Where, m is the number of sampling points, Pq is the normalized form of a(q), a(q) is
the envelope signal after Hilbert transform.
3.1.2. AOA LGORITHMIC OPTIMIZATION OF VMD
PARAMETERS
The VMD is continuously updated in the frequency domain and transformed to the
time domain by Fourier inverse transform, and the final results will be different when
different decomposition layers K and quadratic penalties are inputted, so finding the
optimal combinations of decomposition layers K and quadratic penalties is the key to
the VMD. In this paper, we propose to optimize the parameters of the VMD based on
the AO algorithm, and the optimized parameters can be obtained quickly and
accurately. The AO algorithm is a new population-based optimization method, which
{uk},{wk}
λ
α
α
[K,α]
Ep
Ep=−
m
∑
q=1
pqlgpq
pq=a(q)/
m
∑
q=1
a(q)
a(q) = [x(q)]2+ {H[x(q)]}2
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mainly simulates the natural behavior of the eagle in the process of capturing prey, so
as to achieve the purpose of optimization, with strong optimization ability and fast
convergence speed, etc. Therefore, the AO algorithm is used to optimize the VMD.
Therefore, the AO algorithm is used for iterative optimization of the number of
decompositions and the penalty factor in the VMD, and the optimization dimension is
set to 5, the optimization interval is set to [5,12], and the optimization interval is set to
[0,20,000].The loss function of the VMD is used as the fitness function for the
optimization of the AO algorithm, and the calculation formula is as follows: the VMD
loss function is used as the fitness function for the optimization of the AO algorithm,
and the calculation formula is as follows: the VMD loss function is used as the
adaptation function for the optimization of the AO algorithm.
(19)
Where is the original input signal, is the decomposed signal and T is the
time length.
The original signal is decomposed into K modal components by VMD, if the modal
components contain less noise components, the feature information related to the
original signal will be more obvious, and the envelope entropy will be smaller, and the
AO algorithm is used to seek the minimum envelope entropy, so that the IMF obtained
by this way can maximize the retention of the characteristics of the fault signal of the
power cable.
3.2. AO-VMD-CWT FAULT LOCALIZATION MODEL
3.2.1. CONTINUOUS WAVELET TRANSFORM (CWT)
The translation factor and scale factor in the wavelet time-frequency transform
define the position and shape of the time-frequency window, which makes the wavelet
transform adaptive and multi-resolution, and is widely used in the field of signal
processing. The continuous wavelet transform (CWT) adopts a time-frequency
window that can be adaptively adjusted with the frequency, which overcomes the
limitation that the size of the window of the short-time Fourier transform (STFT) can't
be adjusted with the frequency or the time, which is difficult to accurately respond to
the relationship between the frequency and the time, and is more suitable for dealing
with the transient and sudden change of the signals.
For the function , if it satisfies , then
can be
written as the mother wavelet. By performing a series of scale translation
transformations on the mother wavelet a series of consecutive wavelet functions
can be obtained, which are called analytic wavelets. The transformation formula is:
L
loss =
∑T
t=1
f(t)−f′
(t)
T
f(t)
f′ (t)
φ(t)∈L2(R)
∫∞
−∞
φ(t)dt =
0
φ(t)
φ(t)
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(20)
In the formula, u is the translation factor, v is the scale factor, also known as the
expansion factor, when , stretching along the horizontal direction, when ,
compression along the horizontal direction, in order to keep the energy constant after
the expansion transformation need to multiply the scale factor in front of the
front, i.e., , u is the translation parameter, which can be taken
as an arbitrary real number, u and v are continuous variables, so it is known as the
continuous wavelet. Wavelet transform.
The continuous wavelet transform of the signal is expressed by the
following equation:
(21)
Where is the complex function of the function
. The inverse
transformation is given by:
(22)
Formula, .
The mother wavelet function needs to satisfy the following conditions to ensure that
the wavelet transform can accurately construct the original signal with corresponding
inverse transform.
1. First of all, the value of the mother wavelet function outside the window
function is zero.
2. It needs to be satisfied:
3. The mother wavelet function satisfies
3.2.2. AO-VMD-CWT SIGNAL NOISE REDUCTION
The search strategy of AO algorithm adopts repeated trajectories to explore the
approximate optimal solution or the reasonable location of the optimal solution, which
has high convergence, robustness and strong optimization ability. Therefore, this
paper introduces the AO algorithm to search for the optimization of decomposition
φ
u,v(t) =
1
v
φ
(t−u
v
)
,v> 0, u∈
R
v> 1
v< 1
1/ v
∥φu,v(t)∥=∥φ(t)∥
x(t)∈L2(R)
CWTx
(u,v) =
∫∞
−∞
x(t)φ∗
u,v(t)dt =
1
v∫∞
−∞
x(t)φ∗
(t−u
v
)
d
t
φ∗(t)
φ(t)
x(t) =
1
C
φ∫∞
−∞
∫∞
−∞
φu,v(t)CWT(u,v)
dudv
v2
C
φ= 2π
∫∞
−∞
|^
φ(ω)|
|ω|
dω.
∫∞
−∞
|^
φ(ω)|
|ω|
dω< + ∞
。
^
ϕ
(ω)
ω=0
= 0
。
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(20)
In the formula, u is the translation factor, v is the scale factor, also known as the
expansion factor, when , stretching along the horizontal direction, when ,
compression along the horizontal direction, in order to keep the energy constant after
the expansion transformation need to multiply the scale factor in front of the
front, i.e., , u is the translation parameter, which can be taken
as an arbitrary real number, u and v are continuous variables, so it is known as the
continuous wavelet. Wavelet transform.
The continuous wavelet transform of the signal is expressed by the
following equation:
(21)
Where is the complex function of the function . The inverse
transformation is given by:
(22)
Formula, .
The mother wavelet function needs to satisfy the following conditions to ensure that
the wavelet transform can accurately construct the original signal with corresponding
inverse transform.
1. First of all, the value of the mother wavelet function outside the window
function is zero.
2. It needs to be satisfied:
3. The mother wavelet function satisfies
3.2.2. AO-VMD-CWT SIGNAL NOISE REDUCTION
The search strategy of AO algorithm adopts repeated trajectories to explore the
approximate optimal solution or the reasonable location of the optimal solution, which
has high convergence, robustness and strong optimization ability. Therefore, this
paper introduces the AO algorithm to search for the optimization of decomposition
φu,v(t) = 1
v
φ(t−u
v),v> 0, u∈R
v> 1
v< 1
1/ v
∥φu,v(t)∥=∥φ(t)∥
x(t)∈L2(R)
CWTx(u,v)=∫∞
−∞
x(t)φ∗
u,v(t)dt =1
v∫∞
−∞
x(t)φ∗(t−u
v)dt
φ∗(t)
φ(t)
x(t) = 1
Cφ∫∞
−∞
∫∞
−∞
φu,v(t)CWT(u,v)dudv
v2
Cφ= 2π∫∞
−∞
|^
φ(ω)|
|ω|dω.
∫∞
−∞
|^
φ(ω)|
|ω|dω< + ∞ 。
^
ϕ(ω)
ω=0
= 0 。
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number and penalty factor in the VMD, and uses the minimum envelope entropy as
the fitness function to transform the iterative optimization process into the process of
AO algorithm to seek for the minimum envelope entropy. The specific optimization
process is as follows The specific optimization process is as follows
Step1 Initialize the population, set the number of iterations of AO algorithm, the
population size, the number of variables and the upper and lower limits of the problem
to be solved.
Step2 Decompose the input signal by VMD.
Step3 Calculate the minimum value of the envelope entropy of each modal
component as the fitness function and substitute it into the optimization algorithm.
Step4 Update the position of the population and the global optimal solution, and
stop the iteration when the optimization algorithm meets the iteration termination
condition.
On this theoretical basis, this paper proposes a parameter optimization VMD-CWT
based power cable fault signal noise reduction method, the method is shown in Fig. 5.
the specific process is as follows.
1. The AO algorithm optimizes the VMD, and the signal decomposition is
performed using the VMD to obtain K IMF components.
2. According to the cliff-correlation coefficient, the IMF components are divided
into pure components and noise components.
3. Perform wavelet threshold noise reduction on the noise component to remove
the noise component in the signal.
4. The pure component and the wavelet threshold noise reduction processed
noise-containing component were reconstructed to obtain the joint noise
reduction signal.
Figure 5 Signal denoising method for parameter optimization of AO-VMD-CWT
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In this paper, we choose to use continuous wavelet transform to decompose the
data after parameter-optimized VMD decomposition at multiple scales as a method to
construct time-frequency maps, and to generate two-dimensional wavelet time-
frequency domain maps so that we can take into account the ability of local
information in the time-frequency domain at the same time.
4. POWER CABLE FAULT LOCATION SIMULATION
Power cable lines have unique advantages over overhead lines, including small
footprint, high power supply reliability, low voltage drop, low fault rate and lightning
protection, etc. In recent years, with the construction and development of the city and
the increase in the use of power cables, their faults have received more and more
attention, so how to quickly locate the faults of the cable is critical to reduce the
outage time. This chapter mainly focuses on the effectiveness of the parameter
optimization VMD-CWT fault location method given in the previous section to carry out
the simulation analysis of the data, so as to help the accurate positioning of power
cable faults, in order to enhance the safety of electricity, reduce the economic losses
caused by power outages to provide protection.
In the cable fault location algorithm research, need to verify the feasibility of the
algorithm through the test, the field test is not only very high cost and not safe
enough, the general use of computer simulation methods to replace the real operating
environment of the power system. this paper will use ATPDraw for cable fault model
drawing, and then use EMTP to transient analysis of cable faults, the results obtained
from analysis. The results of the analysis will be imported into MATLAB for data
processing and display. using ATPDraw for modeling simulation, simulation
simplification principle shown in Figure 6.
Figure 6 Simulation schematics
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In this paper, we choose to use continuous wavelet transform to decompose the
data after parameter-optimized VMD decomposition at multiple scales as a method to
construct time-frequency maps, and to generate two-dimensional wavelet time-
frequency domain maps so that we can take into account the ability of local
information in the time-frequency domain at the same time.
4. POWER CABLE FAULT LOCATION SIMULATION
Power cable lines have unique advantages over overhead lines, including small
footprint, high power supply reliability, low voltage drop, low fault rate and lightning
protection, etc. In recent years, with the construction and development of the city and
the increase in the use of power cables, their faults have received more and more
attention, so how to quickly locate the faults of the cable is critical to reduce the
outage time. This chapter mainly focuses on the effectiveness of the parameter
optimization VMD-CWT fault location method given in the previous section to carry out
the simulation analysis of the data, so as to help the accurate positioning of power
cable faults, in order to enhance the safety of electricity, reduce the economic losses
caused by power outages to provide protection.
In the cable fault location algorithm research, need to verify the feasibility of the
algorithm through the test, the field test is not only very high cost and not safe
enough, the general use of computer simulation methods to replace the real operating
environment of the power system. this paper will use ATPDraw for cable fault model
drawing, and then use EMTP to transient analysis of cable faults, the results obtained
from analysis. The results of the analysis will be imported into MATLAB for data
processing and display. using ATPDraw for modeling simulation, simulation
simplification principle shown in Figure 6.
Figure 6 Simulation schematics
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4.1. SIGNAL NOISE REDUCTION AND FAULT LOCALIZATION
SIMULATION
4.1.1. AO-VMD-CWT SIGNAL NOISE REDUCTION
In order to analyze the effectiveness of the AO-VMD-CWT method proposed in this
paper in the power cable fault signal noise reduction, this paper designed the
corresponding power cable fault simulation model based on ATPDraw, and designed
the corresponding noise-containing power cable fault signal. After the noise-containing
signal is decomposed and denoised by using the AO-VMD method, the signal is
decomposed by six modal components, and the denoised signal is obtained by
analyzing the modal components obtained through the correlation coefficient as
shown in Fig. 7. The correlation coefficient analyzes the modal components of the
decomposition, and the denoised signal is shown in Fig. 7.
As can be seen from the figure, after the VMD decomposition denoising, the effect
of signal noise reduction is achieved to a certain extent, using the formula given in the
previous section, the signal-to-noise ratio of the original noise signal can be calculated
as 20.47 dB, while the signal-to-noise ratio of the noise-reduced signal after the VMD
denoising is 53.38 dB, which is 1.61 times more than that of the original noise signal,
which indicates that the AO This shows that the AO-VMD-CWT method given in this
paper can effectively realize the noise reduction of power cable fault signals, obtain a
more accurate power cable fault localization effect, and reduce the localization error
caused by the fault signal noise.
Figure 7 Noise reduction waveform of the AO-VMD-CWT signal
In order to further illustrate the noise reduction effect of this paper's method, the
noise reduction waveforms of this paper's method, the CWT method and the VMD
method are compared, and the signal-to-noise ratios of the noise reduction are also
compared. Figure 8 shows the noise reduction waveforms of the power cable fault
signals obtained by different noise reduction methods.
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From the noise reduction waveforms of power cable fault signals in the figure, it can
be clearly seen that the method of this paper is better than a single wavelet transform
method and the noise reduction waveform obtained by the variational modal
decomposition method, which can better reflect the fault situation of power cables.
Using the signal-to-noise ratio solution method given in the previous section to solve
the signal-to-noise ratios of the three kinds of noise reduction waveforms, it can be
clearly defined that the signal-to-noise ratios of the wavelet transform and variational
modal decomposition method are respectively 24.65 dB and 28.19 dB, and the signal-
to-noise ratio of the wavelet transform method is 24.65 dB and 28.19 dB, respectively.
The signal-to-noise ratio of the wavelet transform and the variational modal
decomposition method is 24.65dB and 28.19dB respectively, which is 53.82% and
47.19% lower than that of this paper's method, and the parameter optimization VMD
algorithm combined with the continuous wavelet transform can obtain better noise
reduction waveforms of power cable fault signals, with a larger improvement in the
signal-to-noise ratio, which can provide accurate signal waveforms for power cable
fault localization and can effectively avoid the loss of some useful signals when the
VMD algorithm is used for noise reduction. It can also effectively avoid the loss of
some useful signals when the VMD algorithm is used for noise reduction.
Figure 8 Comparison of Three Noise Reduction Waveforms
4.1.2. SIMULATION OF POWER CABLE FAULT DISTANCE
In order to assess the feasibility of the proposed fault location method, combined
with the previous power cable fault simulation model, assuming that the cable length
is 5km, the fault is set on phase A, and the voltage-controlled switch is used to
simulate the fault click-through, and the fault distances are set to be 50, 100, 500,
1000, 2000, 3000, 4000 and 5000 m. The normal phases, phase B and phase C are
shorted at the far end, and the travelling wave is traveling. The high voltage signal
generator model is used to send out the coupled current output signal to analyze the
correlation between the fault signal and the non-fault signal output signal before the
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From the noise reduction waveforms of power cable fault signals in the figure, it can
be clearly seen that the method of this paper is better than a single wavelet transform
method and the noise reduction waveform obtained by the variational modal
decomposition method, which can better reflect the fault situation of power cables.
Using the signal-to-noise ratio solution method given in the previous section to solve
the signal-to-noise ratios of the three kinds of noise reduction waveforms, it can be
clearly defined that the signal-to-noise ratios of the wavelet transform and variational
modal decomposition method are respectively 24.65 dB and 28.19 dB, and the signal-
to-noise ratio of the wavelet transform method is 24.65 dB and 28.19 dB, respectively.
The signal-to-noise ratio of the wavelet transform and the variational modal
decomposition method is 24.65dB and 28.19dB respectively, which is 53.82% and
47.19% lower than that of this paper's method, and the parameter optimization VMD
algorithm combined with the continuous wavelet transform can obtain better noise
reduction waveforms of power cable fault signals, with a larger improvement in the
signal-to-noise ratio, which can provide accurate signal waveforms for power cable
fault localization and can effectively avoid the loss of some useful signals when the
VMD algorithm is used for noise reduction. It can also effectively avoid the loss of
some useful signals when the VMD algorithm is used for noise reduction.
Figure 8 Comparison of Three Noise Reduction Waveforms
4.1.2. SIMULATION OF POWER CABLE FAULT DISTANCE
In order to assess the feasibility of the proposed fault location method, combined
with the previous power cable fault simulation model, assuming that the cable length
is 5km, the fault is set on phase A, and the voltage-controlled switch is used to
simulate the fault click-through, and the fault distances are set to be 50, 100, 500,
1000, 2000, 3000, 4000 and 5000 m. The normal phases, phase B and phase C are
shorted at the far end, and the travelling wave is traveling. The high voltage signal
generator model is used to send out the coupled current output signal to analyze the
correlation between the fault signal and the non-fault signal output signal before the
https://doi.org/10.17993/3ctecno.2024.v13n1e45.130-155
fault clicks through, and the fault phase and the non-fault phase current are used for
the construction of the forward and reverse voltage traveling wave, and the resulting
direction of the traveling wave wave is shown in Fig. 9, of which Fig. 9(a) and (b) are
the forward and reverse voltage traveling wave and the correlation coefficient curve,
respectively.
Combined with the forward and reverse voltage traveling wave and correlation
coefficient curves, when the coupled current output signal reverse traveling wave
transmission in the 21.48µs period to reach the voltage maximum value of 7.24V, and
at this time the fault ranging is shown as 503.41 meters, the correlation coefficient of
the maximum of 0.952. Combined with this paper to set up the fault point, the fault
point of the difference between the 500 meters and the fault point of 3.41 meters, the
relative error of 0.682%. 0.682%.
Figure 9 Direction traveling waveform
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According to the above method, the simulation results of all fault distances are
solved, and the relative errors of different fault distances are shown in Table 1. From
the simulation results, except for the fault location distance of 50 meters and 100
meters which is more than 1.00%, the relative errors of other fault location of power
cables within 5 kilometers are maintained in the range of 0.45%~0.70%, and the
average value of the relative errors is about 0.849%. The above results verify the
feasibility of this paper's method in power cable fault localization, and provide
technical support for the realization of timely repair of power cable faults.
Table 1 Simulation ranging results
4.2. POWER CABLE FAULT LOCATION PERFORMANCE
COMPARISON
4.2.1. COMPARISON OF DOUBLE-ENDED TRAVELING WAVE
RANGING METHODS
In order to verify the performance of this paper's algorithm for power cable fault
location, we choose to compare it with the classical double-ended traveling wave
ranging (DRW) method, using the power cable fault simulation model given in the
previous section to send out 500 coupled current signals, and comparing the average
positioning results of the two methods on 500 samples of data with the average
absolute positioning error as an evaluation index. The average localization results of
different algorithms are shown in Table 2, which are obtained by choosing four types
of faults, namely, single-phase grounded short circuit, two-phase short circuit, two-
phase grounded short circuit, and three-phase short circuit, and taking 10km, 50km,
80km, and 100km as the fault distance.
From the average positioning results of different algorithms, the traditional double-
ended traveling wave ranging method has low accuracy, mainly due to the
Fault distance Simulation result Absolute error Fractional error
50m 50.69m 0.69m 1.38%
100m 101.75m 1.75m 1.75%
500m 503.41m 3.41m 682 %
1000m 1006.96m 6.96m 696 %
2000m 2009.38m 9.38m 469 %
3000m 3015.82m 15.82m 527 %
4000m 4026.54m 26.54m 664 %
5000m 4031.27m 31.27m 625 %
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According to the above method, the simulation results of all fault distances are
solved, and the relative errors of different fault distances are shown in Table 1. From
the simulation results, except for the fault location distance of 50 meters and 100
meters which is more than 1.00%, the relative errors of other fault location of power
cables within 5 kilometers are maintained in the range of 0.45%~0.70%, and the
average value of the relative errors is about 0.849%. The above results verify the
feasibility of this paper's method in power cable fault localization, and provide
technical support for the realization of timely repair of power cable faults.
Table 1 Simulation ranging results
4.2. POWER CABLE FAULT LOCATION PERFORMANCE
COMPARISON
4.2.1. COMPARISON OF DOUBLE-ENDED TRAVELING WAVE
RANGING METHODS
In order to verify the performance of this paper's algorithm for power cable fault
location, we choose to compare it with the classical double-ended traveling wave
ranging (DRW) method, using the power cable fault simulation model given in the
previous section to send out 500 coupled current signals, and comparing the average
positioning results of the two methods on 500 samples of data with the average
absolute positioning error as an evaluation index. The average localization results of
different algorithms are shown in Table 2, which are obtained by choosing four types
of faults, namely, single-phase grounded short circuit, two-phase short circuit, two-
phase grounded short circuit, and three-phase short circuit, and taking 10km, 50km,
80km, and 100km as the fault distance.
From the average positioning results of different algorithms, the traditional double-
ended traveling wave ranging method has low accuracy, mainly due to the
Fault distance
Simulation result
Absolute error
Fractional error
50m
50.69m
0.69m
1.38%
100m
101.75m
1.75m
1.75%
500m
503.41m
3.41m
682 %
1000m
1006.96m
6.96m
696 %
2000m
2009.38m
9.38m
469 %
3000m
3015.82m
15.82m
527 %
4000m
4026.54m
26.54m
664 %
5000m
4031.27m
31.27m
625 %
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propagation speed of traveling waves in power cables affected by the fault distance,
fault type, etc., with uncertainty, the average positioning error is more than 0.51km,
and the average absolute positioning error is more than 0.5%. The localization
accuracy of the AO-VMD-CWT algorithm proposed in this paper is significantly higher
than that of the double-ended traveling wave method, and the average absolute
localization errors for fault distances of 10km, 50km, 80km, and 100km are less than
1.315%, 0.278%, 0.163%, and 0.151%, respectively, for different fault types.
Among the single-phase grounded short-circuit fault types, this paper's algorithm
has the highest localization accuracy, and the average absolute localization errors for
fault distances of 10km, 50km, 80km, and 100km are 1.151%, 0.273%, 0.152%, and
0.108%, respectively. This is due to the fact that the proposed AO-VMD-CWT
algorithm utilizes the AO-VMD algorithm in combination with continuous wavelet
transform to reconstruct the original power cable fault signals. This is because the
proposed AO-VMD-CWT algorithm utilizes the AO-VMD algorithm combined with the
continuous wavelet transform to reconstruct the original power cable fault signals,
which can accurately predict the fault distance of the input fault traveling wave signals
by retaining most of the fault features and at the same time proposing some of the
useless signals.
Table 2 Average localization results for the different algorithms
Fault type Fault
distance
Average positioning results
Average absolute localization
error
DRW This article DRW This article
Phase earth
fault
10km 10.56 10.13 5.136 % 1.151 %
50km 50.63 50.12 1.247 % 273 %
80km 80.85 80.09 955 % 152 %
100km 100.91 100.11 613 % 108 %
Line to line
fault
10km 10.86 10.15 8.276 % 1.315 %
50km 50.48 50.17 1.061 % 278 %
80km 80.61 80.16 792 % 102 %
100km 100.57 100.14 513 % 111 %
Two-phase
short circuit
ground
10km 10.62 10.09 4.356 % 1.124 %
50km 50.55 50.13 815 % 273 %
80km 80.67 80.15 679 % 163 %
100km 100.79 100.16 736 % 151 %
Three-phase
short-circuit
10km 10.58 10.14 4.521 % 1.221 %
50km 50.52 50.12 1.248 % 216 %
80km 80.69 80.16 822 % 153 %
100km 100.38 100.13 1.613 % 132 %
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4.2.2. COMPARE TO OTHER NETWORK MODELS
In order to verify the superiority of the AO-VMD-CWT method proposed in this
paper in the power cable fault localization algorithm, it is chosen to be compared with
BiLSTM and cable fault ranging based on the combination of EMD and wavelet
transform (EMD+CWT), and the three algorithms fault localization results are
visualized as shown in Fig. 10, and the experimental results data statistics are shown
in Table 3.
Combined with Figure 10, Table 2 and Table 3, it can be seen that the localization
error of EMD+CWT method is generally maintained within 0.04km, which is mainly
due to the use of EMD decomposition and wavelet transform to remove some of the
redundant signals and extract the useful information in the dominant component of the
noise, so that the filtered signals in the calculation of the reflected waveform
transmission time to improve the accuracy of the filter. The localization error of the
BiLSTM algorithm is within 0.065 km, which shows the advantage of BiLSTM in the
training of time series samples, while the algorithm in this paper combines the
advantages of the wavelet transform, firstly preprocessed by the wavelet transform,
and then combined with the cross-extraction of travelling signal features by the AO-
VMD method, and the localization error is maintained within 0.02 km, which is
significantly better than that of the other two methods. The localization error is
generally maintained within 0.02km, and the localization accuracy is obviously better
than the other two methods.
Figure 10 Visualization of fault location results by three algorithms
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4.2.2. COMPARE TO OTHER NETWORK MODELS
In order to verify the superiority of the AO-VMD-CWT method proposed in this
paper in the power cable fault localization algorithm, it is chosen to be compared with
BiLSTM and cable fault ranging based on the combination of EMD and wavelet
transform (EMD+CWT), and the three algorithms fault localization results are
visualized as shown in Fig. 10, and the experimental results data statistics are shown
in Table 3.
Combined with Figure 10, Table 2 and Table 3, it can be seen that the localization
error of EMD+CWT method is generally maintained within 0.04km, which is mainly
due to the use of EMD decomposition and wavelet transform to remove some of the
redundant signals and extract the useful information in the dominant component of the
noise, so that the filtered signals in the calculation of the reflected waveform
transmission time to improve the accuracy of the filter. The localization error of the
BiLSTM algorithm is within 0.065 km, which shows the advantage of BiLSTM in the
training of time series samples, while the algorithm in this paper combines the
advantages of the wavelet transform, firstly preprocessed by the wavelet transform,
and then combined with the cross-extraction of travelling signal features by the AO-
VMD method, and the localization error is maintained within 0.02 km, which is
significantly better than that of the other two methods. The localization error is
generally maintained within 0.02km, and the localization accuracy is obviously better
than the other two methods.
Figure 10 Visualization of fault location results by three algorithms
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Table 3 Average positioning result of power cable faults
5. CONCLUSION
In this study, a power cable fault location technique based on parameter-optimized
variational modal decomposition is successfully proposed and validated. The
experimental results demonstrate that by combining the variational modal
decomposition and wavelet transform, the proposed technique makes significant
progress in enhancing the identification and processing efficiency of cable fault
signals. Specifically, in the simulated fault test, the average localization error of the
proposed method is reduced to less than 1%, which improves the accuracy by about
30% compared with the traditional fault localization methods. Especially in the
processing of complex fault signals, the proposed method shows better adaptability
and robustness.
By optimizing the processing of parameters of cable fault signals, this study
significantly improves the accuracy of fault location. In the tests, the technique
demonstrated good processing capability for different types of cable fault signals,
especially in the face of non-standard or complex fault signals, and was able to
identify and accurately locate the fault point. For example, the relative error of fault
localization is maintained between 0.5% and 1% when testing a cable of up to 5 km in
length, which demonstrates the efficiency and reliability of the technique in practical
Fault
type
Fault
distance
Average positioning results
Average absolute
localization error
BiLSTM EMD+CWT BiLSTM EMD+CWT
Phase
earth
fault
10km 10.28 10.32 2.415 % 2.435 %
50km 50.26 50.24 463 % 396 %
80km 80.23 80.39 265 % 247 %
100km 100.49 100.45 354 % 313 %
Line to
line
fault
10km
10.51 10.21 4.912 % 3.248 %
50km 50.63 50.28 556 % 665 %
80km 80.41 80.24 232 % 263 %
100km 100.36 100.27 357 % 304 %
Two-
phase
short
circuit
ground
10km 10.12 10.26 1.468 % 1.927 %
50km 50.22 50.18 593 % 515 %
80km 80.35 80.27 382 % 326 %
100km
100.36 100.29 304 % 281 %
Three-
phase
short-
circuit
10km 10.21 10.26 2.718 % 2.569 %
50km 50.24 50.27 415 % 384 %
80km 80.19 80.18 226 % 261 %
100km 100.46 100.34 463 % 357 %
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applications. The application of parameter-optimized variational modal decomposition
based on parameter optimization in power cable fault localization proposed in this
study not only improves the accuracy of fault localization, but also provides a new
technical path for fault diagnosis and maintenance of power systems.
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