N9314831 Madhawa Weerasekara Thesis REV1 · 2019. 6. 11. · Photovoltaic (PV) systems convert...

DC ARC FAULTS IN PHOTOVOLTAIC

SYSTEMS

Submitted in fulfilment of the requirement for the degree of

Master of Philosophy

by

Weerasekara Mudiyanselage Madhawa Kamalajeewa Weerasekara

of

Power Engineering Discipline

School of Electrical Engineering and Computer Science,

Science and Engineering Faculty,

Queensland University of Technology.

2019

DC Arc Faults in Photovoltaic Systems i

Keywords

Arc faults, arc gap, arc impedance, Cassie model, circuit interrupters ,closing,

cooling power, DC arc, dilation, double ground faults, electrodes, erosion, father

wavelet, fault current, frequency domain, function blocks, grid, ground faults, high

frequency, hyperbolic-tangent function, irradiance, MATLAB-Simulink, maximum

power point, Mayr model, micro grids, modelling, Morphology, mother wavelet,

opening, parallel fault, Photo voltaic, power quality, pulse width modulation, random

noise, series fault, S-function, shading, single diode model, solar, strings, structuring

element, test bench, Wavelets.

ii DC Arc Faults in Photovoltaic Systems

DC Arc Faults in Photovoltaic Systems iii

Abstract

Arc faults in PV systems are difficult to study using models developed for

conventional power sources mainly due to non-linear behaviour of PV current and its

dependence on external factors such as irradiance, shading and maximum power

tracking controls. This research presents a unique model derived from fundamentals

of Mayr and Cassie arc models and introducing a hyperbolic tangent function to

approximate arc current at near zero gaps. Arc impedance is widely changed with

heat dissipated through arcs periphery. Unique feature of the proposed model is that

it takes into account this change of impedance with time which could be used to

analyse arcs with changing lengths due to movements of current carrying elements.

A test bench has been built with adjustable gap between two electrodes to conduct

experiments. Both experimental results and simulation outcomes are presented to

verify the proposed model.

Wavelet transform is another technique that can be successfully applied to

detect arc faults in a PV installation. The same test bench was used to capture fault

waveform signatures to develop a wavelet decomposition model that accurately

detected arc faults.

Use of Mathematical Morphology (MM) based filters to detect faults in power

systems has been discussed in recent literature [2-5]. These studies have been

predominantly focused on AC systems and associated arc faults. However, fault

detection applications based on MM filtering in DC systems have not been

adequately discussed. This research also presents how MM based filtering techniques

and its composite operations could be used to successfully detect arc faults in a PV

system. Throughout the analysis, series and parallel arc fault signatures obtained

from an actual PV system with maximum power point tracking (MPPT) control is

used. The effect of MM parameters on detection sensitivity is also explained.

iv DC Arc Faults in Photovoltaic Systems

Table of Contents

Keywords ........................................................................................................................ i

Abstract ......................................................................................................................... iii

Table of Contents .......................................................................................................... iv

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

List of Tables ................................................................................................................. x

List of Abbreviations .................................................................................................... xi

Statement of Original Authorship ................................................................................ xii

Acknowledgements ..................................................................................................... xiii

Chapter 1: Introduction ............................................................................. 1

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

1.2 Context ................................................................................................................. 2

1.3 Purposes ............................................................................................................... 2

1.4 Significance, Scope and Definitions .................................................................... 3

1.5 Thesis Outline ...................................................................................................... 3

Chapter 2: Literature Review .................................................................... 5

2.1 Solar PV System .................................................................................................. 5

2.2 Faults in a pv system ............................................................................................ 6

2.3 Modeling of PV systems ...................................................................................... 7

2.4 Modeling of dc arcs in pv systems ....................................................................... 7

2.5 detection of dc arc faults using wavelet tranform ................................................ 8

DC Arc Faults in Photovoltaic Systems v

2.6 detection of ARC faults in a pv system using mathematical morphology ...........9

Chapter 3: Modelling of DC Arcs in PV Systems .................................... 10

3.1 Introduction ........................................................................................................10

3.2 DC Arc Test Bench ............................................................................................10

3.3 Test Results ........................................................................................................12

3.4 Proposed arc model ............................................................................................15

3.5 Simulation and Model Verification ....................................................................18

3.6 Conclusions ........................................................................................................21

Chapter 4: Detection of DC Faults using Wavelet Transform ................ 23

4.1 Introduction ........................................................................................................23

4.2 Test setup for arc generation ..............................................................................23

4.3 Experimental results ...........................................................................................24

4.4 Wavelet transform ..............................................................................................25

4.5 Reproduction of fault signatures ........................................................................27

4.6 Parallel fault decomposition ...............................................................................29

4.7 Series fault decomposition .................................................................................31

4.8 Conclusions ........................................................................................................33

Chapter 5: Detection of Arc Faults in a PV System using Mathematical

Morphology 34

5.1 Introduction ........................................................................................................34

5.2 Faults in a Grid connected PV System ...............................................................35

5.3 Mathamatical Morphology .................................................................................36

vi DC Arc Faults in Photovoltaic Systems

5.4 Test Setup for Arc Fault Generation .................................................................. 37

5.5 Parallel Arc Faults ............................................................................................. 39

5.6 Series arc faults .................................................................................................. 41

5.7 analysis of Arc waveforms ................................................................................ 43

5.8 Selection of Structured Element (SE) ................................................................ 45

5.9 Arc fault detection ............................................................................................. 45

5.10 Conclusions ..................................................................................................... 57

Chapter 6: Conclusions and future work ................................................. 58

6.1 Wavelet transform.............................................................................................. 58

6.2 Mathematical Morphology ................................................................................ 59

6.3 Future work ........................................................................................................ 59

Bibliography ................................................................................................ 61

DC Arc Faults in Photovoltaic Systems vii

List of Figures

Fig. 2.1. Components of a PV System ....................................................................... 5

Fig. 2.2. Faults in a PV System ................................................................................. 6

Fig. 3.1. Test Apparatus .......................................................................................... 11

Fig. 3.2. Variation of Arcing Gap ............................................................................ 12

Fig. 3.4. Arc voltages at different irradiance levels. ................................................ 13

Fig. 3.5. Behaviour of current through and voltage across the arc. ........................... 14

Fig. 3.6. Arc Voltage and Current (PU Values). ...................................................... 15

Fig. 3.7. Hyperbolic tangent function for Vs representing Vi and Vto ........................ 16

Fig. 3.8. Circuit model ............................................................................................ 17

Fig.3.9. Simulation block in MATLAB-Simulink ................................................... 18

Fig. 3.10. Simulation and Experimental Results ...................................................... 19

Fig.3.11. Simulation Voltage with increasing irradiance.......................................... 20

Fig. 3.12. Simulation Current with increasing irradiance. ........................................ 20

Fig.4.1. Test circuit ................................................................................................. 23

Fig.4.2. Series and parallel arc fault waveforms ...................................................... 25

Fig.4.3. Wavelet decomposition in Simulink ........................................................... 27

Fig.4.4. Parallel fault voltage signature from signal builder ..................................... 28

Fig.4.5. Series fault voltage signature from signal builder ....................................... 28

viii DC Arc Faults in Photovoltaic Systems

Fig.4.6. Decomposition results for parallel fault voltage. ........................................ 30

Fig.4.7. Parallel fault signal (upper) and its wavelet decomposition (lower)

results. ...................................................................................................... 31

Fig.4.8. Series fault decomposition results .............................................................. 32

Fig.4.9. Series fault signal (upper) and its wavelet decomposition (lower)

results. ...................................................................................................... 33

Fig.5.1 Grid connected PV system with nxm number of modules ............................ 35

Fig.5.2 Test circuit (top) and setup (bottom). .......................................................... 38

Fig.5.3. Parallel Arc waveforms ............................................................................. 39

Fig.5.4. Parallel arc current ..................................................................................... 40

Fig.5.5. Parallel arc voltage .................................................................................... 40

Fig.5.6. Series arc waveforms ................................................................................. 41

Fig.5.7. Series arc current ....................................................................................... 42

Fig.5.8. Series arc voltage ....................................................................................... 42

Fig.5.9. Dilation and Erosion of Parallel Fault Current ........................................... 46

Fig.5.10. Closing and Opening of Parallel Fault Current ......................................... 47

Fig.5.11. CODO Operation of Parallel Fault Current .............................................. 48

Fig.5.12. Dilation, Erosion, Closing, Opening and CODO functions of Parallel

Fault Voltage. ........................................................................................... 49

Fig.5.13. Dilation, Erosion, Closing, Opening and CODO functions of Series

Fault Current. ............................................................................................ 50

DC Arc Faults in Photovoltaic Systems ix

Fig.5.14. Dilation, Erosion, Closing, Opening and CODO functions of Series

Fault Voltage............................................................................................. 52

Fig.5.15. Effect of length of SE on CODO for Series Fault Voltage. ....................... 54

Fig.5.16. Effect of length of SE on CODO for Parallel Fault Voltage. ..................... 55

x DC Arc Faults in Photovoltaic Systems

List of Tables

Table.3.1. PV Module characteristics…………………………………………13

Table 5.1. Electrical characteristics of PV Module at normal operating cell

temperatures………………………………………………………………………....38

Table.5.2 Actual data set of arc waveform……………………………...……43

Table.5.3 Normalized data set of arc waveform………………………………44

DC Arc Faults in Photovoltaic Systems xi

List of Abbreviations

AC Alternating current

CODO Closing Opening Difference Operation

FFT Fast Fourier Transform

GFCI Ground Fault Circuit Interrupters

GFPD Ground Fault Protective Devices

HIF High Impedance Fault

HV High Voltage

IEA PVPS International Energy Agency Photovoltaic Power Systems Program

MM Mathematical morphology

MPPT Maximum power point tracking

OCPD Over Current Protective Devices

PV Photovoltaic

PWM Pulse width modulation

SE Structural Element

UHS Ultra-High Speed

WT Wavelet Transform

xii DC Arc Faults in Photovoltaic Systems

Statement of Original Authorship

The work contained in this thesis has not been previously submitted to meet

requirements for an award at this or any other higher education institution. To the

best of my knowledge and belief, the thesis contains no material previously

published or written by another person except where due reference is made.

Signature:

Date: May 2019

QUT Verified Signature

DC Arc Faults in Photovoltaic Systems xiii

Acknowledgements

I would first like to thank my principal supervisor Professor Mahinda

Vilathgamuwa, Science and Engineering Faculty, Queensland University of

Technology. Professor was always there when ever I had a question about my

research or experiments.

I would also like to thank Dr.Yateendra Mishra, my associate supervisor, of

Science and Engineering Faculty. His expertise in practical applications of grid

connected PV systems was extremely helpful. Assistance and encouragements from

members of staff in the faculty is also noteworthy.

Last but not the least, I would like to thank my family, my wife and kids, for

spiritually supporting me during last few years of my study.

Thank you all.

Madhawa Weerasekara

Chapter 1: Introduction 1

Chapter 1: Introduction

1.1 BACKGROUND

Photovoltaic (PV) systems convert energy from solar radiation into useful and

usable electrical energy. As the concerns of environmental effects in the use of fossil

fuels for energy and energy security become critical in global energy scenario, use of

PV systems has increased significantly. For example, annual growth of installed PV

system capacity in 2015 in the International Energy Agency Photovoltaic Power

Systems Program (IEA PVPS) countries was around 26.5% to reach a total installed

capacity of around 230GW [1].

The first PV cell was developed by Fritz in 1883 and it’s efficiency was less

than 1% [6]. After several other developments by various scientists, first Silicon PV

cell with an efficiency of 6% was developed by Ohl in 1941 which was further

developed by Bell Laboratories to achieve 11% efficiency by 1954[6]. In 2019,

demonstrated efficiency of a thin film GaAs is as high as 29%[7].

Solar energy offers important benefits compared to other energy sources.

Availability in abundance, absence of moving parts, renewability and long effective

life are some of them. On the other hand, PV systems have issues such as high

dependency on time and weather conditions, rapid variation of energy output due to

cloud and shading and need of expensive power conversion equipment are

noteworthy. In addition, behaviour of PV systems under various faults is very much

different to that of conventional AC power systems.

As in the case of other energy sources and systems, such as Coal & Hydro

power, PV systems have fault scenarios which affect its life span, reliability,

efficiency and very importantly safety of personnel and property. But these fault

scenarios are very much different from that of other power sources mainly due to

nonlinear output and current-limiting nature of PV arrays’ operation [8] . Arc faults

in the DC side of a PV system in particular raises concerns as they are difficult to

detect using conventional protection equipment used in power systems. These arc

2 Chapter 1: Introduction

faults do not generate large fault currents, though they could create over heating of

cables and surroundings, and hence could remain undetected.

The fire hazards on April 5th

, 2009 in Bakersfield, California, and April 16th

,

2011 in Mount Holly, North Carolina are most quoted examples for evidence of lack

of effective fault isolation in PV systems.

1.2 CONTEXT

A fault in a PV system could create dangerously high temperatures around

faulty sections of the system yet to be undetected by traditional protection devices. A

PV panel is a nonlinear current source and also has very limited generation capacity

during low irradiance levels. Both these facts cause a fault in a PV system to produce

currents smaller than thresholds of protective switchgear. Hence an arc fault in a PV

system could remain undetected for prolong periods and could still generate enough

heat to ignite surrounding structures etc.

Behaviour of system current and voltage during an arc fault in the DC side is

confusingly similar to that of during rapid change of irradiance. Also, DC arc

current does not have periodic zero crossing and could result in sustained fault

currents.[9].

1.3 PURPOSES

This research will focus on a detailed study of various fault scenarios in a PV

system and their detection techniques. It will also look into different types of

inverters and converters that are used in distributed generation systems.

Among various faults, DC arcs are considered one of major reasons for

catastrophic failures that caused electrical fires [10]. Principal objective of the

research is to propose a method to detect DC arc faults by separating it from other

system noises even under low irradiance levels.

Chapter 1: Introduction 3

1.4 SIGNIFICANCE, SCOPE AND DEFINITIONS

Along with the drive to increase renewable energy usage, installed capacity of

solar power systems has grown exponentially. Protection of these systems against arc

faults is a challenge due to non-linear behaviour of PV cell’s voltage-current

relationship and effect of shading. It is of paramount importance to the growth of PV

energy usage that these systems are safe and have adequate protection equipment to

prevent dangers to public and property in case of a fault.

Being one of the most difficult faults to detect, timely detection of DC arc

faults plays a significant role in making PV systems safe.

This research investigates several options to detect arc faults in a PV

installation that consists of MPPT and a charge controller.

Both series and parallel arcs are studied using an experimental set up to

generate arcs and to store voltage and current waveforms. These waveforms are then

analysed with several novel approaches to detect arc faults.

Scope of the study is limited to series and parallel arc faults and does not

consider other faults such as ground, double ground or arc faults between different

strings of a solar power system.

1.5 THESIS OUTLINE

A comprehensive literature review was carried out to gather knowledge on

existing research in the field of arc faults detection in photovoltaic power systems.

Chapter 2 provides details of existing literature in different areas aligned with

boundaries of this thesis. Review is sub divided into several sections to present

information under each heading that forth coming chapters are arranged.

Chapter 3 presents a development of a model to represent DC arcs in PV

systems. Mayr and Cassie arc models were used as the base for this development and

experimental results of arc voltage and current were used to represent the arc in a PV

4 Chapter 1: Introduction

installation. Experimental results show a close match with model output proving the

suitability of this model for studies on DC arcs in PV systems.

Wavelet transform is another technique that could be used to detect arc faults.

An in-depth study as to how wavelet transformed could be used to detect arc faults in

a PV system is described in Chapter 4. It is proven at the end of this chapter that

wavelet transformation could also be used to identify if there is any series or parallel

arc in the electrical circuitry before MPPT/Charge controller of a PV installation.

Most important area of this study is described in Chapter 5 where a novel

method to detect arc faults using Mathematical Morphology is presented. This

section also uses experimental results of arc voltage and current waveforms as the

input for the proposed detection system.

A brief conclusion is given in Chapter 6. This research opens up some avenues

for future studies to develop same concepts further to address arc faults in practical

photovoltaic installations. These future activities are also described in this final

chapter.

Chapter 2: Literature Review 5

Chapter 2: Literature Review

2.1 SOLAR PV SYSTEM

Solar PV systems could either be grid connected or stand along. Stand along

systems feed a local load, generally small in capacity. Grid connected systems are

mostly used in commercial scales and comprises of four main components[11].

a. PV Array

b. MPPT Controller

c. Inverter

d. Grid Interface

Other than the PV array, other three components are usually incorporated

into one unit and it is usually called inverter.

Fig. 2.1. Components of a PV System

MPPT will control power flow in such a way that maximum power at a given

irradiance level is harnessed. The inverter then produces AC power from DC bus fed

from MPPT and grid interface synchronises AC supply with grids main system.

6 Chapter 2: Literature Review

2.2 FAULTS IN A PV SYSTEM

When a PV system is in normal operation, its output current is controlled by

Maximum Power Point Tracking (MPPT) system in order to maximize power

extraction. In case of a sudden fault, MPPT will shift the system to a new operating

point which gives maximum power output under post fault conditions. Hence any

fault detection system will have a very narrow time gap to detect the fault before

system re-settles at new operating points. This makes its challenging for traditional

protection equipment to detect the faults.

Also, if a fault occurs during low irradiance, fault currents may be below the

threshold currents of traditional detection devices. Even though fault currents may

also be very low at the beginning, once the system moves to normal irradiance levels,

for example, during night to day transition, fault currents can increase to dangerous

levels.

Existing literature discuses several fault scenarios in PV systems. These

include;

1. Ground Faults

2. Arc Faults

3. Line –to-line Faults

4. Double ground Faults

Fig. 2.2. Faults in a PV System


A ground fault is a situation where there is an unintentional current path exists

to ground. In a typical AC system, ground faults are detected by ground fault circuit

interrupters (GFCI) which works by detecting mismatch of current flow in incoming

and outgoing conductors. But in case of a PV system, due to the fact that there are

several power sources and locations of potential faults, ground fault detection takes

the form of an overcurrent circuit breaker with a low detection threshold [12]. Three

commercially available ground fault detection equipment and their limitations are

described in [10].

2.3 MODELING OF PV SYSTEMS

A PV system consists of solar PV modules arranged in an arrays and power

electronics converters. PV modules are connected in series to form a string and these

strings are then connected parallel to form the array. Number of PV panels in a string

will determine the voltage capacity of the installation, while current capacity is

determined by the number of strings connected in parallel.

PV systems have nonlinear output characteristics which depend on irradiance

and temperatures and these dependencies become more complicated under partially

shady situations. It is very important to understand behaviour of PV panels under

these different field and load conditions in order to harness maximum energy.

A model with a controlled current source and an S-Function block in

MATLAB-Simulink is presented in [13]. Various array and string combinations

could be set in this model with independent panel parameters such as irradiance and

temperature to model actual field conditions.

Effect of blocking and by-pass diodes is incorporated into a PV model in [14].

This model could be used to analyse MPPT systems under partial shading.

Identification of local and global maximum power points is very important to harness

total power available under shady conditions and this model could assist design of

effective maximum power point tracking circuits.

2.4 MODELING OF DC ARCS IN PV SYSTEMS

Studies on electrical arcs are fundamentally based around developing models to

approximate their behaviour under various supplies and load conditions. These

8 Chapter 2: Literature Review

models are widely used to design detection and isolation methods to protect power

networks from system deterioration and safety hazards. With the increased use of

DC sources and micro-grids, study of arcs in DC systems has become important in

recent years. In case of a Photovoltaic (PV) system, the source is essentially a

nonlinear current source with a magnitude that depends on factors such as irradiance

and panel parameters [15] which create special research space for arc faults in PV

power systems.

A literature survey conducted revealed that most of the studies on arc

modelling published are based on constant supply voltages which do not represent

PV sources [16-19]. An arc model using SPICE is developed in [20] to analyse series

and parallel arc faults in PV arrays. It was also identified different ways that the

inverter will react to arc faults depending on their severity during MPPT tracking

operation.

There exists a research area to investigate arc behaviour of systems fed by

nonlinear current sources and chapter 4 presents a model that could be used in

simulations and further studies of arc faults in PV systems.

2.5 DETECTION OF DC ARC FAULTS USING WAVELET TRANFORM

Prior research in to arc fault detection using frequency domain analysis in

terms of Fast Fourier Transform (FFT) and Wavelet decomposition exist in literature

[21-24]. These studies are either based on simulated arc faults and system noises or

experimental fault signals with simulated system noises in voltage and current

waveforms. Noises generated by MPPT under changing irradiance levels and due to

fault current itself are not considered and hence it creates a research space for a study

of the use of wavelet decomposition of faults in conjunction with MPPT noises.

A detection methodology for on-line voltage transients using wavelet transform

is proposed in [25]. This model detects the presence of voltage transients and also

distinguishes between various sources of these transients. But the proposed approach

works only under constant voltage AC systems and hence not suitable in studies of

arc faults in PV installations.


2.6 DETECTION OF ARC FAULTS IN A PV SYSTEM USING

MATHEMATICAL MORPHOLOGY

Use of Mathematical Morphology (MM) based filters to detect faults in power

systems have been discussed in recent literature [2, 3, 26]. These studies have been

predominantly focused on AC systems and associated arc faults. However, fault

detection applications based on MM filtering in DC systems have not been

adequately discussed. Chapter 6 presents how MM based filtering techniques and

their composite operations could be used to successfully detect arc faults in a PV

system. Throughout the analysis, series and parallel arc fault signatures obtained

from an actual PV system with maximum power point tracking (MPPT) control is

used. Effect of MM parameters on detection sensitivity is explained.

The method described utilizes mathematical morphology to extract waveform

signatures of current and voltage of a PV array during a fault to identify faulty

condition.

A method of combined use of Multi-resolution Morphological Gradient and

Multi-filter units of MM was developed in [27]. It describes how this method could

successfully be used to detect fault generated transients of a HV transmission line.

Mathematical Morphology was used in [5] to propose an Ultra High Speed (UHS)

directional protection technique in AC power transmission lines. Morphological

Transforms are also used in [3] for power quality analysis in AC systems.

10 Chapter 3: Modelling of DC Arcs in PV Systems

Chapter 3: Modelling of DC Arcs in PV

Systems

3.1 INTRODUCTION

Arc faults in a PV system are difficult to study using models developed for

conventional power sources mainly due to non-linear behaviour of PV current and its

dependence on external factors such as irradiance, shading and maximum power

tracking controls.

This paper presents a unique model derived from fundamentals of Mayr and

Cassie arc models and introducing a hyperbolic tangent function to approximate arc

current at near zero gaps. Arc impedance widely changes with heat dissipated

through arcs periphery. Unique feature of the proposed model is that it takes into

account this change of impedance with time which could be used to analyse arcs with

changing lengths due to movements of current carrying elements.

A test bench has been built with adjustable gap between two electrodes to

conduct experiments is presented in para 3.2. Next section presents results of

experiments and finally a conclusion to summarise results. Both experimental results

and simulation outcomes are presented to verify the proposed model.

3.2 DC ARC TEST BENCH

A test apparatus was built with two copper electrodes that are moved away

from each other in axial direction at constant speed. Electrodes are connected in

series with a PV module and the gap between rounded tips of electrodes was kept at

zero distance before commencing the test. Current was allowed to pass through

electrodes while moving them away creating an arc in between. Arc voltage, arc

current and gap were measured and stored.

Chapter 3: Modelling of DC Arcs in PV Systems 11

As shown in Fig. 3.1, moving electrode was connected to a threaded shaft

which allows it to be moved horizontally by rotating drive wheel. Speed of gap

separation is governed by thread pitch of the shaft and speed of rotation of drive

wheel. A linear variable resistor was connected with drive wheel through a belt.

Increase of voltage drop across this resistor during electrodes’ separation was used to

measure gap distance. This allows a synchronized measurement of arc gap with arc

voltage and current using an AGILENT DSO-X 2024 200MHz oscilloscope.

In practical PV installations, arc gap during a fault is uncontrolled and random

and hence the arc impedance. By using a test bench with a controlled gap, it is

intended to study variation of arc impedance across complete range of possible arc

lengths with varying levels of irradiance. The gap between electrodes was increased

from zero at a fairly constant speed as shown in Fig. 3.2, till arc got extinguished.

Fig. 3.1. Test Apparatus


Fig. 3.2. Variation of Arcing Gap

3.3 TEST RESULTS

Tests were conducted at various irradiance levels on a summer day morning

using a Hanwha SF220, 250W PV module.

Fig. 3.3. Measuring arrangement


Arc was allowed to form by moving electrodes away and voltage across and

current through electrodes were measured. Voltage across separating electrodes

under different irradiance levels are illustrated in Fig. 3.4.

Table.3.1. PV Module characteristics.

Parameter Value

Maximum Power (Pmax)

Open Circuit Voltage (Voc)

Short Circuit Current (Isc)

Voltage at Maximum Power (Vmpp)

Current at Maximum Power (Impp)

182 W

34.2 V

7.07 A

27.7 V

6.58A

Fig. 3.4. Arc voltages at different irradiance levels.


Irrespective of the level of irradiance available, there exists a voltage drop, Vi,

across electrodes at zero gap. This is due to touch resistance between surfaces of two

electrodes and is dependent on geometry and material of the same [19]. When the

gap is increased, an arc starts to form across electrodes and arc voltage jumps to a

turn-on voltage, Vto which again is dependent on material composition of electrodes

[19]. Maximum arc voltage before it extinguishes shows firm dependence on

irradiance level. With higher irradiance, PV module could maintain a current flow

through a longer arc which intern resulted in higher arc voltage. Once the arc is

extinguished, voltage settles down at PV module’s open circuit voltage.

Results of a test at 83,000 Lux, i.e. approximately 655 W/m2 irradiance, are

illustrated in Fig.3. 5 below.

Fig. 3.5. Behaviour of current through and voltage across the arc.


Fig. 3.6. Arc Voltage and Current (PU Values).

In Fig. 3.5, as gap is increased linearly with time, waveforms are plotted

against time instead of gap length. At zero gaps, current fed by PV module is

equivalent to its short circuit current. Ultimately current will drop to zero as gap

length, or time, increases.

A sixth order polynomial approximation to power fed into the arc, product of

voltage and current, shows that it reaches a maximum value that closely matches

with PV modules maximum power output at normal operating temperature.

In order to display current and voltage independent of PV panel capacity, per

unit values were calculated by dividing arc current and voltage by panel’s short

circuit current and open circuit voltage respectively. These per unit values are plotted

in Fig. 3.6.

3.4 PROPOSED ARC MODEL

Mayr and Cassie arc models are widely used in literature in modelling arc

behaviour. Both these models are based on the fact that energy stored in the arc is


equal to the difference between energy supplied into the arc by source voltage and

energy dissipated from arc into its surrounding environment.

In Mayr model, arc is assumed to be a cylinder having constant radius where

energy dissipation is only caused by thermal conduction through its outer surfaces.

This model is best applicable to small currents and hence used in this study. Dynamic

characteristics of the arc are governed by the equation (1) in which Z, τ and Pin are

arc impedance, arc time constant and power fed into the arc respectively. P0 is the

cooling power loss.

�� = �

� �1 − �� (1)

P0 is power fed into the arc when arc is stable [28]. In the experiment, as arc

length is increased, P0 is assumed to be time (t) dependent, as a result of linear

relationship of arc gap with time, and can be approximated by a linear relationship

a+bt and equation (1) could be re-written as,

�� = �

� �1 − �� .�(��) (2)

Electric arc is assumed to be purely resistive and power fed into the arc, Pin, is

presented in terms of arc impedance and current flowing through the arc.

Fig. 3.7. Hyperbolic tangent function for Vs representing Vi and Vto


As shown in Fig. 3.7, at the time an arc is formed across the electrodes, there

exist two voltage drops Vi and Vto. Combination of these two voltage drops, Vs, can

be approximated by a hyperbolic-tangent function given by (3) where A,B,α and β

are constants.

�� = �. tanh ��( −∝)" + $ (3)

Fig.4.7. illustrates Vs for A=0.18, B=0.25, α=0.01 and β=300.

In the circuit model given in Fig.3.8, R and L are resistance and inductance of

circuit from PV module to arc location. Z represents arc impedance and Rs

corresponds to the circuit element responsible for voltage Vs.

Fig. 3.8. Circuit model

Circuit equations for this are:

% = &(' + () + ) �� + ��

�� = *+ ,% − &(' + () − �. tanh ��( −∝)" + $- (4)

On the other hand, as derived in [15], single diode model of a PV module could

be used to derive a relationship between PV voltage U and current i, in a PV array

composed of several connected PV cells. This relationship is given in (5):

& = ./0 − .1 23456789:; < − 1= − >�?8�?@ (5)


Ipv and I0 are photovoltaic and saturation currents of the array of Ns cells in

series and Np cells in parallel. Thermal voltage of the array, Vt=Ns k T/q, where q is

the charge of electron (1.60217646×10−19

C) and k is Boltzmann constant

(1.3806503×10−23

J/K). Temperature of p-n junction in Kelvin is T.

3.5 SIMULATION AND MODEL VERIFICATION

Equations (2) to (5) were modelled in MATLAB-Simulink environment. In

order to avoid convergent issues in simulations, PV block of MATLAB was used

instead of equation (5).

Fig.3.9. Simulation block in MATLAB-Simulink

Vz in Fig. 3.8 is obtained by simulating equation (2) to get arc impedance Z and

multiplying it by PV current i. Simulation of equation (3) gives us Vs and hence

voltage drop across the arc (Vz+ Vs). This voltage and PV current i were plotted

against time and compared with experimental results. Time is selected as

independent variable instead of gap length due to linear relationship between them.


Fig. 3.10. Simulation and Experimental Results

Simulation results of arc voltage shows close agreement with test results.

Experimental arc current has slightly higher readings compared to simulation results,

especially towards the end of the arc duration. This still gives a fair match for

modelling purposes. Simulation circuit does not produce any high frequency noise

that is present in actual current and voltage signals during an arc. This difference is

also visible in the results.

Fig. 3.11 and Fig. 3.12 illustrate simulation results at different irradiance

levels.


Fig.3.11. Simulation Voltage with increasing irradiance

Fig. 3.12. Simulation Current with increasing irradiance.

It is evident from Fig. 3.10 that simulated arc voltage and current show close

match with experimental results. Experimental current has high frequency noise


captured by high resolution of measuring instrument whereas simulation current only

shows steady values. Simulation current is slightly less that experimental current

which may have caused by approximations of constants and resistance of cables etc.

Arc voltage curve clearly shows two voltage drops Vi and Vto that were

explained earlier. With increasing irradiance, arc is able to continue to exist for

longer duration that is equivalent to longer arc gap.

Short circuit current of PV module increases with increasing irradiance. This

is visible in Fig. 3.11, where current at zero gap increases with irradiance.

3.6 CONCLUSIONS

An arc model to study high impedance arc faults in a PV system was

developed. Originality of the model is that it considers change of arc length which

improves accuracy of modelling and takes into account resistances that appear just

before and after arc’s initialization.

Simulated and measured currents and voltages show good agreement with

experimental results. Though the model disregards high frequency noise generated

during the arc, it could be used to model general behaviour of arc current and voltage

across the arc in a PV system.

In reality, arc length does not vary smoothly. The length of arc could also

change randomly with time and this was not modelled due to limitations of the

experimental setup.

Modelling under random gap separation instead of constant speed is an area

for further development which could be used to better represent actual field

scenarios.

Chapter 4: Detection of DC Faults using Wavelet Transform 23

Chapter 4: Detection of DC Faults using

Wavelet Transform

4.1 INTRODUCTION

Arc faults in DC systems have become a concern in the recent past due to rapid

growth of PV installations. Presence of cable connectors could lead to series arc

faults due to aging and accidental damages to cables and rodent bites could create

parallel arcs between current carrying parts of an installation [29].

This chapter is structured in the following sections: the test bench used for safe

generation and digitally storing series and parallel arc fault experiments,

experimental results obtained by created arc faults, a description of wavelet

transform, wavelet decomposition of fault signatures and finally a conclusion.

4.2 TEST SETUP FOR ARC GENERATION

A test bench was created with a PV module and a PWM controller having

MPPT as illustrated in Fig.4.1. A digital storage oscilloscope was used to store arc

waveforms.

Fig.4.1. Test circuit

PV module was directly connected to PWM charge controller which has inbuilt

MPPT function. 12Vdc battery and a DC load were connected to create sufficient

24 Chapter 4: Detection of DC Faults using Wavelet Transform

load and series and parallel arc tests were done at approximately 500W/m2 and 330

W/m2 irradiances respectively.

An arc was formed by moving two contact points of Series Fault away from

each other and a parallel arc was formed by a short circuit across positive and

negative sides of the PV module. In each case, waveforms of voltage across PWM

and current through the fault were recorded.

4.3 EXPERIMENTAL RESULTS

Results obtained were the waveforms of current and voltage signatures of arcs.

For comparison purposes, waveforms were recorded from a point of time prior to arc

occurrence. This portion of the waveforms contains noises created by PWM during

its normal operation.

Arc current and arc voltage are plotted against time in Fig.4.2 below and it

gives an indication of high frequency noise and random nature of both current and

voltage.

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3.00

4.00

5.00

6.00

7.00

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

-5.E

-06

-4.E

-06

-2.E

-06

-3.E

-07

1.E

-06

3.E

-06

4.E

-06

6.E

-06

8.E

-06

9.E

-06

Arc

Cu

rre

nt

[A]

Arc

Vo

lta

ge

[V

]

Time [S]

SERIES ARC FAULT

DC Voltage ARC Current


Fig.4.2. Series and parallel arc fault waveforms

Pre fault current of series fault scenario is the load current that flows into

charge controller. This current changes randomly and rapidly during the arc and once

the arc is fully extinguished, it settles down at zero.

Current that flows through the parallel arc prior to the fault is zero as there is

no conductive path across. Once the contacts are closed and opened to create an arc,

this current also changes rapidly and reaches zero once contacts are wide open and

there is no more arc across.

In both series and parallel faults, pre fault voltage is the same and it depends on

irradiance and connected load based on PV modules I-V characteristics. Post fault

voltage of series fault will rise towards PV panels open circuit voltage where as that

of parallel fault settles down at pre fault voltage if there is no change in irradiance

and connected loads.

4.4 WAVELET TRANSFORM

Just like Fourier Transform, Wavelet transform (WT) is a linear transformation

but it allows more accurate time localization of different signal components.

Due to the wide variety of signals and problems encountered in power

engineering, there are various applications of wavelet transform, such as fault

detection, load forecasting, and power system measurement. The wavelet analysis

-2.00

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0.00

1.00

2.00

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4.00

5.00

0.00

5.00

10.00

15.00

20.00

25.00

-3.E

-04

-2.E

-04

-2.E

-04

-1.E

-04

-8.E

-05

-3.E

-05

2.E

-05

7.E

-05

1.E

-04

2.E

-04

Arc

Cu

rre

nt

[A]

Arc

Vo

lta

ge

[V

]

Time [S]

PARALLEL ARC FAULT

ARC Voltage [V] ARC Current [A]


procedure is based on a pair of wavelet prototype functions, called the wavelet

function (mother wavelet) and scaling function (father wavelet) –together they

provide a localized signal processing method to decompose the differential signal

into a series of wavelet components, each of which is a time-domain signal that

covers a specific frequency band [24].

Discrete Wavelet Transform (DWT) is defined as,

A(B, D) = ∑ F(G)HI,J(�)K∈� (1)

B ∈ M, D ∈ (

where s(n) is the signal to be analysed and C(j,k) is the corresponding wavelet

coefficient. Also n is the sample number and gj,k(n) is the discrete scaling function.

Scaling function is defined by

gj ,k (n) = 2g− j /2

g (2− j

n − k ) (2)

In order to analyse fault waveforms, a 12th

order asymmetric Daubechies

Wavelet transform with 10 levels were used in MATLAB Simulink. Signals were

converted into a frame output of 1024 samples before applying wavelet transform.


Fig.4.3. Wavelet decomposition in Simulink

4.5 REPRODUCTION OF FAULT SIGNATURES

Fault signatures recorded in 4.3 above were transformed into a signal builder in

MATLAB-Simulink so that they could be used as the input for Wavelet

decomposition model. Time axis limits were selected in such a way that fault occurs

around the midpoint of measured range. This allows differentiate pre-fault and post

fault regions of the waveform concerned.


Fig.4.4. Parallel fault voltage signature from signal builder

Fig.4.5. Series fault voltage signature from signal builder


4.6 PARALLEL FAULT DECOMPOSITION

Once the parallel fault voltage was generated using a signal builder, it was fed

into wavelet decomposition model and resulted waveforms could be plotted against

time.

Fig.4.6 gives a comparison of decomposition results for each frequency sub

band. Graphs “A” to “K” represent results in frequency sub bands from 1 to 11

respectively.

First few sub band results do not show much difference in the shape of signal

between faulty and non-faulty regions. But, as sub band frequency increases, shape

of the output signal changes in the faulty region and signal “I” appears to represent

faulty region better. After this step, noise in the input signal start to appear in the

non-faulty sections.

All resulted waveforms vary around zero volts and hence the result is

independent of the normal amplitude of the measured signal.


Fig.4.6. Decomposition results for parallel fault voltage.

A close comparison of parallel fault voltage and its wavelet decomposition “I”

result is presented below:


Fig.4.7. Parallel fault signal (upper) and its wavelet decomposition (lower) results.

In order to avoid start up noise being identified as a fault, first 0.5x10-4

seconds

portion of measured signal was omitted. Rest of the measured voltage remains stable

other than during arc fault. During this period of stable voltage, wavelet

decomposition signal remains close to zero. Once the arc starts to form, amplitude of

decomposition signal varies between -25V and +15V approximately.

4.7 SERIES FAULT DECOMPOSITION

Similar to the way that parallel fault voltage was analysed, series fault voltage

was also decomposed using wavelet transform.

As the level of decomposition increases, amplitude of resulted waveform

increases. There is also shift of signal along time axis that results in a delay to detect

arc fault. Third level signal gives adequate separation of faulty region of the signal

and it could be used for detecting purposes.


Fig.4.8. Series fault decomposition results


Fig.4.9. Series fault signal (upper) and its wavelet decomposition (lower) results.

Most importantly, resulted signal amplitude is either zero or very close to zero

during healthy operation of the system. During arc fault its amplitude increases and

varies between -6V and +6V making it a reliable source to detect a series arc fault.

4.8 CONCLUSIONS

Wavelet analysis was used to study two most common real arc faults, series

arcs and parallel arcs, in a PV system. Different frequency sub bands were used to

investigate best suitability to detect series and parallel faults. Separate fault

signatures from the test set up were used to apply proposed detection approach.

Results prove that Wavelet transform approach could be used as a tool to detect and

separate arc faults conditions from healthy operation in a PV system by measuring

voltage across DC side MPTT controller/inverter.

Different frequency sub bands are to be used to detect arc fault depending on

the fact that the fault is a parallel or a series arc fault.

34 Chapter 5: Detection of Arc Faults in a PV System using Mathematical Morphology

Chapter 5: Detection of Arc Faults in a PV

System using Mathematical

Morphology

5.1 INTRODUCTION

Mathematical morphology (MM) is a non-linear signal transformation tool that

could be used to modify the shape of a signal [30]. It provides an approach to process

images based on a function known as Structuring Element (SE) by analysing the way

this SE fits into the original image. MM deals with the shape of a signal in time

domain and hence defers itself from approaches such as Fourier transform and

Wavelet transform which functions in frequency domain.

Arc faults in a PV power network draw much lesser currents that are not

sufficient to activate conventional protective switchgear [31]. Detection of such

faults in a PV system becomes more challenging due to specific nature of Voltage

/Current behaviour of PV modules and also due to effect of MPPT. This Chapter

investigates how MM could be used in detecting series and parallel Arc in a PV

system.

Section 5.2 investigates various faults in grid connected PV systems followed

by explanation of MM in section 5.3. Analysis of parallel and series arc faults are

presented in para 5.5 and 5.6 respectively. The waveforms obtained from

experiments are analysed in section 5.7 which explains modifications done in order

to prepare these waveform data to be able to use in MATLAB.

Section 5.8 describes selection of structural element for MM transformation

and section 5.9 presents results from MM analysis followed by a conclusion.

Chapter 5: Detection of Arc Faults in a PV System using Mathematical Morphology 35

5.2 FAULTS IN A GRID CONNECTED PV SYSTEM

A grid connected PV system typically will have several parallel connected

strings to provide adequate current capacity and each string will have series

connected PV modules which in turn decide DC voltage of the system.

Fig.5.1 below shows major components of a typical grid connected PV system.

Fig.5.1 Grid connected PV system with nxm number of modules

Generally PV systems are protected against over current and earth leakages by

Over Current Protective Devices (OCPD) and Ground Fault Protective Devices

(GFPD) respectively. These devices are located just prior to the inverter which also

operates as MPPT device.

Line to line faults and ground faults are the most common types of faults that

could create hazardous overheating of cables and associated equipment[32]. Line-

line fault could be classified as an accidental short circuiting of two points of PV

array with different potentials. This could be between two points in two different

strings (A of Fig.5.1), between two points in the same string (B of Fig.5.1) or

between two feeder cables (C in Fig.5.1). In case of high impedance faults, all of

these faults could be considered as parallel faults.


A series arc fault could occur at any point of discontinuity in the array and this

chapter only studies a series fault that occurs at a feeder cable (D of Fig.5.1). Any

such imperfect connection could be a result of contact separation that leads to a

series arc condition [19].

All types of parallel faults discussed above provide a closed path for the fault

current that does not pass through the protective devices located at the end of feeder

cables. Furthermore, series arc faults will also reduce the current that flows through

protection devices making it impossible for these devices to detect any of above

faults.

This chapter proposes a method to use variations of the voltage across inverter

terminals, which are a result of currents passing through arc fault to detect faulty

conditions.

5.3 MATHAMATICAL MORPHOLOGY

Mathematical Morphology is a theory that provides an algebraic formulation to

apply neighbourhood operations on signals by interaction between the signal under

analysis and a SE [3] . The signal and SE are considered sets of points and SE acts as

a sliding window which moves through the signal while interacting with the shape of

the signal and detects specific features in the neighbourhood of every point in the

signal.

Erosion and Dilation are two basic operations of MM, which are defined as

below:

Let input signal be denoted by (G) , defined in domain NO = PQ1, Q*, … , QKS , SE by H(T) in domain NU = PV1, V*, … , VWS where G and T are integers such that

G > T.

Dilation of Y(G) by H(T), denoted by (Y ⊕ H)(G), is defined as,

(Y ⊕ H)(G) = T[QPY(G − T) + H(T)S, 0 ≤ (G − T) ≤ G,T ≥ 0 (1)


Erosion of Y(G) by H(T), denoted by (Y ⊖ H)(G), is defined as,

(Y ⊖ H)(G) = T&GPY(G + T) − H(T)S, 0 ≤ (G + T) ≤ G,T ≥ 0 (2)

Basic operations defined above could be used to define two derivatives called

opening and closing. Opening of Y(G) byH(T), defined as dilation of the eroded

signal (Y ⊖ H) by (T) , which is denoted by (Y ∘ H)(G), is defined as

(Y ∘ H)(G) = ((Y ⊖ H) ⊕ H)(G) (3)

Similarly, closing of Y(G) byH(T), defined as erosion of the dilated signal

(Y ⊕ H) by (T) , which is denoted by(Y.H)(G), is defined as

(Y.H)(G) = ((Y ⊕ H) ⊖ H)(G) (4)

There are several composite operators present in literature that are derived

from above four basic operators. Among other operations, Closing Opening

Difference Operation (CODO) explained in [26] , defined by (5), has shown smooth

and very small output for stable input signals.

VCODO = (Y.H)(G) − (Y ∘ H)(G) (5)

5.4 TEST SETUP FOR ARC FAULT GENERATION

Same test bench illustrated in chapter 4 was used in analysing arc faults for

MM as well. Fig.5.1 shows the PV panel, oscilloscope and lux meter that were used

in the experiment. Same apparatus used in previous chapters was used to generate

arcs.

PV

PWM

MPPT

Load

Battery

Series Fault

Parallel Fault


Fig.5.2 Test circuit (top) and setup (bottom).

An arc was formed by moving two contact points of Series Fault away from

each other and a parallel arc was formed by a short circuit across positive and

negative sides of the PV module. In each case, waveforms of voltage across PWM

and current through the fault were recorded.

Table 5.1. Electrical characteristics of PV Module at normal operating cell temperatures.

Parameter Value

Maximum Power (Pmax)

Open Circuit Voltage (Voc)

Short Circuit Current (Isc)

Voltage at Maximum Power (Vmpp)

Current at Maximum Power (Impp)

182 W

34.2 V

7.07 A

27.7 V

6.59A

An AGILENT DSOX2024A digital oscilloscope was used to store current and

voltage traces at 10 Giga samples per second rate.

Results obtained were the waveforms of current and voltage signatures of arcs.

For comparison purposes, waveforms were recorded from a point of time prior to arc

occurrence. This portion of the waveform contains noise created by pulse width

modulation operations of maximum power point tracking algorithms during pre-fault

normal operation of the system.

For each fault scenario, several tests were done and voltage and current

waveforms were recorded. One of the traces was randomly selected for further study.


5.5 PARALLEL ARC FAULTS

Current and voltage traces during a parallel fault are illustrated in Fig. 5.3

below.

Fig.5.3. Parallel Arc waveforms

5.5.1 Parallel Arc Current

Before the fault is introduced, system behaves under normal conditions.

Current drawn is influenced by the connected load and remaining capacity of battery

storage. Based on the irradiance level, MPPT controller adjusts total current. Noise

created by PWM is also visible in the waveforms.

-5.00

0.00

5.00

10.00

15.00

20.00

0.00

5.00

10.00

15.00

20.00

25.00

0.00E+00 9.00E-05 1.80E-04

CU

RR

EN

T [

A]

VO

LTA

GE

[V

]

TIME [SEC]

PARALLEL ARC FAULT

VOLTAGE CURRENT


Fig.5.4. Parallel arc current

At the end of the arc, fault becomes a short circuit between positive and

negative lines from PV panel. There is still a resistance created by cables connecting

PV panel and electrodes as well as contact resistance between two electrodes of test

apparatus. Hence the post fault current is higher than pre-fault current but is limited

by maximum current available at the irradiance level present during testing.

5.5.2 Parallel Arc Voltage

Fig.5.5. Parallel arc voltage


Similar to arc current, voltage has high frequency noise induced by PWM

function of the MPPT controller. Pre fault voltage is determined by irradiance and

connected load. Post fault voltage drops to near zero due to low resistance between

two supply lines due to short circuit across electrodes.

During the fault, voltage trace has more significant random fluctuations

compared to its current counterpart.

5.6 SERIES ARC FAULTS

Series fault was also initiated at around 10ms. The fault lasts for few

milliseconds and then voltage and current settle down to their post-fault values.

MPPT is still in force trying to adjust current drawn and system noises continue to

appear in the waveforms. In addition, spikes of random currents due to arc fault and

corresponding voltage spikes are also visible.

Series fault voltage and current traces are illustrated in Fig.5.6 below.

Fig.5.6. Series arc waveforms

5.6.1 Series Arc Current

In generating an arc across the electrodes that are in series with load of PV

system, there are two initial conditions that the experiment could be started with. The

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1.00

3.00

5.00

7.00

0.00

5.00

10.00

15.00

20.00

0.00E+00 9.00E-05 1.80E-04

CU

RR

EN

T [

A]

VO

LTA

GE

[V

]

TIME [SEC]

SERIES ARC FAULT

VOLTAGE

CURRENT


gap between electrodes could be kept closed or open and then move them toward or

away from each other to create an arc in between.

Arc was generated starting from an open air gap in the experiment and voltage

and current signatures were recorded.

Fig.5.7. Series arc current

During the arc, current increases to a maximum dependent of arc impedance

and connected load. High frequency random noise is visible during the arcing.

5.6.2 Series Arc Voltage

Fig.5.8. Series arc voltage


Voltage across the arc that corresponds to current flowing through could rise

up to a maximum determined by impedance of arc and rest of the load circuit.

Waveform has a significantly different shape during the arc that could be used to

detect its presence.

5.7 ANALYSIS OF ARC WAVEFORMS

Waveforms stored in the oscilloscope have to be streamlined in order to use

with MATLAB for calculation of morphological derivations.

A sample time of 1x10-7

S was selected and waveform data was sampled down.

A total of 2,000 samples were used to represent each waveform. Actual voltages and

currents during a fault depend on the capacity of the PV system concerned. Measured

values could be normalized by dividing actual readings by respective peak values

before analysing with morphology. This help compare results from different systems.

Table.5.2 Actual data set of arc waveform

SAMPLE

# TIME I_Series V_Series I-Parallel V_Parallel

[S] [A] [V] [A] [V]

1 0 - 0.10520 10.19573 8.57726 13.56935

2 0.0000001 - 0.10520 10.01884 4.55716 12.64472

3 0.0000002 - 0.10520 10.01884 8.57726 12.64472

4 0.0000003 - 0.10520 10.01884 4.55716 13.56935

5 0.0000004 - 0.10520 10.01884 6.56721 13.56935

6 0.0000005 - 0.10520 10.19573 4.55716 12.64472

7 0.0000006 0.09580 10.01884 6.56721 12.64472

8 0.0000007 - 0.10520 10.01884 6.56721 13.56935

9 0.0000008 - 0.10520 10.01884 6.56721 13.56935

10 0.0000009 - 0.10520 10.19573 6.56721 13.56935

11 0.000001 - 0.10520 10.01884 6.56721 13.56935

12 0.0000011 - 0.10520 10.01884 4.55716 13.56935

13 0.0000012 - 0.10520 10.01884 6.56721 13.56935

14 0.0000013 - 0.10520 10.01884 6.56721 13.56935

15 0.0000014 0.09580 10.19573 4.55716 12.64472

16 0.0000015 - 0.10520 10.01884 6.56721 12.64472

- - - - - -

- - - - - -

- - - - - -

1,998 0.0001997 - 0.10520 7.71935 8.57726 0.624623

1,999 0.0001998 0.09580 7.71935 8.57726 0.624623

2,000 0.0001999 - 0.30621 7.71935 8.57726 0.624623


I_Series = Actual Current during Series Arc Fault

V_Series = Actual Voltage during Series Arc Fault

I_Parallel = Actual Current during Parallel Arc Fault

V_Parallel = Actual Voltage during Parallel Arc Fault

With an open circuit voltage of 34.2V and a short circuit current of 7.07A,

normalized data set is given below.

Table.5.3 Normalized data set of arc waveform

SAMPLE

# TIME In_Series Vn_Series In-Parallel Vn_Parallel

[S] [A] [V] [A] [V]

1 - - 0.01488 0.29812 1.21319 0.39676

2 0.0000001 - 0.01488 0.29295 0.64458 0.36973

3 0.0000002 - 0.01488 0.29295 1.21319 0.36973

4 0.0000003 - 0.01488 0.29295 0.64458 0.39676

5 0.0000004 - 0.01488 0.29295 0.92888 0.39676

6 0.0000005 - 0.01488 0.29812 0.64458 0.36973

7 0.0000006 0.01355 0.29295 0.92888 0.36973

8 0.0000007 - 0.01488 0.29295 0.92888 0.39676

9 0.0000008 - 0.01488 0.29295 0.92888 0.39676

10 0.0000009 - 0.01488 0.29812 0.92888 0.39676

11 0.0000010 - 0.01488 0.29295 0.92888 0.39676

12 0.0000011 - 0.01488 0.29295 0.64458 0.39676

13 0.0000012 - 0.01488 0.29295 0.92888 0.39676

14 0.0000013 - 0.01488 0.29295 0.92888 0.39676

15 0.0000014 0.01355 0.29812 0.64458 0.36973

16 0.0000015 - 0.01488 0.29295 0.92888 0.36973

- - - - - -

- - - - - -

- - - - - -

1998 0.0001997 - 0.01488 0.22571 1.21319 0.01826

1999 0.0001998 0.01355 0.22571 1.21319 0.01826

2000 0.0001999 - 0.04331 0.22571 1.21319 0.01826


In_Series = Normalized Current during Series Arc Fault

Vn_Series = Normalized Voltage during Series Arc Fault

In_Parallel = Normalized Current during Parallel Arc Fault

Vn_Parallel = Normalized Voltage during Parallel Arc Fault

5.8 SELECTION OF STRUCTURED ELEMENT (SE)

No specific criterion for selection of SE for power system studies is reported in

literature.

Selection of an optimum SE depends on the type and frequency of the

disturbance and sampling rate of measurement [33]. In case of straight line SE, other

variables are the length and angle of SE. Length of SE determines the width of the

data window used for MM transformation. Each operation of Mathematical

Morphology creates a delay that is equal to ∆T(m-1)/2 seconds[2]. Here ∆T is the

sampling interval and m is the length of SE in terms of number of samples.

In general, very high sampling rates could be used to feed in signal data into a

processor that computes MM transformation. But protection equipment may not be

capable of responding to such high frequencies and a slower interface would be more

effective to communicate with protection equipment. In this scenario, a longer SE

could provide adequate time for protection equipment to respond. Effect of size of

SE on secondary equipment responsiveness is also investigated by using different

sized SE with same fault waveform data.

5.9 ARC FAULT DETECTION

Above waveform signatures were analysed in MATLAB. Two functions

“imdilate” and “imerode” were used to calculate dilation and erosion of the

waveform. Closing and Opening functions were derived by “imclose” and “imopen”

operations and then CODO was derived by subtracting opening from closing

functions.


The MATLAB code used for this is as below:

t=(0:0.0000001:0.0001999);%Definition of time span and sampling rate File1='waveform.xlsx'; %Read waveform from excel file. A=xlsread(File1)

SE1=strel('line',10,0); % Straight Line structuring element with

length 10 and angle 0 degree dA1=imdilate(A,SE1); % Calculation of Dilation eA1=imerode(A,SE1); % Calculation of Erosion cA1=imclose(A,SE1); % Calculation of Closing oA1=imopen(A,SE1); % Calculation of opening

CODO1=cA1-oA1; % Calculation of CODO

5.9.1 Morphological functions of parallel fault waveform signatures

In order to illustrate basic functions of MM for parallel fault current waveform,

dilation and erosion were calculated using above MATLAB codes and could be

plotted as shown in Fig.5.9. A straight line SE of length 10 was used for these basic

MM function plots.

Fig.5.9. Dilation and Erosion of Parallel Fault Current

Closing and Opening function of the same current waveform is plotted in

Fig.5.10.


Fig.5.10. Closing and Opening of Parallel Fault Current

All of these basic MM operations outline the boundary of original current

waveform signature. Average of these operations is similar to that of original

waveform under test. Pre fault current varies around 6 Amps mark and all four basic

MM operations resulted in waveforms that vary in the same region. Hence there is no

much difference between actual fault current and waveform of morphological

operations.

On the other hand, during parallel fault, shape of fault current signature and

resulted shapes of morphological basic operations are almost similar other than fact

that those operations represent the contour of fault current waveform.

Both above similarities among waveform signatures make these basic

morphological operations not suitable for differentiating faulty and non-faulty

regions of parallel fault current waveforms.


Fig.5.11. CODO Operation of Parallel Fault Current

CODO function on fault current results in a waveform which is separate and

independent of normal current waveform. During pre-fault time, CODO is a near

zero signal. There are significantly distinguishable spikes in the CODO output during

fault. This is more suitable than results of basic MM operations for detecting faults.

Voltage signature during parallel fault was similarly analysed using same MM

operations and results are plotted in following figures.


Fig.5.12. Dilation, Erosion, Closing, Opening and CODO functions of Parallel Fault Voltage.

Similar to MM functions of fault current, CODO operation provides better

possibility of separating faulty region for Voltage signature as well. Output from

basic MM operations on voltage again only provides signals that are similar to

measured waveform. But in case of CODO operation, pre-fault signal is almost zero

in magnitude and faulty region has large spikes that are easily distinguishable.

5.9.2 Morphological functions of series fault waveform signatures

Current through a series fault and voltage across input terminals of

MPPT/PWM controller were also analysed with mathematical morphology. A

straight line structuring element of length 10 was used with MATLAB functions

described in 6.9 above.


Fig.5.13. Dilation, Erosion, Closing, Opening and CODO functions of Series Fault Current.


Out of all morphological functions used, CODO function produced an outcome

that is easy to recognize compared to current waveform and its fault signature.

CODO output always remain close to zero areas other than during fault. It also

remained close to zero during time slots that current gradually increased or reduced

but generated clearly visible spikes whenever high frequency noise is present in the

fault current. Hence, this will not trigger any protective gears during a normal

increase or decrease of current due to changes in irradiance and shading.

Voltage measured across inverter DC side terminals produced MM results that

are illustrated below. A straight line structured element of length 10 was used for all

these plots.


Fig.5.14. Dilation, Erosion, Closing, Opening and CODO functions of Series Fault Voltage.

Similar to the results from series fault current analysis, opening, closing,

erosion and dilation follow the shape of fault voltage signature. But in case of

CODO, resulted waveform is near zero during pre-fault time span and produced

some spikes during fault. Hence CODO is more suitable to detect series faults using

voltage across inverter DC terminals.

5.9.3 Effect of length of Structuring Element

From the results presented in 5.9.1 and 5.9.2, it is evident that CODO operation

gives most appropriate results for fault detection. Resulted waveforms were produces

with a straight line structured element of length 10 and this section will investigate

the effect of length of SE on CODO function results.

Size of the SE plays a significant role on the shape of final outcome from

CODO operation. Also, it determines the delay involved in filtering the signal as

higher the length of SE higher the number of samples that are taken for MM

operations.


In order to understand the effect of length of SE in filtered signal output,

voltage across charge controller and current fed into the controller were analysed by

CODO operation using a SE of length 10, 20, 100 and 250 samples.


Fig.5.15. Effect of length of SE on CODO for Series Fault Voltage.

Amplitude of CODO signal remains near zero during non-faulty regions and

higher than 1 Volt during fault. Time that the CODO signal remains high increases

with increasing length of SE. Other than the initial peak of CODO signal at the

starting of the fault, SE length 250 produces more than 4 Volts output during fault.

But it could also be seen that shape of pre-fault CODO signal is also affected and it

tend to move away from zero before fault which could adversely affect detection

process.


Fig.5.16. Effect of length of SE on CODO for Parallel Fault Voltage.

Similarly, as illustrated in Fig. 5.16, CODO output of parallel fault voltage

traces gives promising results under different SE lengths. Output value for the faulty


region of the trace is significantly higher than that of during normal operation

irrespective of the presence of system noise.

Though increasing length of SE has a significant effect on the shape of CODO

output signal, it also depends on the shape of original signal which will be totally

different every time a fault occurs. An SE of length 10 displays sufficient separation

of faulty and normal operational regions of measured signal.

Not like in series fault voltage analysis at 250 long SE, parallel fault voltage

pre-fault CODO signal is not affected by the length of SE. Hence, SE 250 samples

length gives a longer and affective CODO output signal. This could be a result of

fairly constant pre-fault voltage that was present during parallel fault analysis.


5.10 CONCLUSIONS

High impedance faults of a PV system were analysed using Mathematical

Morphology and its associated derivatives. All the measurements were done at the

input ports to the MPPT controller which eliminates necessity of additional cabling

to capture fault signatures in a practical installation.

Current and voltage waveforms of series and parallel faults were used as the

measurement for fault detection. Fault current waveforms provide evidence that there

is no much difference of current magnitude during the fault compared to that of

during normal operation. Several current spikes could be present but the duration is

very short that traditional over current protection switchgear may not effectively

detect and isolate faulty circuits.

Among the basic morphological functions and its derivatives, CODO operation

exhibited strong separation of faulty and non-faulty regions of the waveforms

analysed.

It was also revealed that both series and parallel arc faults could be identified

with the use of very short structuring elements, in the range of 10 samples, which

paves the way for speedy detection of faults. Longer SEs slow down detection speed

due to larger number of samples analysed though it makes it easier to separate

faulted waveform from a healthy segment of measured signals.

When it comes to measurement of voltage and current at high sampling rates

similar to that used in this study, it is more economical to use voltage as measured

signal than current. Mathematical morphology could be used effectively to detect

faults by measuring only voltage across MPPT controller for both series and parallel

arcs.

58 Chapter 6: Conclusions and future work

Chapter 6: Conclusions and future work

Photovoltaic systems behave as a current source of which the capacity depends

on factors such as irradiance, shading, configurations of individual PV modules etc.

Hence amount of energy dissipated through an arc fault in a PV installation also

depends on such factors.

Current and voltage magnitudes associated with an arc fault could be smaller

than maximum values that could be present during healthy operation of the system if

the fault occurs during low irradiance or shaded conditions; this makes it impossible

to detect such faults using conventional protection equipment.

In order to successfully detect arc faults in a PV system, protection switchgear

should be capable of identifying changes in the voltage and current signatures in

addition to the magnitudes of those signals.

Two separate methods that could be used to identify changes in shape of arc

fault current and voltage were discussed and tested in this research work. Both those

systems were proved to be effective in detecting arc faults in a PV system whether

the fault is a series or parallel arc.

6.1 WAVELET TRANSFORM

Wavelet transformation of fault voltage could successfully be used to identify

both series and parallel arc faults. Voltage signature itself gives adequate results and

there is no need to monitor current to identify the fault.

Level of decomposition or frequency sub band that gives optimum results is

different for series and parallel faults. But these sub bands are closer to each other

that overall level of decomposition required to detect both types of faults is small. In

this research, it is shown that both series and parallel faults could be detected by

using up to 9th

frequency sub band.

Also, measurement of voltage was done at input terminals to MPPT controller

and hence there is no need for additional cabling or current transformers.

Chapter 6: Conclusions and future work 59

6.2 MATHEMATICAL MORPHOLOGY

Basic morphological functions as well and their derivatives were used to

analyse arc fault voltage and current signatures. Among the basic morphological

functions and its derivatives, CODO operation exhibited most prominent separation

of faulty and non-faulty regions of the waveforms analysed.

Length of the structuring element plays a significant role in the shape of output

waveform signatures. Both series and parallel arc faults could be identified with the

use of very short structuring elements, in the range of 10 samples. Such short SEs

paves the way for speedy detection of faults. Longer SEs slow down detection speed

due to larger number of samples analysed though it makes it easier to separate

faulted waveform from a healthy segment of measured signals.

When it comes to measurement of voltage and current at high sampling rates

similar to that used in this study, it is more economical to use voltage as measured

signal than current. Mathematical morphology could be used effectively to detect

faults by measuring only voltage across MPPT controller for both series and parallel

arcs.

6.3 FUTURE WORK

Throughout this research, arc fault waveforms that were obtained by creating

an arc in the specially designed test bench were used. Arc was formed by manually

adjusting the gap between fixed and moving electrodes.

In reality, arc gap doesn’t change gradually but it also changes rapidly and

randomly. The test bench could be further developed by introducing a controlled way

of changing the gap between electrodes and it could be used to analyse more

complex arc faults. When arc length rapidly changes, frequency composition of

measured signals vary and its worthwhile to see if wavelet transform and

mathematical morphology could still be used to detect arc faults. Such a developed

system could be used to replicate falling cables by separating the gap at acceleration

equal to gravity.

60 Chapter 6: Conclusions and future work

In this research arc faults that occur closer to MPPT controller and between

final positive and negative cables were considered. In a real world PV installation,

arcs could occur at various places of the installation. For example, a series fault

could easily occur at terminal boxes of any PV module. A further study should be

done to see if similar techniques could be used to accurately locate the location of the

arc fault.

In addition to series and parallel arcs, a fault that occurs between live parts and

ground or adjacent structures also poses great risks. Same approach of detection may

be useful to detect and locate such faults and creates space for a future study.

Once the fault is identified and located, the affected portion of the installation

should be isolated to make sure safety of property and human lives. In order to

achieve this, measurement and analysis system could be incorporated with a micro

controller. Another area of further development is to design and program such a

controller and also to investigate possibility of having this as a part of MPPT or

charge controller.

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