Travelling waves for finding the fault location in transmission lines

Journal Electrical and Electronic Engineering 3; (): -9 Published online April, 3 (http://www.sciencepublishinggroup.co/j/jeee) doi:.648/j.jeee.3. Travelling waves for finding the fault location in transission lines Mohaad Abdul Baseer Electrical and Electronics Engineering, Al Majaah University, Riyadh, K.S.A. Eail address:.abdulbaseer@u.edu.sa (M. A. Baseer), abaseer73@gail.co (M. A. Baseer) To cite this article: Mohaad Abdul Baseer. Travelling Waves for Finding the Fault Location in Transission Lines, Journal Electrical and Electronic Engineering. Vol., No., 3, pp. -9. doi:.648/j.jeee.3. Abstract: Transission lines are designed to transfer electric power fro source locations to distribution networks. This project investigates the proble of fault localization using traveling wave voltage and current signals obtained at a single end of a transission line and ulti ends of a transission network. Fourier transfor (FT) is the ost popular transforation that can be applied to traveling wave signals to obtain their frequency coponents appearing in the fault signal. The wavelet ulti resolution analysis is a new and powerful ethod of signal analysis and is well suited to traveling wave signals. Wavelets can provide ultiple resolutions in both tie and frequency doains. Keywords: Transission Lines, Wavelet Theory, Fourier Transfors, Fault Analysis, Localisation Of Faults. Introduction An electric power syste coprises of generation, transission and distribution of electric energy. Transission lines are used to transit electric power to distant large load centres. The rapid growth of electric power systes over the past few decades has resulted in a large increase of the nuber of lines in operation and their total length. These lines are exposed to faults as a result of lightning, short circuits, faulty equipents, is operation, huan errors, overload, and aging. Many electrical faults anifest in echanical daages, which ust be repaired before returning the line to service. The restoration can be expedited if the fault location is either known or can be estiated with a reasonable accuracy. Faults cause short to long ter power outages for custoers and ay lead to significant losses especially for the anufacturing industry. Fast detecting, isolating, locating and repairing of these faults are critical in aintaining a reliable power syste operation. When a fault occurs on a transission line, the voltage at the point of fault suddenly reduces to a low value. This sudden change produces a high frequency electroagnetic ipulse called the travelling wave (TW). These travelling waves propagate away fro the fault in both directions at speeds close to that of light. To find the fault, the captured signal fro instruent transforers has to be filtered and analyzed using different signal processing tools. Then, the filtered signal is used to detect and locate the fault. It is necessary to easure the value, polarity, phase, and tie delay of the incoing wave to find the fault location accurately. The ain objective of this thesis is to analyze the ethods of the fault location based on the theory of travelling waves in high voltage transission lines. In this thesis, we have developed single and ulti end ethods of travelling wave fault location which use current signal recordings of the 5 kv network obtained fro travelling wave recorders (TWR) sparsely located in the transission network. The TWRs are set to record 4 illiseconds of data using an 8 bit resolution and a sapling rate of.5 MHz. The record includes both pre trigger and post trigger data. Although the single ended fault location ethod is less expensive than the double ended ethod, since only one unit is required per line and counication link is not required, the errors reain high when using the advanced signal processing techniques. Furtherore, the fault location error needs ore iproveent considering single end ethod. Multi end ethod shows a proising econoical solution considering few recording units.. Literature Survey A detailed literature survey has to classify the fault and to estiate the fault location. The areas of the work and results obtained by the various researchers are suarized in the chapter. Lin Yong Wu et.al [] explored A New Single Ended

Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines Fault Location Technique Using Travelling Wave Natural Frequencies. In this paper the relationship between the spectra of travelling waves, the fault distance and the terinal conditions of transission lines is discussed. Sia wenxia et.al [] proposed a Fault location for transission line based on travelling waves using correlation analysis ethod. In this paper the principle of transission line fault location based on travelling waves. The principle and of correlation analysis is introduced, then the ethod using correlation analysis in fault location is given. Bian Haihong et.al [3] discussed a Study of Fault Location for Parallel Transissions Lines Using One Terinal Current Travelling Waves the application of fault location using one terinal travelling wave for parallel transission lines. With proper phase odule transforation, parallel lines can be decoposed to the sae directional net and the reverse directional net. This paper analyzes the propagation characteristics of travelling waves in the reverse directional net, and derivates the refraction coefficient at the fault point for a single phase fault firstly and strictly. OU Gui bin et.al [4] developed an Algorith for Ultra High Speed Travelling Wave Protection with Accurate Fault Location. In this paper Basing fault generated current travelling wave, a novel algorith ipleenting ultra high speed protection and fault location for transission lines is proposed. 3. Power Syste Faults 3.. Introduction Power transission and distribution lines are the vital links that achieve the essential continuity of service of electrical power to the end users. Transission lines connect the generating stations and load centres. 3.. Nature and Causes of Faults Faults are caused either by insulation failures and conducting path failures. Most of the faults on transission and distribution lines are caused by over voltage due to lighting and switching surges or by external conducting objects falling on over head lines. Birds, tree branches ay also cause faults on over head lines. Other causes of faults on over head lines are direct lightning strokes, aircraft, snakes, ice and snow loading, stors, earthquakes, creepers etc. In the case of cables, transforers, generators the causes ay be failure of solid insulation due to ageing, heat, oisture or over voltage, accidental contact with earth etc. The over all faults can be classified as two types. Series faults. Shunt faults 3.3. Effects of Faults A fault if unlearned has the following effects on a power syste. Heavy short circuit current ay cause daage to equipent or any other eleent of the power syste due to over heating or flash over and high echanical forces set up due to heavy current. There ay be reduction in the supply voltage of the healthy feeders, resulting in the loss of industrial loads. Short circuits ay cause the unbalancing of the supply voltages and currents, there by heating rotating achines. There ay be a loss of syste stability. The faults ay cause an interruption of supply to consuers. 4. Basic Concepts of Fault Location Process 4.. Historical Background A few years ago, ost power copanies elected to have little or no investent for iproving fault location ethods. This is ainly due to a belief that ost of the faults are transient ones needing no inforation about their locations. Also, the weak or in accurate behaviour of the earlier fault locators ay have played a role in this belief. On the other hand, a huge aount of research contributions were presented for fault location purposes as reported in the literatures. However, these efforts received little consideration fro these copanies. These viewpoints are recently changed due to the new concepts of free arketing and de regulation all over the world. These copetitive arkets force the copanies to change their policies to save oney and tie as well as to provide a better service. This consequently leads to increasingly consider the benefits of fault location estiation ethods. Nowadays, it is quite coon for alost all odern versions of ulti function line protection units to include separate routines for fault Location calculation. 4.. Properties of Transission Line Faults Transission lines are considered the ost vital coponents in power systes connecting both generating and consuer areas with huge interconnected networks. They consist of a group of overhead conductors spreading in a wide area in different geographical and weather circustances. These conductors are dispensed on a special etallic structure towers, in which the conductors are separated fro the tower body with soe insulating copo-

Journal Electrical and Electronic Engineering 3, (): -9 3 nents and fro each other with an adequate spacing to allow the air to serve as a sufficient insulation aong the. Unfortunately these conductors are frequently subjected to a wide variety of fault types. Thus, providing proper protection functions for the is an attractive area for research specialists. Different types of faults can occur including phase faults aong two or ore different conductors or ground faults including one or ore conductors to ground types. However, the doinant type of these faults is ground ones. 4.3. Fault Location Estiation Benefits 4.3.. Tie and Effort Saving After the fault, the related relaying equipent enables the associated circuit breakers to De energize the faulted sections. Once the fault is cleared and the participated faulted phase(s) are declared, the adopted fault locator is enabled to detect the fault position. Then, the aintenance crews can be infored of that location in order to fix the resultant daage. Later, the line can be reenergized again after finishing the aintenance task. Since transission line networks spread for soe hundreds of kiloetres in different environental and geographical circustances, locating these faults based on the huan experience and the available inforation about the status of all breakers in the faulted area is not efficient and tie consuing. These efforts can therefore effectively help to sectionalize the fault (declare the faulted line section) rather than to locate precisely the fault position. Thus the iportance of eploying dedicated fault location Schees are obvious. 4.3.. Iproving the Syste Availability There is no doubt that fast and effective aintenance processes directly lead to iprove the power availability to the consuers. This consequently enhances the overall efficiency of the power nets. These concepts of (availability, efficiency, quality. etc) have an increasingly iportance nowadays due to the new arketing policies resulting fro deregulation and liberalization of power and energy arkets. 4.3.3. Assisting Future Maintenance Plans It is quite right that teporary faults (the ost doinant fault on overhead lines) are self cleared and hence the syste continuity is not peranently affected. However, analyzing the location of these faults can help to pinpoint the wake spots on the overall transission nets effectively. This hopefully assists the future plans of aintenance schedules and consequently leads to avoid further probles in the future. These strategies of preventive aintenance enable to avoid those large probles such as blackouts and help to increase the efficiency of the overall power syste. 4.3.4. Econoic Factor All the entioned benefits can be reviewed fro the econoical perspective. There is no doubt that tie and effort saving, increasing the power availability and avoiding future accidents can be directly interpreted as a cost reduction or a profit increasing. This is an essential concept for copetitive arketing. 4.4. Classification of Developed Fault Location Methods Generally speaking, fault location ethods can be classified into two basic groups, travelling wave based schees and ipedance easureent based ones as shown in Fig.. Travelling wave schees can be used either with injecting a certain travelling wave fro the locator position or with analyzing the generated transients due to the fault occurrence. Ipedance easureent schees are classified whether they depend on the data fro one or both line ends. Fig.. Classification of fault location ethods. 4.4.. Travelling Wave Based Fault Locators Eploying travelling wave phenoena for fault location purposes for both underground cables and overhead lines was reported since 93. In 95, Lewis classified travelling wave based schees into different four types A, B, C and D according to their odes of operation using the travelling voltage waves. Types A and D depend on analyzing the resulting transients fro the fault itself needing no further pulse generating circuitry. Type A is a single end one capturing the transients only at one end. It relies on the generated transients fro the arcing flashover during the fault. However the assuption of getting generated transients at the line end is not always satisfied. Moreover, the arc itself ay extinguish rapidly. They rely on easuring the required tie for the injected pulses to go and to be captured after reflection fro the fault point. This tie can be directly interpreted as a fault distance. 4.4.. Ipedance Measureent Based Fault Locators These schees provide another alternative for the fault location estiation proble. Fig.. shows the one line diagra of a three phase double infeed faulted transission line. A line to ground fault occurred on phase A at point F through a resistance RF at a distance x fro the locator position. The fault current IF is coprised fro two coponents IFs and IFr flowing fro sending and receiving ends respectively. The essential task of the fault location algorith is to estiate the fault distance x as a function of the total line ipedance L using the sending end easureents (for single end algoriths) or both end easureents (for double end algoriths)with the ost possible accuracy.

4 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines Fig.. One line diagra of a faulted transission line. 4.4.3. Non Conventional Fault Locators Instead of the noral atheatical derivation, non conventional fault location algoriths were introduced depending on other processing platfors such as Wavelet Transfor (WT), ANN or GA. These ethods have their own probles that result fro the line odelling accuracy, data availability and the ethod essences. 4.5. Requireents for Fault Location Process Fig. 3 presents a general explanation of the essential requireents for fault locators. Generally speaking, fault locator works in off line ode after perforing the relaying action. Once the fault is detected and the faulty phase(s) are successfully classified, the fault locator is enabled to find out the estiated fault distance. The recorded data by the Digital Fault Recorder (DFR) is passed through the locator input anipulator to the fault locator. A transission line is a syste of conductors connecting one point to another and along which electroagnetic energy can be sent. Power transission lines are a typical exaple of transission lines. The transission line equations that govern general two conductor unifor transission lines, including two and three wire lines, and coaxial cables, are called the telegraph equations. The general transission line equations are naed the telegraph equations because they were forulated for the first tie by Oliver Heaviside (85 95) when he was eployed by a telegraph copany and used to investigate disturbances on telephone wires. When one considers a line segent dx with paraeters resistance ( R ), conductance ( G ), inductance ( L ), and capacitance ( C ), all per unit length, (see Figure. the line constants for segent dx are R dx, G dx, L dx, and C dx. The electric flux ψ and the agnetic flux φ created by the electroagnetic wave, which causes the instantaneous voltage u(x, and current i(x,, are And d ψ ( t ) u ( x, t ) C d x () d φ ( i (x, L d x () Calculating the voltage drop in the positive direction of x of the distance dx obtains u( x, u( x + dx, u( x, du( x, dx (3) ( R + L ) i( x, dx t If dx is cancelled fro both sides of (3), the voltage equation becoes Fig. 3. General requireents for fault location schees. 5. Travelling Wave Theory Studies of transient disturbances on transission systes have shown that changes are followed by travelling waves, which at first approxiation can be treated as step front waves. As this research is focused on travelling wave based fault location, it was decided to eploy an introductory chapter to the basic theory of travelling waves. 5.. Introduction The transission line conductors have resistances and inductances distributed uniforly along the length of the line. Travelling wave fault location ethods are usually ore suitable for application to long lines. 5.. The Transission Line Equation u( x, i( x, L Ri( x, Siilarly, for the current owing through G and the current charging C, Kirchhoff s current law can be applied as i( x, i( x + dx, (4) i( x, di( x, (5) ( G + C ) u( x, dx t If dx is cancelled fro both sides of (5), the current equation becoes i( xt, ) u( xt, ) C Gu( xt, ) (6)

Journal Electrical and Electronic Engineering 3, (): -9 5 The negative sign in these equations is caused by the fact that when the current and voltage waves propagate in the positive x direction, i(x, and u(x, will decrease in aplitude for increasing x. When one substitutes and differentiate once ore with respect to x, we get the second order partial differential equations C ( x, Y G + L( x, R + and and differentiate once ore with respect to x, we get the second order partial differential equations i( xt, ) uxt (, ) Y Yi ( xt, ) γ i( xt, ) i( x, u( x, Y Yi( xt, ) γ i( x, (7) (8) lossless line, the series resistance R and the parallel conductance G are zero, the inductance and capacitance are constants. The transission line equations becoe u i L i x C u t Since there is no daping, substituting the "steady wave" solution u i into Equations (3) and (4), i i L i i C Dividing Equation (5) by Equation (6) yields L C (3) (4) (5) (6) (7) This is the characteristic ipedance of the lossless line. This iplies that the voltage and current waves travel down the line without changing their shapes. Figure 4. Single phase transission line odel. u x LCu (8) In this equation, γ is a coplex quantity which is known as the propagation constant, and is given by γ Y α + jβ (9) where, a is the attenuation constant which has an influence on the aplitude of the travelling wave, and ß is the phase constant which has an influence on the phase shift of the travelling wave. Equation (7) and Equation (8) can be solved by transfor or classical. γx uxt (, ) A() t e + A() t e () γ x γx γx i( x, [ A( e A( e ] () Where is the characteristic ipedance of the line and is given by x. R G + L t + C t Where A and Aare arbitrary functions, independent of 5.3. The Lossless Line () Power transission lines are norally of the three phase type. However, it is uch sipler to understand travelling wave concepts and associated ethods by first considering wave propagation in single phase lines. In the case of the Equation (8) is the so called travellingwave equation of a loss less transission line. The solutions of voltage and current equations reduce to u x v ( x, A( e + A ( e x v, x v x (9) v ( x [ A ( e A ( e ] () i Where v is the travelling wave propagation speed defined as v () LC When Taylor s series is applied to approxiate a function by series, At ( + h) / h // At ( ) + ha ( + ( ) A ( +...! h ( + hp + p +...) At ( ) hp e At ( ) where p is the Heaviside operator p. Applying this to Equation (9) and Equation (), the solutions for the voltage and current waves in the tie doain can be satisfied by the general solution (also as

6 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines showed by D Alebert ) x x u( x, A( t + ) + A( t ) (3) v v x x i( xt, ) [ A( t + ) A( t )] (4) v v x In this expression, A ( t + ) is a function describing a v wave propagating in the negative x direction, usually called the backward wave, and x A ( t v ) is a function describing a wave propagating in the positive x direction, called the forward wave. 5.4. Propagation Speed Fro the voltage drop equation, Since u i then i( x, u( x, ( u + dx, ( Ldx) (5) The line is defined as R ρ rv (9) R + Where is a characteristic ipedance of the line and R is the terination ipedance. Siilar coefficients can be obtained for the currents, but the current reflection coefficient equals the negative of the voltage reflection coefficient value. R ρ ri (3) + R As a special case, terination in a short circuit results in ρ r for the voltage signals and ρ ri for current signals. If the terination is an open circuit, R is infinite and ρr in the liit for the voltage signal and ρ ri for the current signal. For a travelling wave while propagating through the terination, the transission (refraction) coefficient can be calculated as L i( x, i( x, i( x+ dxt, ) ( dx) (6) R ρ t ρr + (3) + R Making i( x, finite we get If the wave propagates intact L i( xt, ) i( x+ dxt, ) i( xt, ) i( x+ dxt, ) ( dx) (7) dx v v (8) dt L LC This is the travelling wave propagation speed. 5.5. Reflection and Refraction of Travelling Waves When an electroagnetic wave propagates along a transission line with certain characteristic ipedance, there is a fixed relation between the voltage and current waves. Therefore, for a line terinated in a short circuit, the voltage of the backward (or reflected) wave is equal and opposite to the voltage of the forward (or inciden wave. 5.6. Modal Analysis Three phase lines have significant electroagnetic coupling between conductors. By eans of odal decoposition, the coupled voltages and currents are decoposed into a new set of odal voltages and currents.for this purpose, the basic equations for a single conductor were described in Section 5.. Here, the introduced analysis is expanded to cover the poly phase lines. Modal transforation is essentially characterized by the ability to decopose a certain group of coupled equations into decoupled ones excluding the utual parts aong these equations. This can be typically applied to the ipedance atrices for coupled conductors as shown in Figure 5.3, where s is the self ipedance, is the utual ipedance, are odal surge ipedances for ground ode and two aerial odes (i, and ). Three of the constant odal transforation atrices for perfectly transposed lines are the Clarke, Wedepohl, and Karrenbauer transforations. Figure 5. Lattice diagra for a fault at the first half of a transission line.

Journal Electrical and Electronic Engineering 3, (): -9 7 s s s Figure 6. Modal transforation decoupling. The odal coponents can be obtained by U T U I I T i u p p (3) (33) Where U and I are the phase voltage and current coponents and the indices and p are related to odal and phase quantities, respectively. T u and T i are the corresponding voltage and current transforation atrices. Thus, the odal ipedance atrix can be found as T T u For transposed lines, the transient current signals i (34) I a, Ib and I c are transfored into their odal coponents using Clarke s transforation as follows I I 3 I 3 I I 3 I a b c Where I is the ground ode current coponent, and I and I are known as the aerial ode current coponents for transposed lines. The ground ode current coponents I are defined as zero sequence coponents of the syetrical coponent syste. The aerial ode current coponents I own in phase a and one half returns in phase b and one half in phase c. I aerial ode current coponents are circulating in phases b and c. 5.7. Characteristics of the Travelling Wave Transients (Tw A fault occurring on a transission line will generate both voltage and current travelling waves. These will travel along the line until they eet a discontinuity on the line, such as fault point and bus bar. At this point, both a reflection and a refraction of the wave will occur. This generates additional waves which will propagate through the power syste. Fig.7 shows a diagra for a solid fault on a single phase transission line. The voltage and current travelling wave at both ends of the line M and N can be expressed as Fig. 7. Fault generated Travelling Wave on a Single Phase Transission Line. u ( et ( τ) + αet ( τ) αet ( 3τ) αet ( 3τ) +..., et ( τ + + + ) αet ( τ) αet ( 3τ) αet ( 3τ)... i(, C u + ( αet ( τ) αet ( 3τ) +..., u ( et ( τ) αet ( 3τ) +... u n( et ( τn) + αnet ( τn) αnet ( 3τn) αnet ( 3τn ) +..., et ( τ + + + n) αnet ( τn) αnet ( 3τn) αnet ( 3τn)... in(, C un + ( αnet ( τn) αnet ( 3τn) +..., un ( et ( τn) αnet ( 3τn) +... Where, n represent voltage and current quantities at end M and N respectively. As shown in Fig. 7. and above equations, the basic characteristics of fault generated travelling wave transients can be suarized as ) The wave characteristics change suddenly with the arrival of successive waves at the busbar. This arks the occurring of the fault and the travelling tie for the journey fro the fault to busbar etc. ) The agnitude of the sudden change depends on the agnitude of the voltage at the fault instant e(. For later waves, it also depends on the reflection and refraction coefficients at the discontinuity and the attenuation characteristics of travelling wave. 3) The polarity of the sudden change depends on the polarity of the fault voltage at the fault instant and the discontinuous characteristics of the wave ipedance. Generally speaking, the polarity of travelling wave has the following characteristics a). Reflected voltage and current waves fro the fault point will have the sae polarity as the incident waves. b).the initial voltage or current waves have the sae polarity at both ends of the line. c). For the reflected positive wave fro the busbar and the reflected negative wave fro the fault point, their initial wave and

8 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines reflected wave have the sae polarity. 5.8. Travelling Wave Fault Location Theory Where c the wave propagation of 99.79 / sec ( ft/ns) The voltage and current at any point x obey the partial differential Equations e L i and i C e Where L and C are the inductance and capacitance of the line per unit length. The resistance is assued to be negligible. The solutions of these equations are where e( x, e ( x v + e ( x v f r + i( x, e f ( x vt ) e r( x + vt ) L is the characteristic ipedance of the C transission line and v LC is the velocity of propagation Forward ( ef and i f ) and reverse ( e r and i r ) waves, as shown in Figure 5.8 leave the disturbed area x travelling in different directions at v,which is a little less than the speed of light, toward transission line 6.Wavelet Analysis 6.. Introduction Figure 8. b. Bewley Lattice Diagra Most of the signals in practice are TIME DOMAIN signals. But in any applications, the ost distinguished inforation is hidden in the frequency content of the signal. Soe ties both frequency and tie related inforation ay be required. In such cases various atheatical transfors are used. 6.. Need for Wavelet Analysis 6... Fourier Analysis Fourier analysis is the analysis, which breaks down a signal into constituent sinusoids of different frequencies and infinite duration. Another way to think of Fourier analysis is as a atheatical technique for transforing our view of the signal fro tie based to frequency based. Figure 8.a. Travelling voltage and current waves ends. The reaining energy will travel to other power syste eleents or transission lines. Figure shows a Bewley lattice diagra, illustrates the ultiple waves (represented by subscripts and 3) generated at line ends. Wave aplitudes are represented by reflection coefficients ka and kb which are deterined by characteristic ipedance ratios at the discontinuities. τa and τ b represent the travel tie fro the fault to the discontinuity. τ a and τ b can be deterined very precisely. By knowing the length (l) of the line and the tie of arrival difference ( τ a τ b), one can calculate the distance (x) to the fault fro substation A by l c( τa τb) X Fig. 6... Fourier analysis. For any signals, Fourier analysis is extreely useful because the signal's frequency content is of great iportance. 6... Short Tie Fourier Analysis

Journal Electrical and Electronic Engineering 3, (): -9 9 In an effort to correct the deficiency of FT, Dennis Gabor (946) adapted the Fourier transfor to analyze only a sall section of the signal at a tie a technique called windowing the signal. Gabor s adaptation, called the Short Tie Fourier Transfor (STFT), aps a signal into a two diensional function of tie and frequency. There is only a inor difference between STFT and FT. In STFT, the signal is divided into sall enough segents, where these segents (portions) of the signal can be assued to be stationary. For this purpose, a window function w is chosen. The width of this window ust be equal to the segent of the signal where its stationary is valid. 6.3.. Definition of Wavelet A wavelet is a wavefor of effectively liited duration that has an average value of zero. Copared to sine waves, the basis of Fourier analysis, which do not have liited duration (they extend fro inus to plus infinity) and are sooth and predictable, wavelets tend to be irregular and asyetric. Fig. 6... Short Tie Fourier analysis. The STFT represents a sort of coproise between the tie and frequency based views of a signal. It provides soe inforation about both when and at what frequencies a signal event occurs. However, we can only obtain this inforation with liited precision, and that precision is deterined by the size of the window. 6.3. Wavelet Analysis Wavelet analysis represents the next logical step a windowing technique with variable sized regions. Wavelet analysis allows the use of long tie intervals where we want ore precise low frequency inforation, and shorter regions where we want high frequency inforation. Wavelet analysis does not use a tie frequency region, but rather a tie scale region. Fig. 6.3.. Sine Wave and a Wavelet wave. 6.3.. Wavelet Properties The ost iportant properties of wavelets are. The wavelet ust be oscillatory.. It ust decay quickly to zero can only be non zero for a short period of the wavelet function 3. The average value of the wavelet in the tie doain ust be zero, ψ ( dt (6.) 4. The wavelet function should have finite energy. ψ ( t ) dt < (6.) 5. The adissibility condition square integrable functions Ψ ( satisfying the Adissibility condition. c ψ π / ( ψ ( ω ) ω ) d ω < (6.3) Can be used to first analyze and then reconstruct a signal without loss of inforation. In eq3.3 ψ(ω) stands for the Fourier transfor of ψ(. The adissibility condition iplies that the Fourier transfor of ( vanishes at the zero frequency, i.e. 6.4. Wavelet Transfors ψ(ω) ω (6.4) Fig. 6.3. Wavelet Analysis. The wavelet transfor, like any other transfors consists of a pair of transfors fro one doain to other doain and vice versa. In case of wavelet transfors the original doain is the tie doain, while the transfored doain is the tie scale doain Wavelet transfors can be

Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines accoplished in different ways. 6.5. The Continuous Wavelet Transfor Matheatically, the process of Fourier analysis is represented by the Fourier transfor Scaling a wavelet siply eans stretching (or copressing) it. The scale factor, often denoted by the letter a. for exaple, the effect of the scale factor with wavelets is, the saller the scale factor, the ore copressed the wavelet. (6.5) Which is the su over all tie of the signal f ( ultiplied by a coplex exponential. Next this coplex exponential can be broken down into real and iaginary sinusoidal coponents. The results of the transfor are the Fourier coefficients, which when ultiplied by a sinusoid of frequency ω, yield the constituent sinusoidal coponents of the original signal. Graphically, the process looks like shown in Figure below Fig. 6.5.. Wavelets of different scales. Fig. 6.5(a) Breaking the signal into sine waves of different aplitudes using FT. Siilarly, the continuous wavelet transfor (CWT) is defined as the su over all tie of the signal ultiplied by scaled, shifted versions of the wavelet function. The results of the CWT are any wavelet coefficients C, which are a function of scale and position. Multiplying each coefficient by the appropriately scaled and shifted wavelet yields the constituent wavelets of the original signal Fig. 6.5(b) Breaking the signal into wavelets of different aplitudes using WT. Matheatically CWT is given by Where 6.5.. Shifting Shifting a wavelet siply eans delaying (or hastening) its onset. Matheatically, delaying a function Ψ ( by k is represented by Ψ (t k) and is shown in Fig6.5.. Fig. 6.5.. delaying a wavelet function by k. 6.5.3. Scale and Frequency The higher scales correspond to the ost stretched wavelets. The ore stretched the wavelet, the longer the portion of the signal with which it is being copared, and thus the coarser the signal features being easured by the wavelet coefficients. Thus, there is a correspondence between wavelet scales and frequency as revealed by wavelet analysis CWT( a, b) x( ψ a, b( dt ψ a, b( ψ(( t b)/ a) a Ψ ( is the base function or the other wavelet, the asterisk denotes a coplex conjugate, and a,b Є R, a, are the dilation and translation paraeters respectively 6.5.. Scaling Wavelet analysis produces a tie scale view of a signal. Fig. 6.5.3. Relation between scale and frequency of the signal.

Journal Electrical and Electronic Engineering 3, (): -9 6.6. The Discrete Wavelet Transfor (DWT) 6.6.. Need for Discrete Wavelet Transfor Although the discretized continuous wavelets transfor enables the coputation of the continuous wavelet transfors by coputers, it is not a true discrete transfor. The DWT is considerably easier to ipleent when copared to the CWT. the basic concepts of the DWT will be introduced in this section along with its properties and the algoriths used to copute it. width.associated scaling filters are iniu phase filters 6.6.. The Discrete Wavelet Transfors (DWT) The foundations of the DWT go back to 976 when croiser, esteban, and galand devised a technique to decopose discrete tie signals. Crochiere, Weber, and Flanagan did a siilar work on coding of speech signals in the sae year. They naed their analysis schee as sub band coding..and the discrete wavelet transfor is given by DWT (, n) k x k k na b a a [ ] ψ ( / (6.8) By coparing the eq (6.8) with general equation for ipulse response (FIR) digital filter y ( n) x[ k ] h[ n k ] / c (6.9) k It can be seen that Ψ (k) is the ipulse response of Low pass digital filter with transfer function Ψ (ω). For a, each dilation of Ψ (k) effectively halves the bandwidth of Ψ (ω). Multilevel DWT filter banks ipleent the DWT eqn (6.9) in the forward transfor stage and the IDWT in the reverse transfor stage. By careful selection of a and b, the faily of dilated other wavelets constitutes an orthonoral basis of L (R). 6.7. Filter Bank A tie scale representation of a digital signal is obtained using digital filtering techniques. The DWT analyzes the signal at different frequency bands with different resolutions by decoposing the signal into a coarse approxiation and detail inforation. Their su is the DWT. Fig. 6.8. Daubechies Wavelets(db5). 7. Siulation Tests &Results Localisation of fault using Travelling wave theory A Transission line odel syste shown in the Figure 7. has siulated by using MATLAB/SIM POWER SYSTEMS. The transission line was represented as a k long, 5 kv ideally transposed transission line, connecting to a load. Fault location is done two different configurations. Single End ethod. Multi End ethod 7.. Fault Location Using Single end Method The electrical characteristics of a transission line depend priarily on the construction oh the line. The values of inductance and capacitance depend on the various physical factors. 6.8. Daubechies Wavelets Figure 6.7. Wavelet transfor filter bank. General characteristics Copactly supported wavelets with external phase and highest Nuber of vanishing oents for a given support Fig. 7.. single line diagra of transission line odel syste. 7.. Siulation Tests &Results Tests are carried out for syetrical and unsyetrical faults which are siulated at different distances like K, 5K, 7K of transission line and the fault

Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines localisation estiated using Travelling Wave Theory. Difference in Tie t t Table 3. Location of Faults using single end ethod for a for a 7K Transission line. V LC is the velocity of propagation. Distance Velocity * Tie %Error between the actual and obtained distances is calculated as The various faults considered are. Line to ground (L G) fault,. Double line (L L) fault, 3. Double line to ground (L L G) fault, 4. 3 Φ (or L L L) fault, and 5. 3 Φ to ground (or L L L G) fault. Tables, & 3 shows the calculated fault distances by using TWT Table. Location of Faults using single end ethod for a K Transission line. 7... Case I. Specifications of a K Transission Line Source Voltage 5kV, 5Hz Transission Line Length K, distributed paraeter transission line odel R.73 Ω/k; R.3864 Ω/k; L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fault is created at.6 and cleared at.9, siulation tie.5 Table. Location of Faults using single end ethod for a for a 5K Transission line. Fig. 7..(b) Voltage wave for, for L G fault at k. The voltage wavefor in Figrepresents an L G fault created at distance of k on a transission line of k long, the fault creation tie is.6 sec and the shift in voltage wave for appears at.934sec this is due to the travelling tie taken by the fault to appear at the relay point. 7... Case II. Specifications of A 5K Length Line with Distributed Paraeters Source Voltage 5kV, 5Hz Transission Line Length 5K, distributed paraeter transission line odel

Journal Electrical and Electronic Engineering 3, (): -9 3 R.73 Ω/k; R.3864 Ω/k; L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fault is created at.3 and cleared at.4, siulation tie.5 Fig. 7..(d) Voltage wave for, for LLL fault at K. Fig. 7..(a) Voltage wave for, for LG fault at 3K. Fig. 7.. (e) Current wave for, for LLL fault at K. Fig. 7..(b) Voltage wave for, for LL fault at K. The above voltage wavefor represents an LG fault created at distance of 3k on a transission line of 5k long, the fault creation tie is.3 sec and the shift in voltage wave for appears at.4sec this is due to the travelling tie taken by the fault to appear at the relay point. 7..3. Case III. Specifications of a 7K Transission Line Source Voltage 5kV, 5Hz Transission Line Length 7K, distributed paraeter transission line odel R.73 Ω/k; R.3864 Ω/k; L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fig. 7..(c) Current wave for, for LL fault at K. Fault is created at.4 sec and cleared at.5 sec, siulation tie.65 sec The above voltage wavefor represents an LG fault created at distance of 5k on a transission line of

4 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines 7k long, the fault creation tie is.4sec and the shift in voltage wave for appears at.56669sec this is due to the travelling tie taken by the fault to appear at the relay point. 7.3. Multi end Method Various ethods and different techniques of fault location have been developed in the literature. In traveling wave based ethod, the fault location can be found by coparing the arrival tie of the initial and reflected transient signals at a single end of the line terinals. Single ended ethods show ore econoical advantages. Faulty Line Estiation The transission line odel considered for this work has been shown in Fig6.4.3 Fig. 7.3. Two Area Transission line network. Fig. 7..3(a) Voltage wave for, LG fault at 5k. 7.3.. CaseI.Specifications Source Voltage 5kV, 5Hz Transission Line Length K, distributed paraeter transission line odel R.73 Ω/k; R.3864 Ω/k; L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fault is created at.8 and cleared at.9, siulation tie.5 The above current wavefor represents an LG fault created at distance of 5k on a transission line of k long, the fault creation tie is.8sec and the shift in voltage wave for appears at.9745sec this is due to the travelling tie taken by the fault to appear at the relay point. Fig. 7..3(b) Voltage wave for, LLG fault at 5k. Fig. 7..3(c) Current wave for, LG fault at 5k. Fig.7.3.(a) MATLAB odel of the syste.

Journal Electrical and Electronic Engineering 3, (): -9 5 Source Voltage 5kV, 5Hz Transission Line Length 5K, distributed paraeter transission line odel R.73 Ω/k; R.3864 Ω/k; L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fault is created at. and cleared at.4, siulation tie.4. Fig. 7.3.(b) Current wave for, L G fault at 5k. Fault is created at.8 Seconds. But the fault appeared at.9745 Seconds. Difference in Tie (.975.8).75 Seconds V LC is the velocity of propagation. V V.9337* *.74* 5.899* K / sec 3 9 Distance Velocity * Tie Distance.899* 5*.75 Distance 5.775. Fig. 7.3.. Current wave for, L G fault at k. The above current wavefor represents an LG fault created at distance of k on a transission line of 5k long, the fault creation tie is.sec and the shift in voltage wave for appears at.6898sec this is due to the travelling tie taken by the fault to appear at the relay point. Table 5. Location of Faults using double end ethod for a 5K Transission line. Table 4. Location of Faults using double end ethod for a K Transission line. 7.3.3. CaseIII. Specifications Source Voltage 5kV, 5Hz Transission Line Length 7K, distributed paraeter transission line odel 7.3.. CaseII. Specifications R.73 Ω/k; R.3864 Ω/k;

6 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines L.9337e 3 H/k; L 4.64e 3 H/k; C.74e 9 F/k C 7.75e 9 F/k Fault is created at.8 and cleared at.6 siulation tie.6 Transission line ends represent a discontinuity or ipedance change where soe of the wave s energy will reflect back to the disturbance. The reaining energy will travel to other power syste eleents or transission lines. Figure 7.4 a Bewley lattice diagra, illustrates the ultiple waves (represented by subscripts and 3) generated at line ends. Wave aplitudes are represented by reflection coefficients ka and kb which are deterined by characteristic ipedance ratios at the discontinuities. τa and τ b represent the travel tie fro the fault to the discontinuity. τ a and τ b can be deterined very precisely. By knowing the length (l) of the line and the tie of arrival difference τ ), one can calculate the distance (x) to the fault ( τ a b fro substation A by X l c τ a ( τ b ) Where c the wave propagation of 99.79 / sec ( ft/ns) Fig. 7.3.3. Current wave for, L G fault at 6k. The above current wavefor represents an LG fault created at distance of 6k on a transission line of 7k long, the fault creation tie is.8sec and the shift in voltage wave for appears at.48694sec this is due to the travelling tie taken by the fault to appear at the relay point. Table 6. Location of Faults using double end ethod for a 7K Transission line. Figure 7.4. Bewley Lattice Diagra. 7.5. Fault Location Signal Processing Techniques A traveling wave, a sharply varying signal, is a real challenge for the traditional atheatical ethods. Typically, the traveling waves are ingled with noise as the traveling wave based fault location systes require a high sapling rate so that the fault inforation can be estiated accurately. The analysis is carried out using TW output signals fro the MATLAB siulations for a typical power syste with a single circuit overhead transission line connecting two 5 kv buses as depicted in Figure 7.5. 7.4. Localisation of faults using Bewley ethod with wavelet transfors Figure 7.5. Lattice diagra for a fault at the first half of a transission line.

Journal Electrical and Electronic Engineering 3, (): -9 7 Frequency Doain Approach Fourier transfor based fault location algoriths have been proposed since a long tie. Most of the proposed algoriths use voltages and currents between fault initiation and fault clearing. To find out the frequency contents of the fault signal, several transforations can be applied, naely, Fourier, STFT, and Wavelet etc. Fourier Transfor Fourier transfor (FT) is the ost popular transforation that can be applied to traveling wave signals to obtain their frequency coponents appearing in the fault signal. Usually, the inforation that cannot be readily seen in the tie doain can be seen in the frequency doain. The FT and its inverse give a one to one relationship between the tie doain x( and the frequency doain x( ω ).Given a signal I (, the FT FT( ω) is defined by the following equation FT I(.e jω t dt Tie Frequency Doain Approach The traveling wave based fault locators utilize high frequency signals, which are filtered fro the easured signal. Discrete Fourier Transfor (DFT) based spectral analysis is the doinant analytical tool for frequency doain analysis. However, the DFT cannot provide any inforation of the spectru changes with respect to tie. Short Tie Fourier Transfor To overcoe the shortcoing of the DFT, short tie Fourier transfor (STFT, Denis Gabor, 946) was developed. In the STFT defined below, the signal is divided into sall segents which can be assued to be stationary. The signal is ultiplied by a window function within the Fourier integral. If the window length is infinite, it becoes the DFT. STFT (t, ω) + I(.w(t τ).e jωt Where I ( is the easured signal, ω is frequency, w(t τ) is a window function, τ is the translation, and t is tie. To separate the negative property of the DFT described above, the signal is to be divided into sall enough segents, where these segents (portion) of the signal can be assued to be stationary. Wavelet Transfor The wavelet ultiresolution analysis is a new and powerful ethod of signal analysis and is well suited to traveling wave signals. Wavelets can provide ultiple resolutions in both tie and frequency doains. The windowing of wavelet transfor is adjusted autoatically for low and high frequencies i.e., it uses short tie intervals for high frequency coponents and long tie intervals for low frequency coponents. Given a function x (, its Continuous Wavelet Transfor (CWT) is defined as follows dt CWT (a, b) a + x ( ψ t b ( )dt a * The transfored signal is a function with two variables b and a, the translation and the scale paraeter respectively. ψ ( is the other wavelet, which is a band pass filter and * ψ is the coplex conjugate for. The factor is used a to ensure that each scaled wavelet function has the sae energy as the wavelet basis function. It should also satisfy the following adissible condition ψ( dt The ter translation refers to the location of the window. As the window is shifted through the signal, tie inforation in the transfor doain is obtained. a is the scale paraeter which is inversely proportional to frequency. Wavelet transfor of sapled wavefors can be obtained by ipleenting the DWT, which is given by DWT( k, n, ) a k nba x[ n] ψ a Where ψ ( is the other wavelet, and the scaling and translation paraeters a and b in (3 3) are replaced by a and nb a respectively, n and being integer variables. In the standard DWT, the coefficients are sapled fro the CWT on a dyadic grid. The wavelet coefficients (WTC) of the signal are derived using atrix equations based on decoposition and reconstruction of a discrete signal. Actual ipleentation of the DWT involves successive pairs of high pass and low pass filters at each scaling stage of the DWT. This can be thought of as successive approxiations of the sae function, each approxiation providing the increental inforation related to a particular scale (frequency range). The first scale covers a broad frequency range at the high frequency end of the spectru and the higher scales cover the lower end of the frequency spectru however with progressively shorter bandwidths. Conversely, the first scale will have the highest tie resolution. Higher scales will cover increasingly longer tie intervals. 7.5.. Case I Single End The syste is siulated at different locations along the 9 line. A sapling tie of 3. 333 sec is used for all siulations and propagation speeds of 899 k/s. The voltage wavefor with ultiple reflections is loaded to wavelet toolbox The distance is calculated as dt x v 899(.849.849 ) 3.333 x 48.3 k 5 5 9

8 Mohaad Abdul Baseer: Travelling waves for finding the fault location in transission lines for LG fault at 5k Fig. 7.5.(a) Voltage Wavefor for L G fault at 5 k with Wavelet Transfor. Fig. 7.5.(d) Voltage Wavefor for Syetrical faults at 5 k with Wavelet Transfor. Table 7. Location of Faults using single end ethod for a k transission line with Wavelet transfors. Fig. 7.5.(b) Voltage Wavefor for L L fault at k with Wavelet Transfor. Fig. 7.5.(c) Voltage Wavefor for L L G fault at k with Wavelet Transfor. 8. Conclusion In this thesis presented a fault locator that is based on the characteristics of the travelling waves initiated fro the fault. This part of the work has addressed the proble of fault distance estiation utilising the easureents of currents as well as voltage travelling wave signals single area and two area transission line systes. The travelling wave theory was introduced and the properties of the travelling waves on transission lines were also discussed. The objective of this thesis was to propose an autoated technique based on travelling waves for finding the fault location in transission lines and to test the perforance of the technique. The proposed ethod uses the easured fault current signals of the fault signals. The error in fault location estiation is a function of the sapling rate and the speed of propagation. The techniques were tested using data generated by executing various cases in MAT- LAB/SIMULINK. Various types of faults were applied at various locations on the transission lines. It is possible to achieve greater accuracy with ulti end ethods devel-