Fault Location and Classification for Transmission Line Based on Wavelet Transform

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,

STOCKHOLM SWEDEN 2016

Fault Location and Classification

for Transmission Line Based on

Wavelet Transform

QIUHONG WANG

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Transmission Line Based on Wavelet

Transform

by 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

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With the rapid development of power systems, locating and classifying faults is critical to the continuity and reliability of the transmission system. In this the-sis, a traveling-wave based technique for fault location and classification on high voltage and extremely high-voltage transmission lines is proposed. The traveling-wave based protection has the advantage of fast response and not being affected by power swing and CTs saturation. In this thesis, the transient characteristics of single line to ground fault (which can be divided into solid fault and arcing fault) and lightning disturbance are extracted by using Clarke transformation and wavelet transformation. The differences among recorded traveling wave arrival times are used to calculate the fault location, and the wavelet energy at different frequency bands 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 identify different 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, and the calculations have been made in MATLAB.

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Sammanfattning

Med den snabba utvecklingen av kraftsystem är lokalisering och klassificering av fel avgör-ande för kontinuiteten och tillförlitligheten hos överföringssystem. I denna avhandling föreslås en vågrörelse-baserad teknik för fellokalisering och klassificering av kraftled-ningar för högspänning och extremt hög spänning. Vågrörelsebaserat skydd har fördelen av snabb respons och att det inte påverkas av kraft fluktuationer och strömtransformsmättnad. I denna avhandling tas momentana egenskaperna av jord till ledningsfel (vilket kan delas in i stumt jordfel och ljusbågefel) och blixtstörning fram med hjälp av Clarke transformation och 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 korrekt och snabbt. Dessutom övervägs påverkan av strömskenans kapacitans, strömtransforma-tor och kopplingskondensaströmtransforma-torspänningsomvandlare. Simuleringen av transmissionssystem har gjorts med ATP/EMTP, och beräkningarna är gjorda med MATLAB.

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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

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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

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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

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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

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6.1 The 400kV simulated system for solid fault . . . 32

6.2 DWT decomposition for aerial mode signal of solid fault . . . 33

6.3 DWT decomposition for ground mode signal of solid fault . . . . 34

6.4 DWT Decomposition for AG fault at 120km from Bus 1 . . . 36

6.5 The 400kV test system in ATP/EMTP . . . 37

6.6 Currents and voltage for the arcing fault . . . 38

6.7 The waveform of arc resistance . . . 38

6.8 DWT decomposition for aerial mode signal of arcing fault . . . . 40

6.9 DWT decomposition for ground mode signal of arcing fault . . . . 41

6.10 The locator response for arcing fault at Bus 1 and Bus 2 . . . 42

6.11 The 400 kV simulated system of lightning fault . . . 43

6.12 DWT decomposition for aerial mode signal of lightning fault . . . 44

6.13 DWT decomposition for ground mode signal of lightning fault . . 45

6.15 The traveling wave reaching a busbar capacitance . . . 46

6.14 The locator response for lightning fault at Bus 1 and Bus 2 . . . . 47

6.16 The equivalent circuit of Figure 6.15 . . . 48

6.17 The reflected wave and refracted wave . . . 48

6.18 EMTP model of single-line to ground fault with different capaci-tance. . . 49

6.19 The voltage (left) and current (right) wave-front for SLG fault, with different capacitance at busbar M . . . 49

6.20 The voltage and current wave-front with different capacitance for arcing fault . . . 50

6.21 The voltage and current wave-front with different capacitance for lightning disturbance . . . 50

7.1 A 230kV transmission line model . . . 56

7.2 Geometrical data of the line considered[2] . . . 57

7.3 The wavelet decomposition D1 of modal voltage for three kinds of fault . . . 59

7.4 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 . . . . 72

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AC Alternating Current

AG Phase A to Ground

CIGRE Council on Large Electric Systems

CTs Current Transformer

CCVTs Coupling Capacitor Voltage Transformers

CWT Continuous Wavelet Transform

DWT Discrete Wavelet Transform

EHV Extra High Voltage

FFT Fast Fourier Transform

HPF High Pass Filter

IEEE Institute of Electrical and Electronics Engineers

LPF Low Pass Filter

SLG Single Line to Ground

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

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

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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 power system and the faults of a transmission line will cause disturbance and endanger the security of the whole system. Therefore, locating and isolating the faults in time are the main tasks of transmission system protection.

When a sudden change, such as a fault or a disturbance occurs on a transmission line, a traveling wave will be generated, and it will propagate at nearly the speed of light. It is a significant amount of work to characterize and locating the transients by only using the original records [3][4]. The wavelet transform is a powerful tool in extracting and analysing the features of traveling wave, the application of wavelet transform on fault location and classification is presented in this thesis. This thesis describes different algorithms to determine fault location and fault types based on sampling of the fault voltage transients at the relay point. For the fault location algorithms, two methods are presented: Single-ended method and Double-ended method. The former one uses the time delay between the modal components of 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 the voltage signals recorded at both terminals. By using these methods, only incident traveling waves are used to perform the fault location, avoiding the utilization of reflected waves at the fault point and, consequently, making the method feasible and reliable. In addition, the simulation results showed that this traveling wave based fault location method does not depend on the fault type [5].

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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 trantran-sients which contain high frequency components. Another important reason that wavelet transform is attractive for engineers is that there are fast calculation algorithms based on filter banks [8].

1.2 Project Objectives

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Transient Overvoltage in Power

System

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 overvoltovervolt-age, which is generated by elements outside the network; lightning is the most common over-voltage in this group. The other one is internal overover-voltage, which is generated by changes in the operating conditions of the network and only depends on the characteristics and structure of the network itself. The internal overvoltage can be separated 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 the different strike points, the lightning overvoltage can be classified as [11]:

• Induced overvoltage: the lightning strikes the ground or other subject near the 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 wire or the tower, and breaks down the phase-ground insulation.

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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 fault initiation and clearing.

2.4 Temporary Overvoltage

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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 introduced at 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 distributed uniformly 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

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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 telegraph equation. 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 and backward traveling wave can be expressed as:

U(x,t) = f1(x − vt) + f2(x + vt) (3.3)

I(x,t) = 1 Z0

f1(x − vt) − f2(x + vt) (3.4)

where v =√1

LCis the surge velocity, Z0= u

i = q

L

Cis the line characteristic impedance, Land 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. A modal transformation matrix is therefore used to decouple the phase signals into their independent equations for each mode as:

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

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

u_0,α,β= T−1ua,b,c (3.7) i_0,α,β= T−1ia,b,c (3.8) T−1=1 3   1 1 1 2 −1 −1 0 √3 −√3   (3.9)

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

3.3 Reflection and Refraction

When a fault occurs on a transmission line, voltage and current surges propagate away from the fault point towards two sides of the transmission line. Assume that there are two ends of the transmission line, end S and end F. These traveling waves will be reflected and refracted when they reach discontinuities on the transmission line. The backwards signal traveling wave fbincident upon end S is given by. [15]

fb(t) = ∞

∑

i=0

aifb(t − τi) (3.10) where ai= (ρfρs)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 to propagate from the fault to the end S, ρf =

Rf−Z0

Rf+Z0 is the fault reflection coefficient,

Rf is the fault resistance, Z0is the surge impedance of the line. ρs=Z_Zs−Z0

s+Z0 is the

reflection coefficient at the end S and Zsis the impedance of sending end.

3.4 Traveling-Wave Fault Location Algorithms

3.4.1 Introduction

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

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

Table 3.1: Traveling Wave Fault Locators Name Operation Mode

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

the line by using a telecommunication channel to transmit the information and a timer to measure the time interval for the arrival of transients at both ends.

Type C uses an active method which can inject an impulse into the line when 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 both end by utilizing a time synchronizing devise (e.g. GPS) at both ends.

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

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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 signal into different frequencies, and more than FT, by using wavelet transform, the signal can be broken up into shifted and scaled versions of the mother wavelet. There are two forms of wavelet transform, the continuous wavelet (CWT) and discrete wavelet transform (DWT).

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

CWTψx(a, b) = 1 p|a| +∞ ˆ −∞ x(t)Ψ∗ t − b a dt (3.11)

where Ψ(t) is called the mother wavelet, the scaling parameters a and b determines the oscillatory frequency, the length of the wavelet and the shifting position respec-tively. The application of wavelet transform in engineering areas usually requires the discrete wavelet transform, the equation of the discrete wavelet transform is given by: DWT(k, n, m) = 1 pam 0

∑

x[n] Ψ k − nb0a m 0 am₀ (3.12)

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

m/2

0 Ψ(a −m

0 t− nb0), where m indicates frequency localization and n denotes time localization.

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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) and a LPF L(n), the outputs from both filters are decimated by 2, which means the sampling rate of the signal is reduced in half, then the detail coefficients and the approximation coefficients at level 1 (A1 and D1) are obtained. After this, the approximation coefficients at level 1 (A1) are sent to the second stage to be de-composed as before. Finally, the signal is dede-composed at the required level by repeating 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 mother wavelet for locating and determining different types of transients. Among these, the Daubechies wavelets are widely used for transient study, especially db4, which is the most localized wavelet in the Daubechies family [23]. Therefore, in this thesis, db4 mother wavelet is chosen to analyze the traveling wave.

3.4.3 Single-ended Method

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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 aerial mode 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)

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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 from the Bewley Lattice diagram, it is cleared that

τ = (3tB− BtA) = 2 L−x v (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 in aerial mode at busbar B.

Then is to utilize the inherent time delay between the different modal components of the incoming three-phase signal to determine the region where the fault is lo-cated. Once the approximate region is determined, according to the equations above, the location of the fault can be calculated based on the Discrete Wavelet Transform (DWT) of the aerial mode (mode 1) signal. The identification method is based on the time delay τd between ground mode and aerial mode of the same three 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 is

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

Figure 3.6: The flow chart of single-ended method

3.4.4 Double-ended Method

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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)

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Figure 3.8: The flow chart of double-ended method

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Fault Classification Algorithms

4.1 Introduction

The faults which occur in power system can cause damage to the equipment of the power system and also affect the power quality. In addition to locating the fault, it is also very important to determine the fault type as soon as possible, and then the corresponding relay operation can clear the fault. Nowadays, the fault generated transients signals are widely used in the fault classification. Based on these 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 the fault transients [26]. The wavelet transform is a powerful method of signal analysis and image processing [27]. The conventional Fast Fourier Transform is based on a Fourier series model [8], which can give a constant resolution for all frequencies, whereas the Wavelet Transform uses multi-resolution technique by which different frequency spectrum are analyzed with different resolutions [28].

4.2 Wavelet Energy

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

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Modeling of Power System in

ATP/EMTP

5.1 Introduction

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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 not available 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 suitable

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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 study how the voltage or current waveforms may look when the traveling wave arrives and partially reflects from these coupled discrete capacitance. CTs are applied at those locations where relays are to be connected. The following figure shows the CTs 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 relays and control application.The equivalent circuit of CCVTs is shown in Figure 5.4.

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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) ; compensating reactor (Rc, Xc, Cc); step-down transformer (Rp, Xp, Cp, Rs, Xs, Rm, Xm); ferrores-onance suppression circuit (Rf, Lf, Cf); and the burden (Rb). The corresponding EMTP model is shown in Figure 5.5. The marked ”CT” in the figure is a step-down transformer. The models and the parameters of CTs and CCVTs in this thesis are collected 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 power system, external and internal overvoltage. For the external case, the lighting is considered 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 back flashover 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. For internal case, the single line-to-ground fault is chosen for study because of it is the most common type of fault on transmission lines [33].

5.3.1 Single Line-to-Ground Fault

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conducting, due to the current flow through ionized air. The energy in a solid fault is released in the conductors in the system, whereas the energy in an arcing fault is dissipated at the point of the fault, which may be inside equipment or in the surrounding environment. Another difference is, in an arcing fault, the fault impedance involves air, therefore the fault impedance in an arcing fault is higher than that in a solid fault, accordingly, the current is lower. The most important difference is that the solid fault can make a very rapid change in voltage, but a realistic arcing fault will have its current increases more slowly. Therefore it is necessary 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 in series with a small grounded resistance. The representation of SLG fault is shown in 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

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

For this work, a dynamic arc model has been implemented in ATP/EMTP based on the Kizilcay fault arc model [35]. It simulates the dynamic interaction between a 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 the following differential equation:

dg dt = 1 τ(G − g) (5.1) τ =α I L (5.2)

where g is the time-varying arc conductance, G is the stationary arc conductance and τ is the time constant, which can be obtained by fitting the experimental 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 × 10−5cm·s/A from the fitting. L is the arc length, which is considered to be constant in this model. 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 arc length, which is considered to be constant in this model. Experimentation shows that over the range of current 1.4 kA to 24 kA, the average arc voltage gradient is V = 15 V/cm. In this case, L = 140 cm, and I = 1861 A, then τ = 3.79 × 10−4s, G=|i|_/_{2.1 kV}

dg dt =

1

τ(G − g) Integrating the above formula, we can get

g(t) = G (t − 4t) − {G (t − 4t) − g (t − 4t)} e−4t/τ

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Figure 5.8: Arc model in ATP

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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 the waveform of arc resistance is more like the pulse wave.

5.3.2 Lightning Fault

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to 400 Ω, which was derived by Bewley [36]. The lightning model is using the Hei-dler (F. HeiHei-dler) 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 + t τ1 10e −t τ2 _(5.5)

where I0is 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 the Heidler model in EMTP.

Figure 5.11: Heidler model in EMTP

5.4 The accuracy of the models

5.4.1 Study Case

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Figure 5.13: Circuit for EMTP analysis

5.4.2 Results of the Study Case

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Figure 5.14: Tower top voltage of study case

Figure 5.15: Phase C voltages of study case

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Figure 5.17: Phase A voltages of study case

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Fault Location

To verify the fault location algorithm proposed in this thesis, a novel extra high voltage 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 the transposition).

Modeling parameters:

The output signals are sampled at the rate fs= 100 kHz. Fault resistance Rf = 0.0001 Ω, the detailed parameters used for simulation are shown in Table 6.1 and Table 6.2.

Table 6.1: System Parameters Source 1 Source 2 Z₁= 2.11 + j56.4 Z₁= 0.816 + j23.6 Z₀= 28.16 + j134.46 Z₀= 11.68 + j40.27 VS= 400ej0kV VS= 400e− j20 ◦ kV

Table 6.2: Line Parameters Positive Sequence Zero Sequence

R1= 0.018Ω/km R0= 0.161Ω/_km L1= 0.864mH/km L0= 0.864mH/km C1= 0.013µ F/km C0= 0.010µ F/km

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6.1 No Shunt Capacitance

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

6.1.1 Solid Fault

The simulated system by ATP/EMTP is shown in Figure 6.1. The switch is closed at 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

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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 = 0.15 ms > τl/2= 0.09 ms

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 × 10}8 2 = 119.09 km Error % = 119.09 × 103− 120 × 103 150 × 103 × 100 % = 0.607 % Double Ended Method

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As is shown in the Figure 6.4, tAand tBare the detected initial transient instants at bus 1 and bus 2 respectively.

x=150 × 10 3_{+ (20.41 × 10}−3_{− 20.11 × 10}−3_{) × 2.943 × 10}8 2 = 119.15 km 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 arcing fault model is connected to a 400 kV transmission line. The fault location is 10 km from busbar 1. The ATP/EMTP model is shown in Figure 6.5.

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Figure 6.6: Currents and voltage for the arcing fault

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Figure 6.6 and Figure 6.7 show that the arc voltage (black line) is similar to the square 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 be found that for the arcing fault, the detail coefficient at level 5 is much smaller than the solid fault. Because the resistance for an arcing fault is far smaller than the permanent grounded fault.

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

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

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 × 10}8 2 = 10.302 km Error % = 10.302 × 103− 10 × 103 150 × 103 × 100 % = 0.201 % Double Ended Method

The identification of t1and t2in arcing fault case is shown in Figure 6.10. Then the fault point location can be calculated as before.

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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 s shape is introduced in each phase because of the coupling between phases. The surge parameters are illustrated in Table 6.3.

Table 6.3: Surge parameters of Heildler model

Amplitude τ1 τ2 n

20 kA 2.5 × 10−6s 4 × 10−5s 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 end are shown in the figures below. The first figure shows the recorded three phase voltages, it can be seen that for lightning fault, the magnitude of voltage wave is much 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 = 0.07 ms > τl_/2= 0.07 ms

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

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Double Ended Method

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

x=150 × 10 3_{+ (20.21 × 10}−3_{− 20.31 × 10}−3_{) × 2.943 × 10}8 2 = 60.283 km 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 double ended recordings of fault voltage signals. First these fault generated transients signals are decoupled into their modal components and then transformed into the time-frequency domain by using the DWT. Then both the single-ended method and double-ended method are applied for fault location. Various types of faults at different location were tested in this chapter, the accuracy of the proposed method for 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 to ground, and Z1and Z2are the different wave impedance for two lines.

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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+C dU2q dt = I2q+CZ2 dI2q dt (6.4)

From the equations above,

I2q= 2U1q Z1+ Z2 (1 − e−Tt) _(6.5) U2q= I2qZ2= 2Z2 Z1+ Z2 U1q(1 − e− t T) = αU_1q(1 − e− t T) _(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+ Z1 U1q− 2Z2 Z1+ Z2 U1q(1 − e− t T) _(6.7)

It can be found that when t = 0, U1 f = −U1q. This is because the voltage on the capacitance 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, as is shown in Figure 6.17, where t = +∞, U1 f = βU1q, where β =(Z2−Z1)/(Z1+Z2).

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Therefore, it can be found that the effect of shunt capacitance is to make the steep-ness of the incoming wave broaden. The steepsteep-ness of U2qis

dU2q dt = 2 Z1CU1qe −t T

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 from busbar M. The values of capacitance are used: 0 μF, 0.1 μF and 0.01 μF. Figure 6.18 is 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 with C= 0 µF,C = 0.1 µF and C = 0.01 µF are shown in Figure 6.19, separately.

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

Figure 6.20: The voltage and current wave-front with different capacitance for arcing 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 for lightning disturbance

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6.2.2 The Influence on The Location Method

Arcing Fault • C_bus= 0 µF

τl/2= 20.40 − 20.31 = 0.09 ms

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 = 0.09 ms

Table 6.5: The characteristics of arcing fault when Cbus= 0.01 µF Time records Single Method Double Method

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Table 6.6: The characteristics of arcing fault when Cbus= 0.1 µF Time records Single Method Double Method

(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 = 0.09 ms

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

Time records Single Method Double Method

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Table 6.8: The characteristics of solid fault when Cbus= 0.01 µF Time records Single Method Double Method

(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 = 0.09 ms

Table 6.9: The characteristics of solid fault when Cbus= 0.1 µF

Time records Single Method Double Method T1M T2M T0M T1N Td Location Error Location Error

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Table 6.10: The characteristics of lightning fault when Cbus= 0 µF Time records Single Method Double Method

(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 20.57 20.41 20.61 20.10 0.16 120.566 0.38 120.622 0.41 • C_bus= 0.01 µF τl_/2= 20.35 − 20.26 = 0.09 ms

Table 6.11: The characteristics of lightning fault when Cbus= 0.01 µF Time records Single Method Double Method

(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 = 0.09 ms

Table 6.12: The characteristics of solid fault when Cbus= 0.1 µF Time records Single Method Double Method

(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

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6.2.3 Conclusion

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Fault Classification

The power system model for case study is based on the EMTP reference model for transmission line relay testing, which is introduced by the IEEE PES Power System Relaying Committee (PSRC) WG D10 [1]. The one-line diagram of the studied 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 Source1

Positive-sequence impedance Zero-sequence impedance Z₁= 6.1 + j16.7 Z₁= 2.7 + j8.37

Table 7.2: Parameters of Source2

Positive-sequence impedance Zero-sequence impedance Z1= 0.69 + j4.12 Z0= 0.34 + j4.77

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

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

Table 7.3: Line Parameters of 230 kV system Positive Sequence Zero Sequence

R1= 0.029Ω/_km R₀= 0.158Ω/_km L1= 1.030mH/km L0= 2.297mH/km C1= 0.011µ F/km C0= 0.008µ F/km

The wave traveling speed and the surge impedance values are:

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v0= 1 √ L₀C₀ = 2.37 × 10 8 m_/_s _Z₀₌L0 C0 = 545 Ω (7.2)

7.1 No CTs and CCVTs

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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, arcing fault and lightning fault. When a fault occurs in the power system, it can be seen that variations within the decomposition coefficients of the voltage signal contain useful fault signature.The total energy of a discrete time signal can be represented by: E= ∞

∑

n=−∞ |x(n)|2 (7.3)

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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 approximations Solid Fault Arcing Fault Lightning Fault

D1 3.17 × 1012 3.60 × 104 6.96 × 1013 D2 1.00 × 1012 _{5.52 × 10}2 _{2.91 × 10}13 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, among the five frequency bands, D1 (2.5 MHz - 5 MHz) has the maximum value. This is because the lightning current can be seen as introducing a high frequency pulse wave 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 ground faults, 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-single-linear resistance of arcing 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 high and low frequency band k can be expressed as

k= ∑ j N ∑ m=1 i2_dm j N ∑ m=1 i2 am (7.4) where, idm

j is the high-frequency components of transient current of the m-ht point

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

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

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The differences of the energy ratio for the three cases are significant, the criterion can 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

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Table 7.5: The wavelet energy for different details and approximations Solid 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 were simulated.

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

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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

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Summary

The first part of the thesis is about the validation on the accuracy of the software ATP/EMTP. A study case of transmission line with a lightning source was simu-lated and then compared with the results reported from experiment literature. The study shows that ATP-EMTP is an reliable software in simulating the transient problem of transmission system, thus ATP-EMTP is chosen as main simulation tool 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. The traveling wave based fault location algorithms are analyzed, the simulation results presented in the preceding Section 6.1 and Section 6.2 show the validity of the proposed algorithm, the percentages of errors for locating the three kinds of faults are very small. In addition, the influence of busbar capacitance on the transmission line is considered, it can be found the busbar capacitance can change the shape of the wave-front when the traveling wave reaches the busbar, but there is no big influence on the time when the wave-front reaches the busbar, therefore the busbar capacitance does not affect the accuracy of the fault location algorithm proposed in this thesis. Furthermore, the fault classification based on the decomposition of fault transient by wavelet transform was examined. A criterion can be proposed according to the distribution of low and high frequency: the energy ratio of high and low frequency band is set as the threshold to distinguish these three kinds of faults. 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 wavelet energy trends of different detail coefficients have no change, the threshold k can be scaled down according to the ratio of the transform.

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

Finally, the use of Wavelet Transform to locate the fault and distinguish the fault types 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 an additional routine in transmission lines protective relays.

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Aerial mode voltages of three

faults for no CTs and CCVTs

model

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

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Aerial mode voltages of three

faults for the model with CTs and

CCVTs

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

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Decomposition details of aerial

mode voltages

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

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