Fault Location using wavelets

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IEEE Transactions on Power D elivery, Vol. 13, No. 4, October 1998

ult

Location Using Wavelets

Fernando

H .

Magnago and Ali Abur

Department of Electrical Engineering

Texas

A& M University

College Station, TX

77843,

U.S.A.

Abstract

This paper describes the use of wavelet transform for

analyzing powe r system fault transients in order to determine the

fault location. Traveling wave theory is utilized in capturing the

travel time of the transients along the monitored lines between the

fault point and the relay. Time resolution for the high frequen cy

components of the fault transients, is provided by the wavelet

transform. Thi s information is related to the travel time of the

signals which are already decomposed into their modal compo-

nents. A erial mode is used for all fault types, whereas the ground

mode is used to resolve problems associated with certain special

cases. Wavelet transform is found to be an excellent discriminant

for identifying the traveling wave reflections from the fault irre-

spective of the fault type and impedance. EM TP simu lations are

used to test and validate the proposed fault location approach f or

typical power system faults.

Keywords: Power System Faults, Electromagnetic Transients,

Wavelet Transform, Fault Location, Traveling Waves.

1

Introduction

Transmission line fault location has lo ng been on e of the primary

concerns of the power industry. Methods of locating power sys-

tem faults introduced so far, can be broadly classified under two

categories: one based on the power frequency components, and

the other utilizing the higher frequency contents of the transient

fault signals. The latter is also referred to

as

traveling wave or

ultra high speed fault location method, due to its use of traveling

wave theory and shorter sampling windows.

The use of traveling wave theory for fault detection was

initially proposed by Dommel and Michels in [I] , where a dis-

criminant was defined based on the transient voltage an d current

waveforms in order to detect

a

transmission line fault. McLaren

et al. have later developed

a

correlation based technique where

the cross correlation between stored sections of the forward and

backward traveling waves were used to estimate the travel times

of transient signals from the relays to the fault point [2,3,4]. An

overview of traveling wave based fault location methods can be

found in [ 5 , 6 ] .

PE-303-PWRD-0-12-1997

A

paper recommended and approved by

the IEEE Transmission and Distribution Committee of the IEEE Power

Engineering Society for publication in the IE EE Transactions on Power

Delivery. Manuscript submitted July 28, 1997; made available for

printing Decem ber 12,

1997.

1475

Among the limitations of the traveling

wave

methods, the

requirement of high sam pling rate is frequently stated. Other

stated problems include the uncertainty in the choice of sampling

window and problems of distinguishing between traveling waves

reflected from the fault and from the remote end of the line.

Recent developments in optical current transducers technology

enabled high sampling rate recording of transient signals during

faults [7]. Availability of such broad bandwidth sampling capa-

bility facilitates better and more efficient use of traveling wave

based methods for fault analysis.

The correlation based fault location method introduced in

[ 2 ] s very effective as long

as

the width of the time window

to save the forward moving wave is properly selected. Since

this selection depends on the fault location which is unknown,

the window width selection remains an unresolved issue for the

practical implem entation of this method . Com bined use of a

short and

a

long window has been proposed as one solution for

this problem in [4].

In this paper,

a

different approach, based on the wavelet

transform of the fault transients, is presented. Wavelet transform

possesses some unique fea tures that make it very suitable for this

particular application. It maps a given function from the time do-

main into time-scaling dom ain. The wavelet, the basis function

used in the wavelet transform, has band pass characteristics wh ich

makes this mapping similar to a mapping to the time-frequency

plane. Unlike the basis func tions used

in

Fourier analysis, the

wavelets are not only localized in frequency but

also

in time.

This localization allows the detection of the time of occurence

of abrupt disturbances, such

as

fault transients. Fault generated

traveling waves appear

a:;

such disturbances superposed on the

powe r frequency signals recorded by th e relays. Processing these

signals using the wavelet transform reveals their travel times

between the fault and the relay locations.

The potential benefits of a pply ing wavelet transform for anal-

ysis of transient signals in pow er systems have been recognized

in the recent years. Robertso n et al. present a comparative

overview of Fourier, short time Fourier and wavelet transforms,

give examples of applying wavelet transform to analyze power

system transients and extraction of their particular features in [8].

A similar overview along with application of wavelet transform

to detect and classify pow er quality d isturbances, are given in

[9].

Advantages of using w avelet transform for analyzing transients

and solution of linear time-invariant differential equations using

wavelet transform is demonstrated in

[101.

In this paper, another

useful application of the wavelet transform in solving the prob-

lem of fault location, will be presented. A brief introduction to

wavelet transform will be given before formulating the problem

and presenting the proposed solution method.

0885-8977/98/ 10.00 0 1997 IEEE



1476

Wavelet transform has been introduced rather recently in math-

ematics, even though the essential ideas that lead to this devel-

opment have been around for

a

longer period

C P ~

ime. It is a

linear transformation much like the Fourier transform, howev-

er with one important difference: it allows time localization of

different frequency components of a given signal. Windowed

Fourier transform also partially achieves this sam e goal, but with

a

limitation of using

a

fixed width windowing function.

As a

result, both frequency and time resolution of the resulting trans-

form will be apriori fixed. In the case of the wavelet transform,

the analyzing functions, which are called wavelets, will adjust

their time-widths to their frequency in such a way that, higher

frequency wavelets will be very narrow and lower frequency

ones will be broader. This property of multi resolution is partic-

ularly useful for analyzing fault transients which contain local-

ized high frequency components superposed on power frequency

signals. Thus, wavelet transform is better suited for analysis of

signals containing short lived high frequen cy disturbances super-

posed on lower frequency continuo us wav eforms by virtue of this

zoom-in capability.

Given a function f ( t ) , its continuous wavelet transform

(WT) will be calculated as follows:

where,

a

and

b

are the scaling (dilation) and translation (tim e

shift) constants respectively, and IQ is the wavelet function which

may not b e real as assumed in the above equation for simplicity.

The choice of the wavelet function (mother wavelet) is flexible

provided that it satisfies the

so

called admissibility conditions

Wavelet transform of sampled wav eforms can b e obtained by

implementing the discrete wavelet transform which is given by:

P11.

where, the parameters a and

b

in

Eq. 1)

are replaced by a; and

ka?, k and m being integer variables. In a standard discrete

wavelet transform, the coefficients are sampled from the contin-

uous WT on a dyadic grid, a

=

2 and

bo = 1

yielding a:

= 1,

U;

= i , tc.

b

= k

x

2- , being an integ er variable.

Actual implementation of the discrete wavelet transform, in-

volves successive pairs of high-pass and low-pass filters at each

scaling stage of the wavelet transform. This can be thought of

as successive approximations of the same function, each approx-

imation providing the incremental information related to a par-

ticular scale (frequency range), the first scale covering a broad

frequency range at the high frequency end of the spectrum and the

higher scales covering the lower end of the frequency spectrum

however with progressively shorter bandwidths. Conversely, the

first scale will have the highest time resolution, higher scales w ill

cover increasingly longer time intervals. While, in principle any

admissible wavelet can be used in the wavelet analysis, we have

chosen to use the Daubechies4 [9],[12] wavelet s the mother

wavelet in all the transformations.

lem

Consider a single phase lossless transmission line of length

e

connected between buses A and B , with a characteristic

impedance

2

and traveling wave velocity of U . If a fault occurs

at a distance x from bus

A,

this will appear as an abrupt injection

at the fault point. T his injection will travei like

a

surge along the

line in both directions and will continue to bounce back and forth

between the fault point, and the two terminal buses

until

the post

fault steady state is reached. Hence, th e recorded fault transients

at the terminals of the line will contain abrup t changes at intervals

commensurate with the travel times of signals between the fault

to the terminals. Using the knowled ge of the velocity oftrav eling

waves along the given line, the distance to the fault point can

be deduced easily. Thi s is the essential idea behind traveling

wave methods. Unlike the correlation based methods where the

forward and backward traveling wave components are computed

and used for the cross correlation, in the wavelet based appro ach,

the composite signal (voltage or current) at the relay location is

directly analyzed.

In three phase transmission lines, the traveling waves are

mutually coupled and therefore

a

single traveling wave velocity

does not exist. In order to implement the traveling wave method

in three phase systems, the phase domain signals are first decom-

posed in to their modal compon ents by means of the modal trans-

formation matrices. In this study, all transmission line models

are assumed to be fully transposed, and therefore the well known

Clarke's constant and real transformation matrix given by:

is

used. The phase signals are transformed in to their modal com-

ponents by using this transformation matrix as follows:

S i n o d e

=

T S p h a s e 4)

where, Smo nd Spha.ve are themodal and phase signals (voltages

or currents) vectors respectively.

Clarke's transformation is real and can be used with any

transposed line. If the studied line is untransposed, then an eigen-

vector based transformation matrix, which is frequency depen-

dent, will have

to

be used. This matrix should be computed at

a frequency equal or close to the frequency of the initial fault

transients.

Recorded phase signals are first transformed into their modal

components. The first mode (mode l ) , s usually referred to as the

ground

mode, and its magnitude is significant only during faults

having

a

path to ground. Hence, this component can not be used

for all types of faults. The second mode (mode 2 ,also known as

the

aerial

mode, how ever is present fo r any kind of fault. Acco rd-

ingly, the fault location problem is formulated based essentially

on the aerial mode, m aking occasional use of the ground m ode

signal for purposes of distinguishing b etween certain peculiar sit-

uations, which will be discussed in the next section. Depending

on the existing communication scheme between the two ends of

the line, fault location problem can be solved in two different

ways described below.

Two

ended sync ronized recording

Fault signals are recorded simultaneously at both ends of the

line by two separate channels both of which are using the same

time reference synchronized using Global Positioning Satellite

(GPS ) receivers. The recorded waveforms w ill be transformed

into modal signals, after which the modal signals will be analyzed

using their wavelet transforms. Let

t~

and t g correspond to the

times at which the modal signal wavelet coefficients in scale

1,

show their initial peaks for the signals recorded at bus

A

and

B

respectively. Assum ing that the recorded sign als at the two

ends of the

l ine

are fully synchronized, the delay between the

fault detection times at the two ends, i.e. t d

=

t g

-

t A can be



1477

Insignificant coefficients will imply that the fault is in the remote

half of the line, and vice versa.

If the fault is determined to be in the near half

o f the

line, then

td in Eq.(6) will simply be the time interval between the first two

peaks of the scale 1 WTC’s for the aerial mode.

If the fault is suspected to be in the second half of the line,

then td in

Eq. 6)

will be replaced by:

7)

d

= t x

where:

t s the travel time for the entire line length, and e is the time

interval between the first two peaks of aerial mode WTC’s in

scale 1.

Figure 1 shows th e flowchart for the proposed fault location

algorithm based on the wavelet transform coefficients. Next

section contains results of simulations used to test this proposed

algorithm for various fault types and line configurations.

determined [13]. The distance between the fault point to bus A

will then be given by:

e - t d

2

=

where,

e is the length of the line,

x

is the distance to fault from bus A,

and U, is the speed of the traveling waves for mode

m .

3.2

Single ended recording

A more robust configuration that does not require remote end

synchronization is when the fault location is determined based

solely on th e recorded signals at one end of the line. However, in

such a case, du e to the lack of any other time reference, all time

measurements will be with respect to the instant when the fault

is first detected. Therefore, fau lt location calculations will be

based on the reflection tim es of the traveling waves fr om the fault

point. Unfortunately, for faults involving a ground connection,

not only those reflections from the fault point, but also from the

remote end bus will be observed at the sending end of the line.

Proper algorithms should therefore be devised in order to dis-

tinguish between close-in and remote faults which may produce

similar reflection patterns f or the grounded faults. T he following

sections describe our proposed approach to accomplish this task.

3.2.1

Approach

I:

Ungrounded faults

It has long been observed that ungrounded faults such as line-to-

line or ungrounded three-phase, do not cause significant reflec-

tions from the remote e nd bus during the fault transients. Thus,

by measuring the time delay between the two consecutive peaks

in the wavelet transform coefficients of the recorded fault signal

at scale

1,

and taking the product of the wav e velocity and half of

this time delay, the distance to the fault can easily be calculated

for these kinds of faults. The fault distance will be given by the

equation:

where,

x is the distance to the fault, v is the wave velocity (for the mode

used), and td is the time difference between two consecutive

peaks of the wavelet transform coefficients.

3.2.2

Approach

11:

Grounded faults

When the fault involves

a

connection to ground, then sending end

signals may contain significant reflections from the remote end

bus in addition to the ones from the fault point. Also, depending

on the location of the fault, the reflections from the remote end

may arrive before or after those reflected from the fault point.

It can be easily verified by using the Lattice diagram method,

that the remote end reflections will arrive later than the fault

reflections if the fault occurs within half the length of the line,

close to the relay location. The opposite will be true if the fault

is situated in the second half of the line. It is observed that, in

the former case the

ground mode

wavelet transform coefficient

(WTC) for scale 1, show s significant peaks, w hile the latter case

ground mode

WTC for scale 1 remains insignificant below the

chosen detection threshold.

Therefore first a decision is made on whether

or

not the

fault

is

grounded, based on scale 2 WTC’s of the ground mode

signals. If these coefficients are found significant, then th e fault

will be assumed to be a ground fault. Next decision will be made

on which half of the line the fault is actually located. Thi s is

done by observing scale 1 WTC’s of the ground mode signals.

Transducer

output

Transformation

Wavelet

Transformation

L-r’

Ungrounded Fault

YE§

calculate the fault loc.

as

in

Section

3.2.1

’

r

Remote half of the line.

Based on Scale

1

Mode

2

calculate td s in Eq. 7)

then calculate the fault

Grounded Faull

Grounded

Fault

Near half of the line.

Based OD Scale 1Mode

2

calculate the fault

loc.

as

in

Section 3.2.1

igure 1: Flowchart of the proposed fa ult location algorithm

4 Simulation results

The ATF’EMTP program

[

141 is used to calculate the transient

signals in the power system. Figure 2 show s the system config-

uration used in the simulations. The frequency dependent model

and

B

for the do uble ended configuration and at busbar A for the

single ended configuration.

For this tower configuration, mode 2 (aerial mode) has

a

propagation velocity of 1.8 182

x

lo5miles/sec. A sampling time

o f l o p s is used. The system is simulated using double and single

is

used

t

model the line [151 The

relays are

ocated at hushar

A



1478

1=

200 miles

c

X

I 345 Kv

- x

D c h

345

KV

Figure

2:

Schematic diagram of the simulated system

ended configurations under various kind of faults. Different type

of balanced and unbalanced faults at different locations along

the line and at different inception angles are simulated. Results

of single phase to ground, phase to phase and three phase to

ground faults for an inception angle of

108

degrees are reported

to illustrate the method. The modal signals are decomposed using

the Daubechies4 wavelet where number 4 represents the number

ofw ave let coefficients. O nly the first two scales, scale

1

and scale

2

of the WTC are used in the proposed fault location method.

In order to minimize the noise effect, we squared the wavelet

coefficients at each scale as also done in [9].

A lattice diagram illustrating the reflection and refraction of

traveling waves initiated by the fault transients, is shown in Fig-

ure

3.

On th e left side of the figure, a line connecting buses A and

B

is

drawn vertically. The line

is

200 miles long.

A

single phase

to ground fault is assumed to occur at point F,120miles from bus

A. The horizontal axis starting from point F, epresents the time.

A set of arrows are shown below the lattice diagram, indicating

the arrival times of various w aves reflected from th e fault as well

as bus

B.

Mode

2

(aerial mode) is considered only. The travel

times from the fault

to

bus A, and from the fault

to

bus

B

are

designated by

TI

and

T2

respectively. G iven the traveling wave

velocity v2 or mode 2,

TI

and

T2

will be given by 12 0 mi I

v

and

80 mi

1 U:

respectively.

Figure

4

shows the WTC at scale

1

calculated fo r the example

of Figure 3. Comparing the WTC peak times with the arrival

times of waveform reflections at bus A, it can be observed that

there is a on e to one correlation between them. Simulation results

for both the tw o ended and single ended fault location approaches

will now be given.

T2 3T2 2Tl T2 5T2

R

,

I I .**‘

‘.

.’

A

T1 T1 2TZ

3T1 T1 4T2

Scale

1

mode 2 (aerial mode)

t

I

t

I I

20

205 21 21 22

5

23

time

(ms)

Figure 4: Single phase to ground fault at 12 0 miles from A Peaks

correspond to the predicted ones in Fig. 3.

5(a) and (b) show the WTC for scale 1, of the voltage transients

recorded at bus A and

B

respectively.

In

this example, the first

WTC

peak at bus A occurs at

tA

=

20.15 m s , and at bus B at

t B =

21ms, yielding

f d

= 0.85ms and

using Eq. 5):

200-

1.81 x

io5

x

0.85

x

1 0 - ~

x = 22.99 miles.

2

B us A: Scale 1

mode

2

21

7

B us

B: Scale

1 mode

2

3 5 3 j

time (ms)

Figure 5: Three phase fault at 20 miles from A.

The arrival time of the first transient peak depends on the

velocity of the line and the f ault distance, it is independent of

the type of fault, hence the method applies to all type of faults

provided the tw o terminal recordings are synchronized in time.

Ilj

igure

3 :

Lattice d iagram for a single phase to ground fau lt at

120

miles from

A.

4.2 Single ended recording

4.2-1 Ungrounded

faults:

Figure 6 shows the WTC’s for an example of a phase to phase

fault at 30 miles from A. It can be seen fro m the figure that mode

1 (ground mode) signals are zero, therefore mod e 1 WTC’s can

be used

to

identify this as an ungrounded fault.

4. ronized recording

Assuming synchronized recording of fau lt transients at both ends

of the line, a three phase fau lt is simulated at

20

miles away from

bus A. Mode 2 (aerial mode) voltage signals ar e used only. Figu re





1480

d)Scale

1 ,

mode

2

c)Scale

1,

mode

1

101 1

t ime ms) time ms)

b)Scale

2.

mode 2

d)Scale 2, mode

1

151 I 4 ,

1

I

J

I

Figure 8: P hase to ground fault at 1 70 miles from A.

345 Kv

45

KV

I \ ‘

345

KV

345 Kv

I I I

100 miles 100

miles

Figure 9: Circuit diagram of the simulated system with mutually

coupled lines.

5

This paper presents

a

new, wavelet transform based fault loca-

tion method. Using the traveling wave theory of transmission

lines, the transient signals are first decoupled into their modal

components. Modal signals are then transformed from the time

domain into the time-frequency domain by applying the wavelet

transform. The w avelet transform coefficients at the two lowest

scales are then used to determine the fault location for various

types of faults and line configurations. The proposed fault loca-

tion method is independent of the fault impedance and is shown

to be suitable for mutually coupled tower geom etries as well as

series capacitor compensated lines. The method can be used both

with single ended and synchronized two ended recording of fault

transients. The fault location estimation error is related to the

sampling time used in recording the fault transient. Furthermo re,

for grounded faults near

the

middle of

the line, mode

1 signals

from the fault and from the far end become comparable increas-

ing the error of the fault location algorithm. Simulation resu lts

are given to demonstrate the performance of the method.

References

[2] S. Wajendra and P.G. McLaren, “Traveling-W ave Tech-

niques Applied to the protection of Teed Circuits: Prin-

ciple of Traveling Wave Techniques”, IEEE Transactions

on Power Apparatus and Systems, Vol. PAS-104, no. 12,

pp.3544-3550, Dec. 1985.

[3] S. Rajendra, and

P.

G. McLaren, “Traveling Wave Tech-

niques Applied to the Protection of Teed Circuits: -

Multi -

Phase Multi Circuit System”,

IEEE Transactions

on

Pow-

er Apparatus and Systems, Vol. PAS- 104, no. 12, pp.355 1-

3557, Dec, 1985.

[4] E.

H.

Shehab-Eldin, and P. G. McLaren, “Traveling Wave

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July 1988.

[5]

“Microprocessor Relays and Protection Systems”, IEEE

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[111

I. Daubechies, Ten Lectures

on

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131 A . Phadke, J. Thorp, ComputerRelayingfor Power System-

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924-930, April 1996.

Fernando

N.

Magnago

obtained the B.S. degree from UNRC,

Arge ntinain 1990 and his M.S. degree from Texas A&M Univer-

sity, College Station, TX in 1997. H e is currently a Ph.D. student

at Texas A&M University.

Ali Abur (SM ’90) received the B.S. degree f rom M E W , Turkey

in 1979, the M.S. and Ph.D. degrees from The O hio State Uni-

versity, Columbus, OH, in 198

1

and 198 5 respectively. Since

late 19 85, he has been with the Dept. of Elect. Eng. at Texas

A&M University, College Station, TX, where he

is

currently an

H.

W.

Dommel, and J. M. Michels, “High Speed Relaying

using Traveling Wave Transient Analysis”, IEEE Publica-

tions NO. 78CH1295 -5 PWR, paper no. A78 21 4-9, IEEE

PES Winter Power Meeting, New York, January 1978,

pp.1-7. Assoc iate Professo r.

Documents

Fault Location using wavelets