IntroductionIntroduction

Locating transmission line faults Locating transmission line faults quickly and accurately is very quickly and accurately is very important for economy, safety and important for economy, safety and reliability of power systemreliability of power system

This paper presents a recent fault This paper presents a recent fault location method based on the double location method based on the double terminal methods of traveling wave terminal methods of traveling wave using WAVELT transformusing WAVELT transform

Wavelet Transform has much better Wavelet Transform has much better resolution for locating a transient resolution for locating a transient event in time-domain over traditional event in time-domain over traditional methods such as fourier transform methods such as fourier transform methodmethod . .

In this presentation, some In this presentation, some concentration will be upon concentration will be upon transmission line system which is transmission line system which is out point of interest in this out point of interest in this project, especially the traveling project, especially the traveling wave theory. wave theory.

Main power system Main power system componentscomponents

Any electric power system consists of Any electric power system consists of three principal divisions:three principal divisions:

generating systemgenerating system transmission systemtransmission system distribution systemdistribution system

transmission lines transmission lines specifications & specifications &

modelingmodeling The transmission network is a high The transmission network is a high

voltage network designed to carry voltage network designed to carry power over long distances from power over long distances from generators to load points. generators to load points.

Transmission systemTransmission system

This transmission system This transmission system consists ofconsists of::

insulated wires or cables for transmission insulated wires or cables for transmission of powerof power

transformers for converting from one transformers for converting from one voltage level to anothervoltage level to another

protective devices, such as circuit protective devices, such as circuit breakers, relays.breakers, relays.

physical structures such as towers and physical structures such as towers and substations substations

Any transmission line Any transmission line connecting two nodes may be connecting two nodes may be

represented by its basic represented by its basic parameters, namelyparameters, namely ::

1. Resistance (R)1. Resistance (R) 2. Inductance (L)2. Inductance (L) 3. Capacitance (C)3. Capacitance (C)

See next picture: pi-networkSee next picture: pi-network

TL equivalent circuitTL equivalent circuit

Transmission lines may be Transmission lines may be modeled asmodeled as::

short lines ( < 80 km )short lines ( < 80 km )

oror medium-length line ( 80 km < length medium-length line ( 80 km < length

< 240 km )< 240 km )

oror long lines ( > 240km )long lines ( > 240km )

Types of faults on Types of faults on Transmission lines:Transmission lines:

The normal mode of operation of a The normal mode of operation of a power system is a balanced 3-phase power system is a balanced 3-phase AC. There are undesirable incidents AC. There are undesirable incidents that may disrupt normal conditions, that may disrupt normal conditions, as when the insulation of the system as when the insulation of the system fails at any point. Then we say a fault fails at any point. Then we say a fault occurs. occurs.

Protection schemes for Protection schemes for transmission linestransmission lines

The protection system is The protection system is designed to disconnect the designed to disconnect the faulted system element faulted system element automatically when the short automatically when the short circuit currents are high enough circuit currents are high enough to present a direct danger to to present a direct danger to the element or to the system as the element or to the system as a whole. a whole.

Any protection system Any protection system consists of three principal consists of three principal

componentscomponents

sensorsensor protective relayprotective relay circuit breakercircuit breaker

There are two types of There are two types of protectionprotection::

primary protectionprimary protection

backup protectionbackup protection

Faults may be classified under Faults may be classified under four typesfour types::

single line-to-ground fault SLGsingle line-to-ground fault SLGline-to-line fault L-Lline-to-line fault L-Ldouble line-to-ground fault 2LGdouble line-to-ground fault 2LGbalanced three-phase faultbalanced three-phase fault

Fault detection methods in Fault detection methods in transmission linestransmission lines

Some of the fault location techniquesSome of the fault location techniques

Several fault location algorithms Several fault location algorithms based on one-terminal have based on one-terminal have developed since several years developed since several years ago.ago.

They can be divided into They can be divided into two categoriestwo categories::

algorithm based on impedance in algorithm based on impedance in last yearslast years

algorithm based on traveling algorithm based on traveling wavewave

algorithm based on algorithm based on impedanceimpedance

uses current and voltage uses current and voltage sampling data to measure post-fault sampling data to measure post-fault impedance. Based on the impedance. Based on the knowledge of line impedance per knowledge of line impedance per unit length, the fault distance can unit length, the fault distance can be calculated. be calculated.

algorithm based on traveling algorithm based on traveling wavewave

While in the later, traveling wave While in the later, traveling wave determines fault location with the determines fault location with the time difference between initial wave time difference between initial wave and its reflection one's arrival at the and its reflection one's arrival at the point of fault locator.point of fault locator.

Algorithms of fault location Algorithms of fault location based on traveling wavesbased on traveling waves

When a line fault occurs, abrupt When a line fault occurs, abrupt change in voltage or in current at the change in voltage or in current at the fault point generates a high fault point generates a high frequency electromagnetic signal frequency electromagnetic signal called traveling wave. This traveling called traveling wave. This traveling wave propagates along the line in wave propagates along the line in both directions away from the fault both directions away from the fault point.point.

11 ) )Single-ended fault Single-ended fault location algorithmlocation algorithm

Single terminal methods are that the Single terminal methods are that the fault point is calculated by the fault point is calculated by the traveling time between the first traveling time between the first arrival of the traveling wave and the arrival of the traveling wave and the second arrival of the reflection wave second arrival of the reflection wave at end of the line. at end of the line.

11 ) )Single-ended fault Single-ended fault location algorithmlocation algorithm

This time is proportional to the fault This time is proportional to the fault distance and the key is to analyze distance and the key is to analyze the reflection process of traveling the reflection process of traveling wave. A correlation technique is used wave. A correlation technique is used to recognize the surge returning from to recognize the surge returning from the fault point and distinguish it from the fault point and distinguish it from other surges present on the system. other surges present on the system.

11 ) )Single-ended fault Single-ended fault location algorithmlocation algorithm

The method is suitable for a typical The method is suitable for a typical long line, but surely is inadequate for long line, but surely is inadequate for a close-in fault only a few kilometers a close-in fault only a few kilometers from the measuring point. It thinks of from the measuring point. It thinks of the different velocities of earth mode the different velocities of earth mode and aerial mode, but the fault and aerial mode, but the fault location error is great for the velocity location error is great for the velocity chosen is not reliable.chosen is not reliable.

22 ) )Double-ended fault Double-ended fault location algorithmlocation algorithm

~ ~l

l1l2Es1 Es2345 kV 345 kV

AB

22 ) )Double-ended fault Double-ended fault location algorithmlocation algorithm

The double terminals methods are The double terminals methods are that fault point is determined by that fault point is determined by accurately time tagging the arrival of accurately time tagging the arrival of traveling wave at each end of the traveling wave at each end of the lineline. . This method depends less on This method depends less on grounding resistance and system grounding resistance and system running-way, etc... This method is running-way, etc... This method is used widely. used widely.

22 ) )Double-ended fault Double-ended fault location algorithmlocation algorithm

The velocity is determined by the The velocity is determined by the distributed parameters ABCD of the distributed parameters ABCD of the line and usually varies in the range line and usually varies in the range 295-29m/us for 500 kV line295-29m/us for 500 kV line. . The The accuracy is improved by right of accuracy is improved by right of higher frequency components of higher frequency components of traveling wave generated by lighting traveling wave generated by lighting strikes strikes

Wavelet and its transform Wavelet and its transform fundamentalsfundamentals

WT has become well known as WT has become well known as a new useful tool for various a new useful tool for various signal-processing applications. signal-processing applications. The wavelet transform of a The wavelet transform of a signal signal f(t)f(t) L2 ( R)L2 ( R) is defined is defined by the inner-product between by the inner-product between abab (t)(t) and and f (t)f (t) as: as:

Features and propertiesFeatures and properties

1) Mother wavelet1) Mother wavelet

(t)(t) is a basic wavelet or mother is a basic wavelet or mother wavelet, which can be taken as a band-wavelet, which can be taken as a band-pass function (filter).pass function (filter).

The asterisk denotes a complex The asterisk denotes a complex conjugate, and a,b conjugate, and a,b R, a=/ 0, are the R, a=/ 0, are the dilation and translation parameters. dilation and translation parameters.

2) Scaling wavelet2) Scaling wavelet

In the previous wavelet function, the In the previous wavelet function, the time remains continuous but time-time remains continuous but time-scale parameters (b,a) are sampled scale parameters (b,a) are sampled on a so-called “dyadic” grid in the on a so-called “dyadic” grid in the time-scale plane (b,a). time-scale plane (b,a).

Therefore, instead of continuous Therefore, instead of continuous dilation and translation the mother dilation and translation the mother wavelet may be dilated and wavelet may be dilated and translated discretely by selecting translated discretely by selecting appropriate values of a and bappropriate values of a and b

Reconstruction of original Reconstruction of original signalsignal

It is possible to perfectly recover the It is possible to perfectly recover the original signaloriginal signal f(t) f(t) from its coefficientsfrom its coefficients Wf(a,b) Wf(a,b) The reconstructed signal is The reconstructed signal is defined asdefined as::

Hence, Wavelets exist locally in both the domains of time and frequency, owing to the good localization and the dilation/translation operation

Analysis by orthogonal wavelets shows Analysis by orthogonal wavelets shows little hope for achieving good time little hope for achieving good time localization. We study how to use CWT localization. We study how to use CWT to solve the problems of fault location to solve the problems of fault location in transmission lines. It is very in transmission lines. It is very advantageous for expanding the advantageous for expanding the applied fields of WT and improving applied fields of WT and improving safety and reliability of power system safety and reliability of power system

Advantages of wavelet Advantages of wavelet transformation over other transformation over other

conventional methodsconventional methods

Two fundamental tools in signal analysis Two fundamental tools in signal analysis are the Windowed (or short-time) Fourier are the Windowed (or short-time) Fourier Transform (WFT) and the CWT. Both Transform (WFT) and the CWT. Both methods decompose a signal by methods decompose a signal by performing inner products with a collection performing inner products with a collection of running analysis functionsof running analysis functions

FourierFourier For the WFT, the signal is decomposed into a summation For the WFT, the signal is decomposed into a summation

of periodic and sinusoidal function. The time and of periodic and sinusoidal function. The time and frequency resolution are both fixed. That makes this frequency resolution are both fixed. That makes this approach particularly suitable for the analysis of signals approach particularly suitable for the analysis of signals with slowly varying periodic stationary characteristics. with slowly varying periodic stationary characteristics. Hence, Fourier transform doesn’t indicate when an Hence, Fourier transform doesn’t indicate when an “event” occurs and doesn’t work well on discontinuous.“event” occurs and doesn’t work well on discontinuous.

WaveletWavelet

For the CWT, the analysis functions are For the CWT, the analysis functions are obtained by dilation of a single (band-obtained by dilation of a single (band-pass) wavelet. CWT uses short windows pass) wavelet. CWT uses short windows at high frequencies and long windows at at high frequencies and long windows at low frequencies. This property enables low frequencies. This property enables the CWT to “zoom in” on discontinuous the CWT to “zoom in” on discontinuous and makes it very attractive for the and makes it very attractive for the analysis of transient signals. The analysis of transient signals. The following figures are illustration of both following figures are illustration of both methodmethod..

Wavelet applications areasWavelet applications areas

WT has been applied inWT has been applied in 1. signal processing1. signal processing

2. power engineering2. power engineering

power engineeringpower engineering

analysis for power quality problems analysis for power quality problems resolutionresolution

power system transient classificationpower system transient classification power quality disturbance data power quality disturbance data

compression and incipient failure compression and incipient failure detection.detection.

Problem FormulationProblem Formulation

consider our previous double-consider our previous double-ended lineended line

Lossless line, characteristic Lossless line, characteristic impedance Zcimpedance Zc

Assume the traveling wave velocity of v.Assume the traveling wave velocity of v.

if a fault occurs at a distanceif a fault occurs at a distance l1 l1 from bus from bus A, this will appear as an abrupt injection A, this will appear as an abrupt injection at the fault point. This injection at the fault point. This injection will will travel like a wavetravel like a wave "surge" along the line "surge" along the line in both directions and will continue to in both directions and will continue to bounce back and forth between fault bounce back and forth between fault point, and the two terminal buses until point, and the two terminal buses until the post-fault steady state is reached.the post-fault steady state is reached.

Using the knowledge of the velocity Using the knowledge of the velocity of traveling waves of traveling waves vv along the given along the given line, the distance to the fault point line, the distance to the fault point can be deduced easily can be deduced easily

Proposed Method Proposed Method AnalysisAnalysis

Fault typeFault type: 3-phase fault: 3-phase fault AlgorithmAlgorithm: The double-ended line : The double-ended line

recording of fault signals method is used recording of fault signals method is used at both ends.at both ends.

The recorded waveforms will be The recorded waveforms will be transformed into modal signals. transformed into modal signals.

Fault locator methodFault locator method: The modal signals : The modal signals will be analyzed using their will be analyzed using their wavelet wavelet transformstransforms....

Let Let t1t1 and and t2t2 corresponds to the corresponds to the times at which the modal signals times at which the modal signals wavelet coefficients in scale wavelet coefficients in scale 11, show , show their initial peaks for signals recorder their initial peaks for signals recorder at bus at bus AA and bus and bus BB. the . the delaydelay between the fault detection times at between the fault detection times at the two ends is the two ends is t1-t2t1-t2, can be , can be determined. When determined. When tdtd is determined is determined we could obtain the fault location we could obtain the fault location from bus from bus AA According to: According to:

the v is assumed to be 1.8182x105 miles/sec

sampling time is 10 usthe total line length is 200 miles.

A Programming Simulation A Programming Simulation Using Matlab LanguageUsing Matlab Language

The modal signals are decomposed The modal signals are decomposed using daubechies 4 which is using daubechies 4 which is represent by command represent by command db4db4 in in Matlab. Number Matlab. Number 44 represents the represents the number of wavelets coefficients. number of wavelets coefficients. Only Only the first twothe first two numbers "scales" numbers "scales" 11 and and 22 are used in the proposed fault are used in the proposed fault location method: location method:

% generate faulted signal% generate faulted signal signal=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 signal=[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0.08 0 .01 0 0 0 0 0 0 0 0 0 0 0 0 0 0.08 0 .01 0 0 0 0 0 0 0 0 0];0];

s=signal.*signal; s=signal.*signal; % square it CWT^2% square it CWT^2 [ca1,cd1]=[ca1,cd1]=dwtdwt(s,'(s,'db4db4');');

dwtdwt: WAVELT DISCRETE TRANSFORM: WAVELT DISCRETE TRANSFORM db4db4: daubechies 4: daubechies 4

% reconstructs detail coeffs at % reconstructs detail coeffs at levels 1,2, from the wavelet levels 1,2, from the wavelet decopmposition structure [c,l]decopmposition structure [c,l]

d2=d2=wrcoefwrcoef('d',c,l,'db4',('d',c,l,'db4',22);); d1=d1=wrcoefwrcoef('d',c,l,'db4',('d',c,l,'db4',11););

wrcoef: obtain first and wrcoef: obtain first and second element of db4.second element of db4.

Results and discussionsResults and discussions

three phase fault is simulated at three phase fault is simulated at 20 km miles away from bus A.20 km miles away from bus A.

The fault waveform is shown in The fault waveform is shown in next figure:next figure:

In this example, In this example,

The first WTC peak occurs:The first WTC peak occurs:

at bus A is at bus A is t1 = 21.15ms t1 = 21.15ms (from WF plot (from WF plot 1)1)

at bus B at bus B t2=21 ms t2=21 ms (from WF plot 2)(from WF plot 2)