fault location and classification for transmission line ...931073/fulltext01.pdffault location and...

IN DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2016

Fault Location and Classification for Transmission Line Based on Wavelet Transform

QIUHONG WANG

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING

Fault Location and Classification forTransmission Line Based on Wavelet

Transformby

Qiuhong Wang

M.Sc., KTH - Royal Institute of Technology, 2015

MSC THESIS

in

School of Electical Engineering

(Department of Electromagnetic Engineering)

KTH - ROYAL INSTITUTE OF TECHNOLOGY

(Stockholm)

March 19, 2016

c© Qiuhong Wang 2015

Abstract

With the rapid development of power systems, locating and classifying faults iscritical to the continuity and reliability of the transmission system. In this the-sis, a traveling-wave based technique for fault location and classification on highvoltage and extremely high-voltage transmission lines is proposed. The traveling-wave based protection has the advantage of fast response and not being affectedby power swing and CTs saturation. In this thesis, the transient characteristics ofsingle line to ground fault (which can be divided into solid fault and arcing fault)and lightning disturbance are extracted by using Clarke transformation and wavelettransformation. The differences among recorded traveling wave arrival times areused to calculate the fault location, and the wavelet energy at different frequencybands is utilized to distinguish between lightning and different kinds of fault. A cri-terion is proposed according to the energy ratio. The proposed scheme can identifydifferent faults correctly and quickly. In addition, the influence of busbar capaci-tance, current transformer and coupling capacitor voltage transformer are consid-ered. The simulation of a transmission system has been made in ATP/EMTP, andthe calculations have been made in MATLAB.

Keywords: Traveling wave, fault location, fault classification, wavelet transform,ATP/EMTP.

ii

Abstract

Sammanfattning

Med den snabba utvecklingen av kraftsystem är lokalisering och klassificering av fel avgör-ande för kontinuiteten och tillförlitligheten hos överföringssystem. I denna avhandlingföreslås en vågrörelse-baserad teknik för fellokalisering och klassificering av kraftled-ningar för högspänning och extremt hög spänning. Vågrörelsebaserat skydd har fördelen avsnabb respons och att det inte påverkas av kraft fluktuationer och strömtransformsmättnad.I denna avhandling tas momentana egenskaperna av jord till ledningsfel (vilket kan delas ini stumt jordfel och ljusbågefel) och blixtstörning fram med hjälp av Clarke transformationoch wavelet transformation. Skillnaderna mellan de uppmätta vågrörelsernas ankomst-tider används för att beräkna fellokalisering och wavelet energin vid olika frekvensband,vilket används för att skilja mellan blixt och olika sorters fel. Ett kriterium föreslås en-ligt energiförhållandet. Det föreslagna systemet kan identifiera olika sorters fel korrektoch snabbt. Dessutom övervägs påverkan av strömskenans kapacitans, strömtransforma-tor och kopplingskondensatorspänningsomvandlare. Simuleringen av transmissionssystemhar gjorts med ATP/EMTP, och beräkningarna är gjorda med MATLAB.

Nyckelord: Vågrörelse, fellokalisering, felklassificering, wavelet transformation, ATP/EMTP

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Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

List of Abbreviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Project Background . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Transient Overvoltage in Power System . . . . . . . . . . . . . . . . 3

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Lightning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.3 Switching Overvoltage . . . . . . . . . . . . . . . . . . . . . . . 4

2.4 Temporary Overvoltage . . . . . . . . . . . . . . . . . . . . . . 4

3 Traveling Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Transmission Line . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . 7

3.4 Traveling-Wave Fault Location Algorithms . . . . . . . . . . . . 7

iv

Contents

4 Fault Classification Algorithms . . . . . . . . . . . . . . . . . . . . 16

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Wavelet Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Modeling of Power System in ATP/EMTP . . . . . . . . . . . . . . 18

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2 Models of Transmission System . . . . . . . . . . . . . . . . . . 19

5.3 Models of Fault Cases . . . . . . . . . . . . . . . . . . . . . . . 21

5.4 The accuracy of the models . . . . . . . . . . . . . . . . . . . . 26

6 Fault Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1 No Shunt Capacitance . . . . . . . . . . . . . . . . . . . . . . . 32

6.2 With Shunt Capacitance . . . . . . . . . . . . . . . . . . . . . . 46

7 Fault Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.1 No CTs and CCVTs . . . . . . . . . . . . . . . . . . . . . . . . 58

7.2 With CTs and CCVTs . . . . . . . . . . . . . . . . . . . . . . . 61

7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

Appendices

A Aerial mode voltages of three faults for no CTs and CCVTs model . 72

B Aerial mode voltages of three faults for the model with CTs and CCVTs74

C Decomposition details of aerial mode voltages . . . . . . . . . . . . 76

v

List of Tables

3.1 Traveling Wave Fault Locators . . . . . . . . . . . . . . . . . . . 8

6.1 System Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.2 Line Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.3 Surge parameters of Heildler model . . . . . . . . . . . . . . . . 43

6.4 The characteristics of arcing fault when Cbus = 0 µF . . . . . . . . 51

6.5 The characteristics of arcing fault when Cbus = 0.01 µF . . . . . . 51

6.6 The characteristics of arcing fault when Cbus = 0.1 µF . . . . . . . 52

6.7 The characteristics of solid fault when Cbus = 0 µF . . . . . . . . 52

6.8 The characteristics of solid fault when Cbus = 0.01 µF . . . . . . . 53


6.10 The characteristics of lightning fault when Cbus = 0 µF . . . . . . 54

6.11 The characteristics of lightning fault when Cbus = 0.01 µF . . . . . 54


7.1 Parameters of Source1 . . . . . . . . . . . . . . . . . . . . . . . 56

7.2 Parameters of Source2 . . . . . . . . . . . . . . . . . . . . . . . 56

7.3 Line Parameters of 230 kV system . . . . . . . . . . . . . . . . . 57

7.4 The wavelet energy for different details and approximations . . . . 60

7.5 The wavelet energy for different details and approximations . . . . 63

7.6 The wavelet energy for different details and approximations (30 km) 63

7.7 The wavelet energy for different details and approximations (120 km) 64

vi

List of Figures

3.1 Transmission line equivalent circuit . . . . . . . . . . . . . . . . 5

3.2 Line section of length . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3 Multiple level decomposition of the signal using DWT . . . . . . 10

3.4 The fault location is at the first half of the line . . . . . . . . . . . 11

3.5 The fault location is at the second half of the line . . . . . . . . . 12

3.6 The flow chart of single-ended method . . . . . . . . . . . . . . . 13

3.7 The use of a D-type wave locator . . . . . . . . . . . . . . . . . . 14

3.8 The flow chart of double-ended method . . . . . . . . . . . . . . 15

5.1 The Main window of ATPDraw . . . . . . . . . . . . . . . . . . . 19

5.2 CTs Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . 20

5.3 EMTP model of CTs . . . . . . . . . . . . . . . . . . . . . . . . 20

5.4 CCVTs Equivalent Circuit [1] . . . . . . . . . . . . . . . . . . . 20

5.5 EMTP model of CCVTs . . . . . . . . . . . . . . . . . . . . . . 21

5.6 Equivalent Circuit of Solid Fault . . . . . . . . . . . . . . . . . . 22

5.7 EMTP Model of a Solid Fault . . . . . . . . . . . . . . . . . . . 22

5.8 Arc model in ATP . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.9 Currents and voltage for the arcing fault . . . . . . . . . . . . . . 25

5.10 The waveform of arc resistance . . . . . . . . . . . . . . . . . . . 25

5.11 Heidler model in EMTP . . . . . . . . . . . . . . . . . . . . . . . 26

5.12 Plan of the transmission line implemented in the EMTP . . . . . . 27

5.13 Circuit for EMTP analysis . . . . . . . . . . . . . . . . . . . . . 28

5.14 Tower top voltage of study case . . . . . . . . . . . . . . . . . . . 29

5.15 Phase C voltages of study case . . . . . . . . . . . . . . . . . . . 29

5.16 Phase B voltages of study case . . . . . . . . . . . . . . . . . . . 29

5.17 Phase A voltages of study case . . . . . . . . . . . . . . . . . . . 30

vii

List of Figures

6.1 The 400kV simulated system for solid fault . . . . . . . . . . . . 326.2 DWT decomposition for aerial mode signal of solid fault . . . . . 336.3 DWT decomposition for ground mode signal of solid fault . . . . 346.4 DWT Decomposition for AG fault at 120km from Bus 1 . . . . . 366.5 The 400kV test system in ATP/EMTP . . . . . . . . . . . . . . . 376.6 Currents and voltage for the arcing fault . . . . . . . . . . . . . . 386.7 The waveform of arc resistance . . . . . . . . . . . . . . . . . . . 386.8 DWT decomposition for aerial mode signal of arcing fault . . . . 406.9 DWT decomposition for ground mode signal of arcing fault . . . . 416.10 The locator response for arcing fault at Bus 1 and Bus 2 . . . . . . 426.11 The 400 kV simulated system of lightning fault . . . . . . . . . . 436.12 DWT decomposition for aerial mode signal of lightning fault . . . 446.13 DWT decomposition for ground mode signal of lightning fault . . 456.15 The traveling wave reaching a busbar capacitance . . . . . . . . . 466.14 The locator response for lightning fault at Bus 1 and Bus 2 . . . . 476.16 The equivalent circuit of Figure 6.15 . . . . . . . . . . . . . . . . 486.17 The reflected wave and refracted wave . . . . . . . . . . . . . . . 486.18 EMTP model of single-line to ground fault with different capaci-

tance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.19 The voltage (left) and current (right) wave-front for SLG fault, with

different capacitance at busbar M . . . . . . . . . . . . . . . . . . 496.20 The voltage and current wave-front with different capacitance for

arcing fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.21 The voltage and current wave-front with different capacitance for

lightning disturbance . . . . . . . . . . . . . . . . . . . . . . . . 50

7.1 A 230kV transmission line model . . . . . . . . . . . . . . . . . 567.2 Geometrical data of the line considered[2] . . . . . . . . . . . . . 577.3 The wavelet decomposition D1 of modal voltage for three kinds of

fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597.4 The wavelet decomposition D1 of modal voltage for three kinds of

fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

A.1 The aerial mode of phase voltage and current for solid fault . . . . 72A.2 The aerial mode of phase voltage and current for arcing fault . . . 73

viii

List of Figures

A.3 The aerial mode of phase voltage and current for lightning fault . . 73

B.1 The aerial mode of phase voltage and current for solid fault . . . . 74

B.2 The aerial mode of phase voltage and current for arcing fault . . . 75

B.3 The aerial mode of phase voltage and current for lightning fault . . 75

C.1 The wavelet decomposition of modal voltage for solid fault . . . . 76

C.2 The wavelet decomposition of modal voltage for arcing fault . . . 77

C.3 The wavelet decomposition of modal voltage for lightning fault . . 77

ix

List of Abbreviation

AC Alternating CurrentAG Phase A to GroundCIGRE Council on Large Electric SystemsCTs Current TransformerCCVTs Coupling Capacitor Voltage TransformersCWT Continuous Wavelet TransformDWT Discrete Wavelet TransformEHV Extra High VoltageFFT Fast Fourier TransformHPF High Pass FilterIEEE Institute of Electrical and Electronics EngineersLPF Low Pass FilterSLG Single Line to GroundWT Wavelet Transform

x

Acknowledgements

I would like to express my sincere gratitude to my supervisor, Nathaniel Taylor, forhis assistance, guidance and encouragement throughout the entire work.

I also gratefully thank Professor Hans Edin for examining my thesis work andtechnical support.

Finally, I am extremely thankful to my family and friends for their support andunderstanding in all my studies.

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Chapter 1

Introduction

1.1 Project Background

In recent years, with fast extension of the power system, the research of an au-tomatic and reliable technique for protection system has aroused widespread at-tention. It is well known that transmission lines are an important part in a powersystem and the faults of a transmission line will cause disturbance and endangerthe security of the whole system. Therefore, locating and isolating the faults intime are the main tasks of transmission system protection.When a sudden change, such as a fault or a disturbance occurs on a transmissionline, a traveling wave will be generated, and it will propagate at nearly the speed oflight. It is a significant amount of work to characterize and locating the transientsby only using the original records [3][4]. The wavelet transform is a powerfultool in extracting and analysing the features of traveling wave, the application ofwavelet transform on fault location and classification is presented in this thesis.This thesis describes different algorithms to determine fault location and fault typesbased on sampling of the fault voltage transients at the relay point. For the faultlocation algorithms, two methods are presented: Single-ended method and Double-ended method. The former one uses the time delay between the modal componentsof the fault generated voltage signal which are received at the relay point to deter-mine the location of the fault. The latter one utilizes the time interval between thevoltage signals recorded at both terminals. By using these methods, only incidenttraveling waves are used to perform the fault location, avoiding the utilization ofreflected waves at the fault point and, consequently, making the method feasibleand reliable. In addition, the simulation results showed that this traveling wavebased fault location method does not depend on the fault type [5].The fault classification algorithm is established by using a Wavelet Transformbased technique. Normally the fault generated current and voltage transients con-tain long duration low frequency components and short duration high frequencycomponents, the information contained in these signals are analyzed by WaveletTransforms for the purpose of line protection. Unlike conventional Fourier Trans-form, the WT uses a multi-resolution technique by which different frequency bands

1

1.2. Project Objectives

are analyzed with different resolutions [6]. The WT can be localized in both fre-quency and time domain [7]. Therefore for the analysis of the fault generated tran-sient signal, the wavelet transform is more suitable for analyzing fault transientswhich contain high frequency components. Another important reason that wavelettransform is attractive for engineers is that there are fast calculation algorithmsbased on filter banks [8].

1.2 Project Objectives

The purpose of this thesis is to provide the overview of different methods to cal-culate the fault distance and to distinguish two kinds of transients faults, singleline-to-ground fault and lightning induced wave. In addition, the single line-to-ground fault is presented by two types, one is solid fault and the other one is arcingfault. on a transmission line. A dynamic arcing -fault model needs to be imple-mented. All the simulations and calculations are realized by using ATP/EMTP andMATLAB software. Different methods of fault location and classification based onDiscrete Wavelet Transform are discussed in this thesis. In addition, the influenceof CTs and CCVTs on the proposed algorithm is considered. Accordingly, the fea-sible CTs and CCVTs models are necessary for this case. Then the accuracy of theproposed fault location and classification algorithm should be analyzed.

2

Chapter 2

Transient Overvoltage in PowerSystem

2.1 Introduction

Electromagnetic transient overvoltage is the voltage stress appearing on the equip-ment in power system and exceeding the normal operating voltage. The overvolt-age can be classified into two groups [9]: One is external overvoltage, which isgenerated by elements outside the network; lightning is the most common over-voltage in this group. The other one is internal overvoltage, which is generatedby changes in the operating conditions of the network and only depends on thecharacteristics and structure of the network itself. The internal overvoltage can beseparated into temporary overvoltage and switching overvoltage [10].

2.2 Lightning

Lightning phenomenon is caused by a discharge during which the charge accu-mulated in the clouds discharges into the other clouds or to the earth. Due to thedifferent strike points, the lightning overvoltage can be classified as [11]:

• Induced overvoltage: the lightning strikes the ground or other subject nearthe line, and generates a transient in the line by its electromagnetic field.

• Overvoltages caused by shielding failures: the lightning strikes a phase con-ductor.

• Overvoltages due to back-flashovers: the lightning strikes the shielding wireor the tower, and breaks down the phase-ground insulation.

Among these conditions, the most severe lightning overvoltage is the second one,in which lightning strikes a phase conductor, as it produces the highest overvoltagefor a given stroke current [12].

3

2.3. Switching Overvoltage

2.3 Switching Overvoltage

Switching overvoltage is one of the internal overvoltages. It is caused by the sud-den change in the circuit. The switching overvoltage can be classified as [13]:line energization and re-energization, switching on and off of equipment, and faultinitiation and clearing.

2.4 Temporary Overvoltage

The difference between temporary overvoltage and switching overvoltage is thatthe former overvoltage can last for longer duration, generally from a few cyclesto a few seconds. Some of the most important events leading to the generationof temporary overvoltages are discussed as [11]: ferranti effect, load rejection andground faults.

4

Chapter 3

Traveling Waves

3.1 Introduction

When a disturbance occurs on a transmission line, such as sudden opening or clos-ing a line, a short circuit or a fault, an overvoltage or overcurrent will be introducedat that point. This disturbance will propagate away as a traveling wave to both di-rections at nearly the speed of light [9].

3.2 Transmission Line

All conductors of a transmission line have resistances and inductances distributeduniformly along the longitude of the line. A typical distributed parameter trans-mission lines model can be represented by the circuits shown in Figure 3.1

Figure 3.1: Transmission line equivalent circuit

As is shown in Figure 3.2, each infinitesimal length dx of transmission line consistsof a series impedance z = Rdx+ jωLdx and a shunt admittance y = Gdx+ jωCdx.

5

3.2. Transmission Line

Figure 3.2: Line section of length

In a distributed parameter model representation of a transmission line, the relation-ship between voltage, current, time and distance is fully described by the telegraphequation. If the losses are negligible, it reverts to the well-known wave equation:

− ∂u∂x

= L∂ i∂ t

(3.1)

− ∂ i∂x

=C∂u∂ t

(3.2)

The solution of the wave equation for a lossless line in terms of a forward andbackward traveling wave can be expressed as:

U(x, t) = f1(x− vt)+ f2(x+ vt) (3.3)

I(x, t) =1Z0

f1(x− vt)− f2(x+ vt) (3.4)

where v= 1√LC

is the surge velocity, Z0 =ui =√

LC is the line characteristic impedance,

L and C are the inductance and capacitance per unit length. In a three-phase sys-tem the above equations are functions of the voltages (currents) in all phases. Amodal transformation matrix is therefore used to decouple the phase signals intotheir independent equations for each mode as:

U(x, t) = TvUm(x, t) (3.5)

I(x, t) = TiIm(x, t) (3.6)

6

3.3. Reflection and Refraction

In this thesis, the Clarke’s transformation[14] is selected to transform the threephase voltage (current) signals into their modal components:

u0,α,β = T−1ua,b,c (3.7)

i0,α,β = T−1ia,b,c (3.8)

T−1 =13

1 1 12 −1 −10√

3 −√

3

(3.9)

Where T−1 is the Clarke transformation matrix, u0 and i0 are the ground modecomponents, α and β are the aerial modes, here the aerial mode α is used in thefault location estimation and fault type classification.

3.3 Reflection and Refraction

When a fault occurs on a transmission line, voltage and current surges propagateaway from the fault point towards two sides of the transmission line. Assume thatthere are two ends of the transmission line, end S and end F. These traveling waveswill be reflected and refracted when they reach discontinuities on the transmissionline. The backwards signal traveling wave fb incident upon end S is given by. [15]

fb(t) =∞

∑i=0

ai fb(t− τi) (3.10)

where ai = (ρ f ρs)i, τi = (2i+ 1)Ta, fb(t) is the backwards traveling wave caused

by the occurrence of the fault, Ta is the time required for the traveling waves topropagate from the fault to the end S, ρ f =

R f−Z0R f +Z0

is the fault reflection coefficient,

R f is the fault resistance, Z0 is the surge impedance of the line. ρs =Zs−Z0Zs+Z0

is thereflection coefficient at the end S and Zs is the impedance of sending end.

3.4 Traveling-Wave Fault Location Algorithms

3.4.1 Introduction

The accurate determination of fault location on transmission lines is a crucial issuefor the power system protection. A detailed review of different fault location tech-niques has been made in [16]. The theory of traveling waves has been recently used

7

3.4. Traveling-Wave Fault Location Algorithms

for fault location. This method is based on the measurements of fault-generatedtransient signals and the implementation of signal analysis techniques. A travelingwave based fault location technique was proposed in [17], the propagation velocityof the traveling wave, the line length and the reflection information were needed todetermine the location.

According to different operation modes, the traveling wave fault locators can beclassified into five types: A, B, C, D [18] and E [19]. The table below gives thedescriptions of these operation modes.

Table 3.1: Traveling Wave Fault LocatorsName Operation Mode

Type A capture the transients generated by the fault at a single end of theline, give the fault distance by analyzing these transient signals.

Type B capture the transients generated by the fault at double ends ofthe line by using a telecommunication channel to transmit theinformation and a timer to measure the time interval for the arrivalof transients at both ends.

Type C uses an active method which can inject an impulse into the linewhen detecting a fault on the line, then uses the time interval be-tween the impulse and the reflection to determine the fault posi-tion.

Type D measures the arrival times of the fault generated transients at bothend by utilizing a time synchronizing devise (e.g. GPS) at bothends.

Type E measures the transients generated by the fault at a single end ofthe line.

In most of traveling wave methods, the high frequency transients generated byfault are important for the determination of fault location, therefore some signalprocessing tools are needed to capture these transient signals correctly. Like themethod proposed in [7], the wavelet transform is used to improve the wave headdetection and the analysis of transient signals. In this thesis, the Single-endedmethod and Double-ended method of fault location are based on type A and typeD, separately, since for modern traveling wave locators, type B and C are obsoleteand are not used often. A wavelet transform is used to extract the transient featuresof fault-generated traveling wave signals [20].

8


3.4.2 Wavelet Transform

The Wavelet Transform is a powerful tool to analyze power system transients [21].Similar to a Fourier Transform (FT), wavelet transform can decomposes the signalinto different frequencies, and more than FT, by using wavelet transform, the signalcan be broken up into shifted and scaled versions of the mother wavelet. Thereare two forms of wavelet transform, the continuous wavelet (CWT) and discretewavelet transform (DWT).

The Continuous Wavelet Transform (CWT) of a signal x(t) is defined as:

CWTψx(a,b) =1√|a|

+∞ˆ

−∞

x(t)Ψ∗(

t−ba

)dt (3.11)

where Ψ(t) is called the mother wavelet, the scaling parameters a and b determinesthe oscillatory frequency, the length of the wavelet and the shifting position respec-tively. The application of wavelet transform in engineering areas usually requiresthe discrete wavelet transform, the equation of the discrete wavelet transform isgiven by:

DWT(k,n,m) =1√am

0∑x [n]Ψ

(k−nb0am

0am

0

)(3.12)

In DWT, the mother wavelet becomes Ψm,n(t) = a−m/2

0 Ψ(a−m0 t − nb0), where m

indicates frequency localization and n denotes time localization.

In CWT, the scaling parameters a and b are continuous. When the length andposition are changing continuously, a big mass of data are generated. It is not eco-nomical in practice, therefore the DWT is introduced to solve this problem, whereboth of the scaling parameters can be discretized. In DWT, the transient signalscan be efficiently analyzed with multi-resolution analysis and decomposed by us-ing two filters, one is a high pass filter (HPF) and the other is a low pass filter(LPF). The high pass filter is derived from the wavelet function (mother wavelet)and measures the details in a certain input. The low pass filter on the other handdelivers a smoothed version of the input signal and is derived from a scaling func-tion, associated to the mother wavelet [22]. Figure 3.3 shows the multiple leveldecomposition of a signal by using DWT.

9


Figure 3.3: Multiple level decomposition of the signal using DWT

As is shown in Figure 3.3, first, the signal is passed through the HPF H(n) anda LPF L(n), the outputs from both filters are decimated by 2, which means thesampling rate of the signal is reduced in half, then the detail coefficients and theapproximation coefficients at level 1 (A1 and D1) are obtained. After this, theapproximation coefficients at level 1 (A1) are sent to the second stage to be de-composed as before. Finally, the signal is decomposed at the required level byrepeating this procedure.

There are different kinds of mother wavelets, such as Symlets (sym), Daubechies(db), Coiflets (coif), etc. it is very important to choose the right type of motherwavelet for locating and determining different types of transients. Among these,the Daubechies wavelets are widely used for transient study, especially db4, whichis the most localized wavelet in the Daubechies family [23]. Therefore, in thisthesis, db4 mother wavelet is chosen to analyze the traveling wave.

3.4.3 Single-ended Method

In the single-ended fault location method, only the transients signals at one end arecaptured.

10


Figure 3.4: The fault location is at the first half of the line

As shown in Figure 3.4, if the fault is determined to be in the first half of the line,then τ will simply be the time interval between the first two peaks of the aerialmode at the busbar A.

τ = 3tA− tA = 2(x/v) (3.13)

Then, the fault location can be determined by

x =vτ

2(3.14)

where x is the distance to the fault, v is the wave velocity of aerial mode, and τ isthe time delay between two consecutive peaks of the transient signal in aerial modeat busbar A.

11


Figure 3.5: The fault location is at the second half of the line

Figure 3.5 shows the fault location is that in the second half of the line, then fromthe Bewley Lattice diagram, it is cleared that

τ = (3tB−BtA) = 2(

L− xv

)(3.15)

The fault location can be calculated by

x = L− vτ

2(3.16)

Here τ is the time delay between two consecutive peaks of the transient signal inaerial mode at busbar B.Then is to utilize the inherent time delay between the different modal componentsof the incoming three-phase signal to determine the region where the fault is lo-cated. Once the approximate region is determined, according to the equationsabove, the location of the fault can be calculated based on the Discrete WaveletTransform (DWT) of the aerial mode (mode 1) signal. The identification methodis based on the time delay τd between ground mode and aerial mode of the samethree phase signal.

• If τd < τl/2, the fault is suspected to be in the first half of the line

• If τd > τl/2, the fault is suspected to be in the second half of the line

where τl/2 is time delay between ground mode and aerial mode when the fault islocated at the center of the line.

12


The steps of the signal processing of the single ended traveling wave fault locationmethod are presented in Figure 3.6.

Figure 3.6: The flow chart of single-ended method

3.4.4 Double-ended Method

The double ended fault location method means the measurement is taken fromboth ends of the line. Usually a D-type locator requires the use of two devicessynchronized with each other in time (e.g. by means of GPS), installed on twoends of the line. The locator determines the moment at which the wave is comingto station A and station B, then they are used to calculate the distance from faultlocation. The examined network system and diagram of traveling waves is shown

13


in Figure 3.7.

Figure 3.7: The use of a D-type wave locator

The distance to the fault location from station A is found from the following de-pendence:

x =L+(tA− tB)× v

2(3.17)

where tA is the time at which the first wave generated at the fault location reachesstation A and tB is the time at which the first wave generated at the fault locationreaches station B.

14


Figure 3.8: The flow chart of double-ended method

Figure 3.8 shows the flow chart of the double ended traveling wave fault loca-tion method. The transient currents of each phase are recorded as IA, IB and IC.These calculated signals are first decomposed into their modal components by us-ing Clarke Transformation, which are turned into Iα , Iβ and I0, and then DWT isapplied for analyzing traveling wave transients. Finally, the arriving time of thetraveling wave can be well-recognized due to the inherent time-frequency localiza-tion characteristics of DWT.

15

Chapter 4

Fault Classification Algorithms

4.1 Introduction

The faults which occur in power system can cause damage to the equipment ofthe power system and also affect the power quality. In addition to locating thefault, it is also very important to determine the fault type as soon as possible, andthen the corresponding relay operation can clear the fault. Nowadays, the faultgenerated transients signals are widely used in the fault classification. Based onthese fault transients, several algorithms have been proposed for fault classification[24][25]. Among them, Wavelet transform (WT), which has the desirable time-frequency localization ability, is considered as an effective tool for analyzing thefault transients [26]. The wavelet transform is a powerful method of signal analysisand image processing [27]. The conventional Fast Fourier Transform is based on aFourier series model [8], which can give a constant resolution for all frequencies,whereas the Wavelet Transform uses multi-resolution technique by which differentfrequency spectrum are analyzed with different resolutions [28].

4.2 Wavelet Energy

The fault classification algorithm can be proposed based on the wavelet energy atdifferent levels. Based on Parseval’s theorem, the energy of the transient signalcan be decomposed at different levels [29]. The ratio of wavelet energy at differentlevel can be regarded as a criterion for the fault classification. Mathematically thewavelet energy can be presented as:

EDi =N

∑j=1

∣∣D2i j

∣∣ , i = 1, . . . , l (4.1)

EAi =N

∑j=1

∣∣A2i j

∣∣ (4.2)

16

4.2. Wavelet Energy

where i = 1, . . . , l is the wavelet decomposition level from level 1 to level l. Nis the number of the coefficients of detail or approximate at each decompositionlevel. EDi is the energy of the detail at decomposition level and EAi is the energyof the approximate at decomposition level l.

17

Chapter 5

Modeling of Power System inATP/EMTP

5.1 Introduction

The transient simulation software used for modeling of the power system is theAlternative Transients Program (ATP/EMTP)[30]. As a program with wide in-ternational use for digital simulation of electromagnetic transients in power sys-tem, ATP contains extensive modeling capabilities for transmission lines, cables,breakers, loads, converters, protection devices, non-linear elements, electromag-netic coupling, and major power electronics devices and equipment. ATP/EMTPconsists of various separate supporting programs, data initialization files and thesolver program. A graphical user interface called ATPDraw was introduced as apreprocessor for ATP, it assists to create and edit the model of the electrical net-work to be simulated interactively[31]. ATPDraw is a Microsoft Windows baseduser interface; the main window is shown as the figure below.

18

5.2. Models of Transmission System

Figure 5.1: The Main window of ATPDraw

5.2 Models of Transmission System

5.2.1 Transmission Line

ATP-EMTP offers a few models that have been used for transmission line system[30]:

• PI: The PI model is a lumped parameters model, it is useful for short lines.

• Bergeron: The Bergeron model is a constant-frequency model which is suit-able for studies at fundamental frequency in steady state.

• Semlyen: The Semlyen is a frequency-dependent fitted model, but it is notavailable for high frequency oscillations.

• Noda: This frequency-dependent model is used in the phase domain.

• J. Marti: J. Marti is a common frequency-dependent model. It is suitablefor traveling wave simulation in long lines. This model can develop a morereliable model and a wider frequency range for transmission lines by usingthe constant matrix than earlier frequency model such as the Semlyen model.

In this thesis, there are two kinds of line models: A 400 kV transmission line rep-resented by lumped parameter sections, and a 230 kV line modeled by using aconstant parameter line model (Bergeron model) according to the EMTP reference[1].

19

5.2. Models of Transmission System

5.2.2 CTs and CCVTs

In high voltage transmission lines usually Current Transformers (CTs) and Cou-pling Capacitor Voltage Transformers (CCVTs) are used for monitoring the trav-eling wave transients. In this thesis, the CTs and CCVTs are introduced to studyhow the voltage or current waveforms may look when the traveling wave arrivesand partially reflects from these coupled discrete capacitance. CTs are applied atthose locations where relays are to be connected. The following figure shows theCTs equivalent circuit and the corresponding EMTP model .

Figure 5.2: CTs Equivalent Circuit

Figure 5.3: EMTP model of CTs

CCVTs are used for collecting the voltage signals for monitoring, protection relaysand control application.The equivalent circuit of CCVTs is shown in Figure 5.4.

Figure 5.4: CCVTs Equivalent Circuit [1]

20

5.3. Models of Fault Cases

As can be seen from Figure 5.4, it is a generic CCVTs model for relaying stud-ies, the components are simplified as: coupling capacitor (C1, C2) ; compensatingreactor (Rc, Xc, Cc); step-down transformer (Rp, Xp, Cp, Rs, Xs, Rm, Xm); ferrores-onance suppression circuit (R f , L f , C f ); and the burden (Rb). The correspondingEMTP model is shown in Figure 5.5. The marked ”CT” in the figure is a step-downtransformer. The models and the parameters of CTs and CCVTs in this thesis arecollected from the EMTP reference [1].

Figure 5.5: EMTP model of CCVTs

5.3 Models of Fault Cases

As is presented in Section 2.1, there are two main types of overvoltage in a powersystem, external and internal overvoltage. For the external case, the lighting isconsidered as the major source to damage the power system and among the differ-ent lightning strike conditions, the shielding failure is the more severe than backflashover due to more significant voltage [32]. Hence in this thesis, a direct light-ing strike on a phase conductor is selected as the study case for external fault. Forinternal case, the single line-to-ground fault is chosen for study because of it is themost common type of fault on transmission lines [33].

5.3.1 Single Line-to-Ground Fault

Single line-to-ground (SLG) fault is very common in transmission system. It canbe classified into two categories: solid fault and arcing faults [34]. A solid faultoccurs when the conductors are solidly connected, during this fault, the currentflow through the connection is very high. For an arcing fault, the air becomes

21


conducting, due to the current flow through ionized air. The energy in a solidfault is released in the conductors in the system, whereas the energy in an arcingfault is dissipated at the point of the fault, which may be inside equipment or inthe surrounding environment. Another difference is, in an arcing fault, the faultimpedance involves air, therefore the fault impedance in an arcing fault is higherthan that in a solid fault, accordingly, the current is lower. The most importantdifference is that the solid fault can make a very rapid change in voltage, but arealistic arcing fault will have its current increases more slowly. Therefore it isnecessary to distinguish these two kinds of SLG fault.

Solid Fault

In this thesis, the solid fault is simply modeled by using a time-control switch inseries with a small grounded resistance. The representation of SLG fault is shownin the Figure 5.6 and Figure 5.7.

Figure 5.6: Equivalent Circuit of Solid Fault

Figure 5.7: EMTP Model of a Solid Fault

Arcing Fault

The arc model can be divided into the primary arc and the secondary arc, the pri-mary arc happens when the fault occurs, which means before the breakers trip,

22


whereas the secondary arc refers to the arc after the breakers trip. Hence only theprimary arc was considered in this study.

For this work, a dynamic arc model has been implemented in ATP/EMTP basedon the Kizilcay fault arc model [35]. It simulates the dynamic interaction betweena fault arc and the power network based on the energy balance in the arc column.According to this model, the dynamic arc characteristics can be described by thefollowing differential equation:

dgdt

=1τ(G−g) (5.1)

τ =αIL

(5.2)

where g is the time-varying arc conductance, G is the stationary arc conductanceand τ is the time constant, which can be obtained by fitting the experimental volt-ampere cyclograms. In the second equation, I is the peak current of the arc volt-ampere characteristic curve, α is constant, normally set α = 2.85× 10−5 cm·s/Afrom the fitting. L is the arc length, which is considered to be constant in thismodel. The stationary primary arc conductance is determined by

G =|i|

V ·L(5.3)

where |i| the arc instantaneous current, V is the arc voltage gradient and L is the arclength, which is considered to be constant in this model. Experimentation showsthat over the range of current 1.4 kA to 24 kA, the average arc voltage gradient isV = 15 V/cm. In this case, L = 140 cm, and I = 1861 A, then τ = 3.79× 10−4 s,G = |i|/2.1kV

dgdt

=1τ(G−g)

Integrating the above formula, we can get

g(t) = G(t−4t)−G(t−4t)−g(t−4t)e−4t/τ (5.4)

This can be implemented by using Type-58 TACS/MODELS (a controlled integra-tor) in ATP/EMTP.

23


Figure 5.8: Arc model in ATP

As is shown in Figure 5.8 to get the absolute value. Then it is used with V and Lto give G, V L = 2100 is already known from above equations. Then the G needto minus the arc conductance g, which is updated at each step. Next, the result isdivided by the time constant τ = 3.79×10−4, and finally the resulting value is fedinto the Type-58 integrator which gives the instantaneous arc conductance . Thesimulation results are shown in the figures below.

24


Figure 5.9: Currents and voltage for the arcing fault

Figure 5.10: The waveform of arc resistance

From the above figures, it can be found that the waveform of arc voltage is sim-ilar to the square wave and the current is approximately the sine wave, and thewaveform of arc resistance is more like the pulse wave.

5.3.2 Lightning Fault

In ATP-EMTP, a lightning stroke is represented as a current source with lightning-path impedance. The value of lightning-path impedance is typically assumed equal

25

5.4. The accuracy of the models

to 400Ω, which was derived by Bewley [36]. The lightning model is using the Hei-dler (F. Heidler) model [37], which is recommended by the CIGRE study group[38]. This model used can present the time-varying lightning current with an ad-justable current steepness, the Heidler model can be determined by this equation[38]:

i(t) =I0

h·

(t

τ1

)10

1+(

tτ1

)10 e−t

τ2 (5.5)

where I0 is the peak current, h the correction factor (2 ∼ 10) for the peak current,τ1 the time constant for the first wave, and τ2 the time constant for the wave tail.In this study, Heidler model is selected as the lightning source. Figure 5.11 is theHeidler model in EMTP.

Figure 5.11: Heidler model in EMTP

5.4 The accuracy of the models

5.4.1 Study Case

Input data gathered from the article [39] for the line models consist of conductor’sgeometric configuration, their diameters, geometry of bundles. Line parameterswere calculated using LINE CONSTANTS routine of the EMTP. As is shown inFigure 5.12, the JMARTI model is used for the transmission line sections, and thefrequency-dependent model is used for propagation within towers

26


Figure 5.12: Plan of the transmission line implemented in the EMTP

27


Figure 5.13: Circuit for EMTP analysis

5.4.2 Results of the Study Case

Figures 5.14, 5.15, 5.16 and 5.17 illustrate the comparison between the results fromthe article [40] and simulation, including the tower top voltage, the cross-arm ofupper, middle and lower position and the voltage induced into the phase conductorfrom the ground wires, for phase C, B and A respectively.

28


Figure 5.14: Tower top voltage of study case

Figure 5.15: Phase C voltages of study case

Figure 5.16: Phase B voltages of study case

29


Figure 5.17: Phase A voltages of study case

From these simulation results, it can be found that the shape of recorded wave-form and simulation results are similar, the different amplitudes are because of thelightning source for these two cases have different order of magnitude. Therefore,ATP-EMTP is a reliable software in simulating the transient problem of transmis-sion system.

30

Chapter 6

Fault Location

To verify the fault location algorithm proposed in this thesis, a novel extra highvoltage transmission system is first considered, the total length of the transmis-sion line is 150 km. The line is represented by Clarke-distributed model (with thetransposition).Modeling parameters:The output signals are sampled at the rate fs = 100kHz. Fault resistance R f =0.0001Ω, the detailed parameters used for simulation are shown in Table 6.1 andTable 6.2.

Table 6.1: System ParametersSource 1 Source 2

Z1 = 2.11+ j56.4 Z1 = 0.816+ j23.6

Z0 = 28.16+ j134.46 Z0 = 11.68+ j40.27

VS = 400e j0 kV VS = 400e− j20 kV

Table 6.2: Line ParametersPositive Sequence Zero Sequence

R1 = 0.018 Ω/km R0 = 0.161Ω/km

L1 = 0.864 mH/km L0 = 0.864 mH/km

C1 = 0.013 µF/km C0 = 0.010 µF/km

Then the velocity of traveling waves can be calculated as:

v1 =1√

L1C1= 2.943×108 m/s (6.1)

v0 =1√

L0C0= 2.147×108 m/s (6.2)

31

6.1. No Shunt Capacitance

6.1 No Shunt Capacitance

Three kinds of faults are simulated and the proposed technique is applied to analyzethe performance of the algorithm.

6.1.1 Solid Fault

The simulated system by ATP/EMTP is shown in Figure 6.1. The switch is closedat 0.02 s, i.e. after one AC cycle, the fault is applied to the unfaulted circuit.

Figure 6.1: The 400kV simulated system for solid fault

Single Ended Method

An AG fault (phase-A to ground) is simulated, at 120 km from bus 1. The voltagewaveforms at the sending end and the aerial mode voltage are shown in the Figure6.2. For the wavelet analysis, the detailed coefficient at level 5 is used to detectthe first and second transient instants at bus 1, since level 5 contains the highestfrequency component among the total five levels. Figure 6.3 shows the detailedcoefficient at level 5 of ground mode.

32


Figure 6.2: DWT decomposition for aerial mode signal of solid fault

33


Figure 6.3: DWT decomposition for ground mode signal of solid fault

From Figure 6.2 and Figure 6.3, it can be calculated that:

τd = 20.56−20.41 = 0.15ms > τl/2 = 0.09ms

Therefore the fault is located at the second half of the transmission line,

x = 150×103− (20.62×10−3−20.41×10−3)×2.943×108

2= 119.09km

Error% =

∣∣119.09×103−120×103∣∣

150×103 ×100% = 0.607%

Double Ended Method

The current signals from both transmission line ends are used to detect the first tran-sient instants tA and tB at buses 1 and 2 (as shown in Figure 3.7). The identification

34


of tA and tB are shown in Figure 6.4. Since the line length and the propagationvelocity of aerial modes are known, the fault point location can be calculated.

35


Figure 6.4: DWT Decomposition for AG fault at 120km from Bus 1

36


As is shown in the Figure 6.4, tA and tB are the detected initial transient instants atbus 1 and bus 2 respectively.

x =150×103 +(20.41×10−3−20.11×10−3)×2.943×108

2= 119.15km

Error% =

∣∣119.15×103−120×103∣∣

150×103 ×100% = 0.567%

6.1.2 Arcing Fault

To study the characteristics of the arcing fault in a transmission system, an arcingfault model is connected to a 400 kV transmission line. The fault location is 10 kmfrom busbar 1. The ATP/EMTP model is shown in Figure 6.5.

Figure 6.5: The 400kV test system in ATP/EMTP

The simulation results are shown in the figures below.

37


Figure 6.6: Currents and voltage for the arcing fault

Figure 6.7: The waveform of arc resistance

38


Figure 6.6 and Figure 6.7 show that the arc voltage (black line) is similar to thesquare wave and the current (red line) is approximately a sine wave, and the wave-form of arc resistance is more like the pulse wave, as is discussed in Section 5.3.2.It’s clear that the arc has a highly nonlinear behavior.

Single Ended Method

The voltage waveform of arcing fault at bus1 is shown in Figure 6.8, it can befound that for the arcing fault, the detail coefficient at level 5 is much smaller thanthe solid fault. Because the resistance for an arcing fault is far smaller than thepermanent grounded fault.

From Figure 6.8 and Figure 6.9, it can be calculated that

τd = 20.09−20.08 = 0.01ms > τl/2 = 0.09ms

Therefore the fault is located at the second half of the transmission line,

x = 150×103− (20.15×10−3−20.08×10−3)×2.943×108

2= 10.302km

Error% =

∣∣10.302×103−10×103∣∣

150×103 ×100% = 0.201%

Double Ended Method

The identification of t1 and t2 in arcing fault case is shown in Figure 6.10. Then thefault point location can be calculated as before.

x =150×103 +(20.08×10−3−20.52×10−3)×2.943×108

2= 10.25km

Error% =

∣∣10.25×103−10×103∣∣

150×103 ×100% = 0.164%

39


Figure 6.8: DWT decomposition for aerial mode signal of arcing fault

40


Figure 6.9: DWT decomposition for ground mode signal of arcing fault

41


Figure 6.10: The locator response for arcing fault at Bus 1 and Bus 2

42


Figure 6.11: The 400 kV simulated system of lightning fault

6.1.3 Lightning Fault

Assume that the lighting stroke hits one of the three phase line, the location is 60 sshape is introduced in each phase because of the coupling between phases. Thesurge parameters are illustrated in Table 6.3.

Table 6.3: Surge parameters of Heildler modelAmplitude τ1 τ2 n

20 kA 2.5×10−6 s 4×10−5 s 1

The simulated system by ATP/EMTP is shown in Figure 35.

Single Ended Method

The current and voltage waveform at the sending end and at the receiving endare shown in the figures below. The first figure shows the recorded three phasevoltages, it can be seen that for lightning fault, the magnitude of voltage wave ismuch bigger than for the solid fault and the arcing fault.From Figure 6.12 and Figure 6.13, it can be calculated that

τd = 20.28−20.21 = 0.07ms > τl/2 = 0.07ms

Therefore the fault is located at the first half of the transmission line and its locationcan be calculated as:

x =(20.61×10−3−20.21×10−3)×2.943×108

2= 58.867km

Error% =

∣∣58.867×103−60×103∣∣

150×103 ×100% = 0.755%

43


Figure 6.12: DWT decomposition for aerial mode signal of lightning fault

44


Figure 6.13: DWT decomposition for ground mode signal of lightning fault

45

6.2. With Shunt Capacitance

Double Ended Method

The identification of t1 and t2 is shown in Figure 6.14, the aerial mode voltagesat bus1 and bus 2 are illustrated, the figures below are the corresponding detailcoefficient at level 5. The calculation method is the as same as before.

x =150×103 +(20.21×10−3−20.31×10−3)×2.943×108

2= 60.283km

Error% =

∣∣60.283×103−60×103∣∣

150×103 ×100% = 0.189%

6.1.4 Conclusion

This chapter presents two fault location algorithms that use single ended and doubleended recordings of fault voltage signals. First these fault generated transientssignals are decoupled into their modal components and then transformed into thetime-frequency domain by using the DWT. Then both the single-ended methodand double-ended method are applied for fault location. Various types of faults atdifferent location were tested in this chapter, the accuracy of the proposed methodfor different cases is satisfactory with a maximum error of 0.755 %.

6.2 With Shunt Capacitance

The analyses above neglected the effect of the busbar capacitance, but in practice,the substation equipment connected to it, such as transformer, breaker, CTs, PT,contain stray capacitance to ground. Let us model this as shown in Figure 6.15,where the surge is assumed to be a rectangular wave Uq, C is the capacitance toground, and Z1 and Z2 are the different wave impedance for two lines.

Figure 6.15: The traveling wave reaching a busbar capacitance

46


Figure 6.14: The locator response for lightning fault at Bus 1 and Bus 2

47


Figure 6.16: The equivalent circuit of Figure 6.15

Figure 6.16 shows the equivalent circuit, then

2U1q = I1Z1 + I2qZ2 (6.3)

I1 = I2q +CdU2q

dt= I2q +CZ2

dI2q

dt(6.4)

From the equations above,

I2q =2U1q

Z1 +Z2(1− e−

tT ) (6.5)

U2q = I2qZ2 =2Z2

Z1 +Z2U1q(1− e−

tT ) = αU1q(1− e−

tT ) (6.6)

where T = Z1Z2C/(Z1+Z2) is the time constants, α = 2Z2/(Z1+Z2) is the voltage refrac-tion coefficient. Since U1 =U1q +U1 f =U2q, therefore

U1 f =U2q−U1q =Z2−Z1

Z2 +Z1U1q−

2Z2

Z1 +Z2U1q(1− e−

tT ) (6.7)

It can be found that when t = 0, U1 f = −U1q. This is because the voltage on thecapacitance cannot have sudden change, t = 0 can be seen as short circuit (Z2 = 0).Then the reflected voltage wave will vary according to the exponential relation, asis shown in Figure 6.17, where t =+∞, U1 f = βU1q, where β = (Z2−Z1)/(Z1+Z2).

Figure 6.17: The reflected wave and refracted wave

48


Therefore, it can be found that the effect of shunt capacitance is to make the steep-ness of the incoming wave broaden. The steepness of U2q is dU2q

dt = 2Z1CU1qe−

tT

6.2.1 The Busbar Influence on The Wave Shape

In the simulation case, the first one is a line to ground fault occurring 60 km frombusbar M. The values of capacitance are used: 0 μF, 0.1 μF and 0.01 μF. Figure 6.18is the EMTP model for this case.

Figure 6.18: EMTP model of single-line to ground fault with different capacitance.

The wave-front shape of the fault phase voltages and currents at busbar M withC = 0 µF,C = 0.1 µF and C = 0.01 µF are shown in Figure 6.19, separately.

Figure 6.19: The voltage (left) and current (right) wave-front for SLG fault, withdifferent capacitance at busbar M

49


The second case is arcing fault at 10 km of busbar M, the wave-fronts of voltagesand currents are represented in the figures below.

Figure 6.20: The voltage and current wave-front with different capacitance forarcing fault

Figure 6.21 shows the wave-front of lightning disturbance at 120 km of busbar M.

Figure 6.21: The voltage and current wave-front with different capacitance forlightning disturbance

From all the simulated cases in this section, it can be found that as the capacitanceincreases, the wave-front of voltage is flattened, the average rate of rise and theamplitude of the resulting wave decrease. In addition, the slope of the wave-frontof current and the amplitude are rising as the capacitance increases, in contrast tothe way the voltage changes.

50


6.2.2 The Influence on The Location Method

Arcing Fault

• Cbus = 0 µF

τl/2 = 20.40−20.31 = 0.09ms

Table 6.4: The characteristics of arcing fault when Cbus = 0 µF

Time records Single Method Double Method

T1M T2M T0M T1N Td Location Error Location Error(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.10 20.09 20.15 20.53 0.01 8.830 -0.78 10.246 0.16

60 20.33 20.26 20.66 20.36 0.07 58.867 -0.75 60.283 0.19

120 20.61 20.46 20.66 20.15 0.15 120.566 0.38 120.622 0.41

• Cbus = 0.01 µF

τl/2 = 20.40−20.31 = 0.09ms

Table 6.5: The characteristics of arcing fault when Cbus = 0.01 µF



10 20.10 20.09 20.16 20.53 0.01 10.301 0.20 10.246 0.16

60 20.33 20.26 20.67 20.36 0.07 60.339 0.23 60.283 0.19

120 20.61 20.46 20.67 20.16 0.15 119.095 -0.60 119.150 -0.57

• Cbus = 0.1 µF

τl/2 = 20.40−20.30 = 0.10ms

51


Table 6.6: The characteristics of arcing fault when Cbus = 0.1 µF


T1M T2M T0M T1N Td Location Error Location Error

(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.09 20.08 20.16 20.53 0.01 8.830 -0.78 10.246 0.16

60 20.33 20.25 20.67 20.36 0.08 58.867 -0.75 60.283 0.19

120 20.61 20.46 20.67 20.16 0.15 120.566 0.38 120.622 0.41

Solid Fault

• Cbus = 0 µF

τl/2 = 20.35−20.26 = 0.09ms

Table 6.7: The characteristics of solid fault when Cbus = 0 µF



(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.28 20.21 20.61 20.31 0.07 58.867 -0.75 60.283 0.19

120 20.56 20.41 20.62 20.10 0.15 119.095 -0.60 120.622 0.41

• Cbus = 0.01 µF

τl/2 = 20.35−20.26 = 0.09ms

52


Table 6.8: The characteristics of solid fault when Cbus = 0.01 µF



(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.28 20.21 20.62 20.31 0.07 60.338 0.23 60.283 0.19

120 20.56 20.41 20.61 20.11 0.15 120.566 0.38 119.150 -0.57

• Cbus = 0.1 µF

τl/2 = 20.35−20.26 = 0.09ms




(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.08 20.21 20.62 20.31 0.07 60.338 0.23 60.283 0.19

120 20.56 20.41 20.61 20.11 0.15 120.566 0.38 119.150 -0.57

Lightning Fault

• Cbus = 0 µF

τl/2 = 20.35−20.26 = 0.09ms

53


Table 6.10: The characteristics of lightning fault when Cbus = 0 µF



10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.28 20.21 20.62 20.31 0.07 60.338 0.23 60.283 0.19

120 20.57 20.41 20.61 20.10 0.16 120.566 0.38 120.622 0.41

• Cbus = 0.01 µF

τl/2 = 20.35−20.26 = 0.09ms

Table 6.11: The characteristics of lightning fault when Cbus = 0.01 µF



(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.28 20.21 20.62 20.31 0.07 60.338 0.23 60.283 0.19

120 20.56 20.41 20.61 20.11 0.15 120.566 0.38 119.150 -0.57

• Cbus = 0.1 µF

τl/2 = 20.35−20.26 = 0.09ms




(ms) (ms) (ms) (ms) (ms) (km) (%) (km) (%)

10 20.05 20.04 20.11 20.48 0.01 10.301 0.20 10.246 0.16

60 20.08 20.21 20.62 20.31 0.07 60.338 0.23 60.283 0.19

120 20.57 20.41 20.61 20.11 0.16 120.566 0.38 119.150 -0.57

54


6.2.3 Conclusion

From the discussion above, it can be concluded that the busbar capacitance canchange the shape of wave-fronts when the traveling wave reaches the busbar, butthere is no big influence on the time when the wave-front reaches the busbar. Theerror of the Single-end method is relatively higher than the error of the Double-endmethod, which means the capacitance influence is smaller on the time of first wavearriving the busbar than the second wave. Overall the busbar capacitance will nothave big effect on location method based on traveling wave.

55

Chapter 7

Fault Classification

The power system model for case study is based on the EMTP reference modelfor transmission line relay testing, which is introduced by the IEEE PES PowerSystem Relaying Committee (PSRC) WG D10 [1]. The one-line diagram of thestudied system and its ATP model are shown in Figure 7.1.

Figure 7.1: A 230kV transmission line model

The needed parameters taken from the reference are indicated in Table7.1 and Ta-ble7.2.

Table 7.1: Parameters of Source1Positive-sequence impedance Zero-sequence impedance

Z1 = 6.1+ j16.7 Z1 = 2.7+ j8.37

Table 7.2: Parameters of Source2Positive-sequence impedance Zero-sequence impedance

Z1 = 0.69+ j4.12 Z0 = 0.34+ j4.77

The geometrical dimensions of the line are shown in Figure 7.2.

56

Chapter 7. Fault Classification

Figure 7.2: Geometrical data of the line considered[2]

The line parameter calculations for the fundamental frequency f = 50Hz are car-ried out by using Line Parameters GUI in MATLAB, their values are shown inTable

Table 7.3: Line Parameters of 230 kV systemPositive Sequence Zero Sequence

R1 = 0.029Ω/km R0 = 0.158Ω/km

L1 = 1.030 mH/km L0 = 2.297 mH/km

C1 = 0.011 µF/km C0 = 0.008 µF/km

The wave traveling speed and the surge impedance values are:

v1 =1√

L1C1= 2.94×108 m/s Z1 =

L1

C1= 303Ω (7.1)

57

7.1. No CTs and CCVTs

v0 =1√

L0C0= 2.37×108 m/s Z0 =

L0

C0= 545Ω (7.2)

7.1 No CTs and CCVTs

In this subsection, each of the three kinds of faults is simulated as occurring at60 km from busbar M. In each case, the fault time is 0.02 s, the sampling time pe-riod is from 0 s to 0.08 s, the signals are sampled at a frequency of 10 MHz, andall the voltage signals are collected directly, i.e. without modeling the effect of aCCVTs or CTs. Since the modal measurement contains the fault information ofits own line and can reflect the fault characteristic of the corresponding line, theaerial mode is employed in this thesis. By using Clarke transformation, the phasecurrent and voltage are transformed to modal voltage Va1 and current Ia1, respec-tively. The aerial mode of phase voltage and current for all the three cases areshown in Appendix A. to perform well. Using multi-resolution wavelet analysisof all the three voltage signals their detail coefficients D1 to D5 components areextracted. The five details coefficients D1 to D5 (high frequency components) con-tain harmonics ranging from 2.5 MHz - 5 MHz, 1.25 MHz - 2.5 MHz, 0.625 MHz -1.25 MHz, 312.5 kHz - 625 kHz, 156.25 kHz - 312.5 kHz, respectively. The rangeof approximation A5 (low frequency component) is from 0 to 156.25 kHz.

58


Figure 7.3: The wavelet decomposition D1 of modal voltage for three kinds of fault

Figure 7.3 shows the detail decomposition D1 waveform for solid fault, arcingfault and lightning fault. When a fault occurs in the power system, it can be seenthat variations within the decomposition coefficients of the voltage signal containuseful fault signature.The total energy of a discrete time signal can be representedby:

E =∞

∑n=−∞

|x(n)|2 (7.3)

For calculating the energy of a signal for a particular duration, the limit of datanumbers will change accordingly. A program was developed in MATLAB to find

59


the energy in the first five cycles . The energy for different details and approxima-tions are shown in Table 7.4. (More information can be found in Appendix).

Table 7.4: The wavelet energy for different details and approximationsSolid Fault Arcing Fault Lightning Fault

D1 3.17×1012 3.60×104 6.96×1013

D2 1.00×1012 5.52×102 2.91×1013

D3 1.47×1011 6.64×101 4.05×1012

D4 5.89×1010 2.13×102 1.95×1012

D5 5.06×109 5.30 1.04×1011

A5 1.16×1011 1.15×1011 1.24×1011

The table above shows that all three cases have significant energies at A5 (0 -156.25 kHz) , but the lightning fault has more energy than the other cases, amongthe five frequency bands, D1 (2.5 MHz - 5 MHz) has the maximum value. Thisis because the lightning current can be seen as introducing a high frequency pulsewave to the system, and there are more high-frequency components in this case.For the single-line to ground fault and the arcing fault, they are both line to groundfaults, it can be found that the energy for an arcing fault is lower than for a single-line to ground fault. The reason is that the value for the non-linear resistance ofarcing fault is bigger than that of single-line to ground fault.

Based on the multi-resolution wavelet analysis, a criterion can be proposed accord-ing to the distribution of low and high frequencies [41]. The energy ratio of highand low frequency band k can be expressed as

k =∑j

N∑

m=1i2dm

j

N∑

m=1i2am

(7.4)

where, idmj

is the high-frequency components of transient current of the m-ht pointat j scale, iam is the low-frequency components of transient current of the m-htpoint, N is number of the sampling points.

Then, according to Table 7.4, it can be calculated that

karc = 3.2×10−7, kground = 38 klightning = 8.5×102

60

7.2. With CTs and CCVTs

The differences of the energy ratio for the three cases are significant, the criterioncan be revised by set k1 = 1 and k2 = 100,

• if k < k1, it can be identified as an arcing fault,

• if k1 < k < k2, it is an instantaneous solid single-line to ground fault,

• if k > k2, it is a lightning fault.

7.2 With CTs and CCVTs

In reality, the relay will collect the voltage signals and current signals from aCCVTs and CTs. In order to check if the CTs and CCVTs will influence theaccuracy of the fault classification algorithm, the system with CTs and CCVTsmodels are simulated by ATP/EMTP. By using Clarke transformation, the phasecurrent and voltage are transformed to modal voltage Va1 and current Ia1, respec-tively. The waveform are presented in Appendix B. Then, make the decompositionfor the three kinds of faults, and the decomposition details of aerial mode voltagesare shown in the Appendix C separately. It is noticeable that the waveform of thesethree kinds of faults did not change too much compared to the previous results,but there are more high-frequency components at D1. The Figure 7.4 shows thewavelet decomposition of D1 for the three cases.

61


Figure 7.4: The wavelet decomposition D1 of modal voltage for three kinds of fault

From Figure 7.4 , it can be found that before the fault inception, there is hardly anyhigh-frequency component because the waveforms are very smooth; while afterfault inception, the waveforms of the modal voltage and current become turbulentdue to the large amount of transient information. The energies of different detailsand approximations are shown in Table 7.5.

62


Table 7.5: The wavelet energy for different details and approximationsSolid Fault Arcing Fault Lightning Fault

D1 270.67 7.28×10−5 5633.07

D2 29.03 1.53×10−6 900.87

D3 1.21 1.66×10−7 49.09

D4 2.06×10−2 5.19×10−7 1.09

D5 7.28×10−5 2.08×10−8 3.77×10−3

A5 609.80 575.04 640.82

According to Table 7.5, it can be calculated that

karc = 1.3×10−7, kground = 0.49 klightning = 10

To study the accuracy of the method, more cases of different fault locations weresimulated.

Fault location at 30 km

Table 7.6: The wavelet energy for different details and approximations (30 km)Solid Fault Arcing Fault Lightning Fault

D1 307.08 4.49×10−5 6185.09

D2 32.26 9.59×10−7 828.07

D3 1.32 9.91×10−8 25.31

D4 2.55×10−2 3.02×10−7 1.10

D5 1.29×10−4 1.77×10−8 4.33×10−3

A5 528.89 542.46 642.20


karc = 8.5×10−8, kground = 0.64 klightning = 11

63

7.3. Conclusion

Fault location at 120 km

Table 7.7: The wavelet energy for different details and approximations (120 km)Solid Fault Arcing Fault Lightning Fault

D1 225.80 2.13×10−5 5449.03

D2 24.53 4.49×10−7 640.70

D3 1.07 4.97×10−7 49.46

D4 1.99×10−2 1.55×10−7 1.07

D5 4.77×10−5 1.99×10−8 3.13×10−3

A5 564.32 582.29 677.08


karc = 3.8×10−8, kground = 0.45 klightning = 9.1

The differences of the energy ratio for the three cases are significant, thus the cri-terion can be proposed by set two values k1 = 0.01 and k2 = 1,

• if k < k1, it can be identified as an arcing fault,

• if k1 < k < k2, it is an instantaneous solid single-line to ground fault,

• if k > k2, it is a lightning fault.

7.3 Conclusion

By comparing the case in Section 7.1 and Section 7.2, it can be concluded that forall the three kinds of faults, the wavelet energy trends of different detail coefficientshave no big change. Only the threshold k needs to be scaled down. And accordingto the data in Table 7.4, Table 7.5, Table 7.6 and Table 7.7, it can be found thatas the frequency band decreases (from D1 to A5), the wavelet energies decreasefor all the three kinds of faults, but the lightning fault always has more energythan the other cases. In addition, among the five detail coefficients, D1 (2.5 MHz-5 MHz) has the maximum value. This is because the lightning current can be seenas introducing a high frequency pulse wave to the system, there are more high-frequency components in this case. Furthermore, for the single-line to ground fault

64

7.3. Conclusion

and the arcing fault, they are both line to ground fault, it can be found that theenergy for an arcing fault is lower than for a single-line to ground fault, the reasonis that the value for the non-linear resistance of arcing fault is bigger than that ofsingle-line to ground fault.

65

Chapter 8

Summary

The first part of the thesis is about the validation on the accuracy of the softwareATP/EMTP. A study case of transmission line with a lightning source was simu-lated and then compared with the results reported from experiment literature. Thestudy shows that ATP-EMTP is an reliable software in simulating the transientproblem of transmission system, thus ATP-EMTP is chosen as main simulationtool for this thesis work.

Then two types of faults, i.e. single line-to-ground fault and lightning fault are pre-sented and studied as simulation cases in terms of location and classification. Thetraveling wave based fault location algorithms are analyzed, the simulation resultspresented in the preceding Section 6.1 and Section 6.2 show the validity of theproposed algorithm, the percentages of errors for locating the three kinds of faultsare very small. In addition, the influence of busbar capacitance on the transmissionline is considered, it can be found the busbar capacitance can change the shapeof the wave-front when the traveling wave reaches the busbar, but there is no biginfluence on the time when the wave-front reaches the busbar, therefore the busbarcapacitance does not affect the accuracy of the fault location algorithm proposedin this thesis. Furthermore, the fault classification based on the decomposition offault transient by wavelet transform was examined. A criterion can be proposedaccording to the distribution of low and high frequency: the energy ratio of highand low frequency band is set as the threshold to distinguish these three kinds offaults. Moreover, the influence of CTs and CCVTs on this algorithm is simulated,from which it can be concluded that for all the three kinds of fault, the waveletenergy trends of different detail coefficients have no change, the threshold k can bescaled down according to the ratio of the transform.

The advantage of the proposed fault location and classification algorithm is thatonly the voltage signals at the sending end are used (for double-ended method offault location, the voltage samples at the receiving end are also needed). The faultlocation algorithm presented in this thesis is based on the time interval of the fault-generated traveling wave at source ends and the fault distance is calculated by thistime and the wave speed. Therefore the accuracy of this algorithm is independentof the fault types and the stray capacitance.

66

Chapter 8. Summary

The adaptive fault classification scheme in this thesis is based on the wavelet energyin different frequency bands of the fault signals. It has been tested under the twotypes of transients: single line-to-ground fault and direct lightning stroke to phaseconductor, at different locations. Being more precise, the SLG fault is dividedinto solid fault and arcing fault, this is very necessary since the arcing fault lastslonger than the solid fault generally, and more heat will be created during an arcingfault. In order to classify the faults fast and efficiently, a threshold for the waveletenergy ratio is used to distinguish the proposed three faults. The simulation resultsin Section 7.1 and Section 7.2 demonstrate that the fault classification algorithmin this thesis can detect lightning faults and SLG fault, even solid fault and arcingfault cases correctly.

Finally, the use of Wavelet Transform to locate the fault and distinguish the faulttypes has been presented in this thesis. The proposed fault location and classifica-tion algorithms are simple and accurate, they are sensitive and can be used as anadditional routine in transmission lines protective relays.

In the future, the work can be expanded for more models with different faultimpedances and with different types of terminal structures. The influence of noiseand wavelet types will also be studied for both fault location and classification algo-rithms. And if possible, experimental work should be done to verify the proposedalgorithms, since they are derived from pure theoretical simulations.

67

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71

Appendix A

Aerial mode voltages of threefaults for no CTs and CCVTsmodel

Figure A.1: The aerial mode of phase voltage and current for solid fault

72

Appendix A. Aerial mode voltages of three faults for no CTs and CCVTs model

Figure A.2: The aerial mode of phase voltage and current for arcing fault

Figure A.3: The aerial mode of phase voltage and current for lightning fault

73

Appendix B

Aerial mode voltages of threefaults for the model with CTs andCCVTs

Figure B.1: The aerial mode of phase voltage and current for solid fault

74

Appendix B. Aerial mode voltages of three faults for the model with CTs and CCVTs

Figure B.2: The aerial mode of phase voltage and current for arcing fault

Figure B.3: The aerial mode of phase voltage and current for lightning fault

75

Appendix C

Decomposition details of aerialmode voltages

Figure C.1: The wavelet decomposition of modal voltage for solid fault

76

Appendix C. Decomposition details of aerial mode voltages

Figure C.2: The wavelet decomposition of modal voltage for arcing fault

Figure C.3: The wavelet decomposition of modal voltage for lightning fault

77

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