Applied Science, Faculty of
Electrical and Computer Engineering, Department of
DSpace
UBCV
Martinez, Gervasio
Master of Applied Science - MASc
University of British Columbia
Photovoltaic (PV) systems are an increasingly important source of renewable energy, providing clean, sustainable power for residential and industrial applications. However, they face safety challenges, particularly the risk of arc faults, which occur when electrical current flows through unintended paths, potentially leading to fires or safety risks. Servicing the installation helps prevent this issue, but it is typically expensive and seldom carried out. Therefore, detecting arc faults becomes crucial not only to prevent these hazards but also to comply with safety standards such as UL1699B. This work explores several arc fault detection methods, focusing on computationally efficient techniques suitable for low-cost microcontrollers commonly found in commercial PV systems. Key techniques examined include frequency-domain analysis, wavelet transforms, and digital signal processing, all chosen to balance performance with the hardware limitations imposed by cost constraints. By expanding on the standard test cases defined in UL1699B, a more comprehensive and robust analysis was performed, introducing various real-world disturbances such as converter noise and power line communication (PLC) signals. These additional perturbations allow for more rigorous testing of the detection methods, ensuring a robust performance under challenging operational conditions and reducing false positives. The proposed WIK strategy, which integrates Wavelet transforms, IIR filtering, and Kurtosis analysis, is introduced as an innovative and highly effective solution for arc fault detection. This method balances high detection accuracy with low computational demand, making it ideal for cost-sensitive applications. Extensive testing shows that the WIK strategy is not only compliant with safety standards but also capable of filtering out noise and disturbances, ensuring optimal performance, reliability, and safety for PV installations.
Digital Filters For PV Arc FaultDetectionbyGervasio MartinezIng., Universidad Nacional del Comahue, 2019A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Electrical and Computer Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2024© Gervasio Martinez 2024The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Digital Filters for PV Arc Fault Detection submitted by Gervasio Martinez in partial fulfilment of the requirements for the degree of Master of Applied Science in Electrical and Computer Engineering Examining Committee: Dr. Martin Ordonez, Professor, Electrical and Computer Engineering, UBC Supervisor Dr. Shahriar Mirabbasi, Professor, Electrical and Computer Engineering, UBC Supervisory Committee Member Dr. Sudip Shekhar, Professor, Electrical and Computer Engineering, UBC Supervisory Committee Member iiAbstractPhotovoltaic (PV) systems are an increasingly important source of renew-able energy, providing clean, sustainable power for residential and industrialapplications. However, they face safety challenges, particularly the risk ofarc faults, which occur when electrical current flows through unintendedpaths, potentially leading to fires or safety risks. Servicing the installationhelps prevent this issue, but it is typically expensive and seldom carriedout. Therefore, detecting arc faults becomes crucial not only to preventthese hazards but also to comply with safety standards such as UL1699B.This work explores several arc fault detection methods, focusing on com-putationally efficient techniques suitable for low-cost microcontrollers com-monly found in commercial PV systems. Key techniques examined includefrequency-domain analysis, wavelet transforms, and digital signal processing,all chosen to balance performance with the hardware limitations imposed bycost constraints.By expanding on the standard test cases defined in UL1699B, a morecomprehensive and robust analysis was performed, introducing various real-world disturbances such as converter noise and power line communication(PLC) signals. These additional perturbations allow for more rigorous test-ing of the detection methods, ensuring a robust performance under challeng-ing operational conditions and reducing false positives.The proposed WIK strategy, which integrates Wavelet transforms, IIRfiltering, and Kurtosis analysis, is introduced as an innovative and highly ef-fective solution for arc fault detection. This method balances high detectionaccuracy with low computational demand, making it ideal for cost-sensitiveapplications. Extensive testing shows that the WIK strategy is not onlycompliant with safety standards but also capable of filtering out noise anddisturbances, ensuring optimal performance, reliability, and safety for PVinstallations.iiiLay SummarySolar power is a clean and growing energy source, but photovoltaic (PV)systems can face safety risks from arc faults, where electricity flows throughunintended paths, potentially causing fires or damage. While servicing PVinstallations can help prevent these arcs, it is usually expensive, making ahighly reliable detection strategy crucial. This thesis explores methods todetect arc faults, focusing on analyzing electrical signals to identify faultsearly. The research aims to develop a detection strategy that is both accu-rate and cost-effective, without requiring complex hardware, while ensuringit meets safety standards like UL 1699B. By testing the proposed methodon real equipment, this study offers a solution to enhance the safety andreliability of solar power systems.ivPrefaceThis thesis entitled “Digital Filters For PV Arc Fault Detection” presentsthe original, unpublished, and independent work of the author, GervasioMartinez under the supervision of Dr. Martin Ordonez over the course of aMaster of Applied Science (MASc) program at UBC Electrical & ComputerEngineering.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Hazards In Photovoltaic Systems . . . . . . . . . . . . . . . 21.3 Arc Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Challenges and Research Objectives . . . . . . . . . . . . . . 41.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Photovoltaic Systems . . . . . . . . . . . . . . . . . . . . . . 72.2 The Power Converter In PV System . . . . . . . . . . . . . . 92.3 Arc Faults In PV Arrays . . . . . . . . . . . . . . . . . . . . 102.3.1 The Arc Characteristics . . . . . . . . . . . . . . . . . 132.3.2 Steady State V-I . . . . . . . . . . . . . . . . . . . . . 132.3.3 High Frequency Response . . . . . . . . . . . . . . . . 142.3.4 Transient Response . . . . . . . . . . . . . . . . . . . 152.4 Arc Fault Detection . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Disturbances In DC Arc Faults . . . . . . . . . . . . 16vi2.5 Detection Techniques . . . . . . . . . . . . . . . . . . . . . . 182.5.1 Statistical Analysis . . . . . . . . . . . . . . . . . . . 192.5.2 Fast Fourier Transform . . . . . . . . . . . . . . . . . 192.5.3 Short Time Fourier Transform . . . . . . . . . . . . . 212.5.4 Wavelet Transform . . . . . . . . . . . . . . . . . . . 232.5.5 Artificial Intelligence And Machine Learning . . . . . 252.6 Summary And Challenges In DC Arc Fault Detection . . . . 283 System Design and Experimental Setup . . . . . . . . . . . 303.1 Standards and Safety Regulations . . . . . . . . . . . . . . . 303.1.1 Arc Fault Detection Tests . . . . . . . . . . . . . . . 313.1.2 Unwanted Tripping Tests . . . . . . . . . . . . . . . . 313.2 Decoupling Network and Line Impedance . . . . . . . . . . . 323.2.1 Arc Fault Generator . . . . . . . . . . . . . . . . . . . 353.3 Analog Front-End . . . . . . . . . . . . . . . . . . . . . . . . 363.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4 Experimental Testing . . . . . . . . . . . . . . . . . . . . . . 373.4.1 Detection System Setup . . . . . . . . . . . . . . . . . 373.4.2 Other Components . . . . . . . . . . . . . . . . . . . 383.4.3 Analog front End Performance . . . . . . . . . . . . . 383.4.4 UL Network Frequency Response . . . . . . . . . . . 403.5 Summary of Hardware Setup . . . . . . . . . . . . . . . . . . 424 Detection Strategy and Experimental Results . . . . . . . . 434.1 Arc Fault Tests . . . . . . . . . . . . . . . . . . . . . . . . . 434.1.1 Test Recordings . . . . . . . . . . . . . . . . . . . . . 434.1.2 The Arc Signature . . . . . . . . . . . . . . . . . . . . 444.2 Feature Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 454.2.1 Methodology And Chosen Features . . . . . . . . . . 454.2.2 Accuracy Analysis . . . . . . . . . . . . . . . . . . . . 474.2.3 Summary of Performance . . . . . . . . . . . . . . . . 474.3 Detection Strategy . . . . . . . . . . . . . . . . . . . . . . . . 564.3.1 Wavelet Decomposition And Moving Minimum . . . . 564.3.2 The IIR Filter . . . . . . . . . . . . . . . . . . . . . . 574.3.3 Robustness Improvement Through Kurtosis . . . . . 604.3.4 Experimental Results . . . . . . . . . . . . . . . . . . 614.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66vii5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78A Haar Discrete Wavelet Transform . . . . . . . . . . . . . . . 78viiiList of Tables3.1 Decoupling Network And Line Impedance Parameters . . . . 343.2 Current And Gap Requirements For Arc Faults . . . . . . . . 354.1 Performance Summary Of The Time And Frequency DomainFeatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Computation Complexity of Features . . . . . . . . . . . . . . 554.3 Comparison of Commonly Used Detection Methods and Pro-posed WIK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.4 Summary of Selected Features and IIR Filter . . . . . . . . . 67ixList of Figures1.1 Solar Radiation Intensity (kWh/kWp) Map Of Canada . . . . 21.2 Examples Of Possible Locations Of Arc Faults . . . . . . . . 42.1 Typical System Configuration Of a PV System . . . . . . . . 72.2 DC Arc fault Between Two Copper Bars . . . . . . . . . . . . 112.3 Process For Assembling a PV Array . . . . . . . . . . . . . . 122.4 Model Of An Arc Fault As a Dynamic Series Resistance . . . 132.5 V-I Curve For An Arc Fault For Different Gaps . . . . . . . 142.6 Typical AC Arc Fault Current And Voltage . . . . . . . . . . 162.7 Difference In Voltage And Current Noise . . . . . . . . . . . 172.8 Typical Sources Of Disturbances In DC Arc Fault Detection 182.9 Short Time Fourier Transform And The Overlapping Method 222.10 Comparison Of STFT Resolution For Different Windows . . . 222.11 Comparison Of FFT, STFT And Wavelets Frequency Reso-lution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.12 Different Types of Mother Wavelets . . . . . . . . . . . . . . 242.13 Graphical Representation Of Discrete Wavelet Transform AndWavelet Packet Decomposition . . . . . . . . . . . . . . . . . 242.14 Graphical Representation Of Support Vector Machines . . . . 273.1 Location of Arc Faults For Testing According To UL 1699b . 313.2 Unwanted Trip Testing According To The UL Standard . . . 323.3 Hardware Setup Required For Arc Fault Tests . . . . . . . . . 333.4 Frequency Response Of The UL Network . . . . . . . . . . . 343.5 Hardware Setup Required For Unwanted Tripping Tests . . . 343.6 Arc fault Generator Diagram. . . . . . . . . . . . . . . . . . . 353.7 Proposed Arc Fault Detector . . . . . . . . . . . . . . . . . . 363.8 Analog Front End Circuit . . . . . . . . . . . . . . . . . . . . 373.9 Experimental Setup Diagram . . . . . . . . . . . . . . . . . . 383.10 Comparison Of The Frequency Response Between AC AndDC Measurement Of The Arc . . . . . . . . . . . . . . . . . . 393.11 Performance Of The Analog Front End Against Disturbances 39x3.12 Arc Frequency Signature For Different Line’s Impedance . . . 413.13 Frequency Signature For Different Arc Locations . . . . . . . 424.1 Power Spectral Density Of The Arc For Various Scenarios . . 444.2 Methodology For Processing The Arc Measurements . . . . . 454.3 Performance Analysis Through Decision Stump . . . . . . . . 454.4 Frequency Response Of The Details Coefficients Of DWT . . 464.5 Frequency Response Of The Multi Band STFT . . . . . . . . 464.6 Statistical Features During An Arc Fault . . . . . . . . . . . 484.7 Performance of Statistical Features . . . . . . . . . . . . . . . 494.8 Frequency Band Features During An Arc Fault . . . . . . . . 504.9 Performance Of The Frequency Band Features . . . . . . . . 514.10 DWT Db1 And Db5 Coefficients During An Arc Fault . . . . 524.11 Performance Of The DWT Db1 Coefficients . . . . . . . . . . 534.12 Performance Of The DWT Db5 Coefficients . . . . . . . . . . 544.13 Wavelet Transform And Minimum Filtering . . . . . . . . . . 574.14 IIR Filtering Effect In The Detection Algorithm . . . . . . . 594.15 Proposed Arc Fault Detection Algorithm (WIK) . . . . . . . 614.16 Detection Strategy Performance Against The Converter Noise AndArc Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.17 Kurtosis Behavior In Uniform Signals And Arc Faults . . . . . . . 644.18 False Trip Sources, Mitigation And Kurtosis Influence . . . . . . . 65xiAcknowledgementsI would like to express my sincere gratitude to my supervisor, Dr. MartinOrdonez, for welcoming me into his research team. His enthusiasm, consis-tent support, dedication, and mentorship made my Master’s journey a trulyenriching and captivating experience.I would also like to extend my thanks to my lab mates and all membersof Dr. Ordonez’s research team. Their feedback, suggestions, and insight-ful discussions greatly contributed to making my time in the lab not onlyproductive but also enjoyable, far beyond just the technical aspects. A spe-cial mention goes to Glenn Fawcett, whose invaluable guidance, time, andunwavering support, both technically and personally, made a significant dif-ference throughout my work.I am deeply grateful to the University of British Columbia, the Facultyof Graduate and Postdoctoral Studies, and the Department of Electricaland Computer Engineering for providing me with this opportunity and forthe support I received throughout. I especially want to acknowledge theprofessors whose courses I attended during the program for sharing theirinvaluable knowledge.I would like to express my heartfelt gratitude to my family, who have al-ways stood by me and supported every step and decision I’ve made through-out my life. I am especially thankful to my brother, Joaquin, whose constantinspiration and encouragement have guided me, particularly during my mostdifficult times.Finally, I extend my sincere thanks to you for taking the time to readthis work.xiiDedicationTo my family and friends.xiiiChapter 1Introduction1.1 OverviewEnergy is a main driver of wealth creation and a big factor in any country’seconomic growth and its people’s quality of life [1]. Therefore, the globaldemand for energy, especially electricity, is always growing [2]. Even thoughthere is still plenty of petroleum-based energy, worldwide environmental con-cerns have been strongly promoting renewable energy alternatives. Amongthe different kinds of renewable energy, solar power, especially photovoltaicenergy, is the most promising sustainable source because it doesn’t haveproblems with supply or create environmental hazards. Solar PV is ex-pected to be the biggest supplier of sustainable power by 2040 [2] , and itsgreatest advantage compared to other forms of energy is that it is environ-mentally friendly, abundant , and can be supplied without any pollution [1].Consequently, Photovoltaic (PV) systems have become a key elementfor countries in their efforts to shift toward renewable energy. Not only dothey provide a clean energy source from sunlight, but their scalability andrelatively low maintenance costs have made these systems popular acrossresidential and industrial sectors. In Canada, for example, the potential forPV development is significant, considering its vast territory and favorableradiation in areas like Alberta, Saskatchewan, Manitoba and Ontario, asshown in Fig 1.1 . According to Romel et al. [3], the country is expected toincrease its solar installation deployments, with a substantial grow in bothurban and rural areas. Moreover this study also highlights that, thanks toCanada’s commitment to a greener country through strategic policies andinvestments in renewable energies, the nation could potentially become aleading solar energy producer.Some case studies like the one conducted in Lethbridge, Alberta alsoreveals the economic feasibility of PV on rooftops, which could help pro-vide a significant portion of the residential electrical needs [4]. Floating PVsystems, which are becoming a growing trend in solar production, could ex-1pand Canada’s potentially even further given the huge availability of bodiesof water across the country [5].Figure 1.1: Solar radiation intensity (kWh/kWp) map of Canada with itsprovinces and territories [6]1.2 Hazards In Photovoltaic SystemsDespite their many environmental and economic benefits, PV systems alsocome with particular risks. Electrical hazards like over voltages, groundfaults and lighting strikes, can degrade the performance of photovoltaic mod-ules, damage power converters and even lead to fires in extreme cases [7] [8]. Lightning strikes, for example, inject surge currents into the system thatcan cause both immediate damage and degradation, raising a serious con-cern for some PV installations [9].However, among the most significant hazards in these systems are arcfaults, which constitute serious threats such as fires, equipment damage andpersonal harm [10]. These faults occur when electrical current flows throughan unintended path, rising temperature and possibly igniting surroundingmaterials, such as plastic covers or isolations [11]. Arcs are particularlydangerous in high-voltage DC systems. As opposed to AC systems with2their natural alternating current at zero crossing, the current in DC circuitsremains almost constant and sustains the arc, hindering its extinction andincreasing the risk of fires or damage to the system.Several PV accidents have raised concerns and highlighted the devas-tating consequences of arc faults. Wu et al [11], reported various incidentsoriginated by arc faults in both residential and commercial PV deployments,emphasizing the importance of these hazards and their prevention. The dan-ger worsens in those installations where the DC voltage is higher, as normallyseen in large-scale systems, because arc faults are more likely to take placethere [12].1.3 Arc FaultsArc faults are a special kind of hazard, not only because they can go un-noticed for a long time, but also they can slowly damage or degrade thesystem without tripping the conventional safety mechanisms [7] . In manyreported cases of rooftop fires, it was found that the main cause of themwere unextinguished arc faults, raising public awareness about them andleading to efforts to detect and prevent them [13].These types of faults are classified depending on the topology of thecircuit into two: parallel and series. Parallel arc faults occur between con-ductors of different potentials or between a conductor and ground, the latternormally referred as ground arc fault. Series arc faults happen when a singleconductor have a loose connection, likely because it wasn’t properly assem-bled or the cable was worn out [14]. Both faults are depicted in Figure 1.2.While parallel arc faults are typically more straightforward to detect [15],since the changes in the current and voltage are evident, series arc faultspresent a peculiar challenge [16]. These last ones often go undetected intheir early stages and cause a slow, but steady, deterioration of system com-ponents, that eventually leads to catastrophic failures if not addressed[17].The challenge in their detection has to do with the fact that they do not gen-erate a sudden change in current or voltage, and therefore can not be easilyidentified by traditional hardware protections (such as breakers or fuses) [18].3Ground faultSeries arc faultPV ArrayParallel arc faultCombiner BoxSeries and parallel arc fault in combiner boxFigure 1.2: Examples of possible locations where an arc fault might occurin a PV system.[13]Furthermore, those changes in the electrical magnitudes produced bythe series arc faults can also be mistaken for mere variations in solar ir-radiance or sudden shadows on the panels. Then, the standard controlprograms inside the converters (i.e., overcurrent, overvoltage, or maximumpower tracker algorithms) fail to detect them as well, as they interpret themas normal operating conditions of the PV system [19]. These faults exhibitmore subtle electrical signature[20], requiring advanced detection methodsthat can identify them before they produce damage or injuries.1.4 Challenges and Research ObjectivesArc fault detection (AFD) is not just a safety measure; it is essential forensuring the operational effectiveness and longevity of solar power systems.Given that servicing PV installations can be costly, implementing a highlyreliable detection strategy is essential for reducing risks, ensuring systemuptime, and promoting wider adoption of renewable technologies. Detect-ing arcs early helps prevent severe damage to system components, therebyavoiding expensive repairs [21], and also meets the safety regulations man-dated in many countries, such as UL 1699B [22].Despite the importance of AFD, many current detection algorithms rely4on complex computations [13], which significantly increase the processingrequirements of embedded controllers [23]. This, in turn, raises the overallcost of manufacturing power converters. Additionally, in certain applica-tions, arc fault detection depends on external devices such as antennas [24][25], which not only complicate installation but also increase the total sys-tem cost.Moreover, the challenges of existing arc fault detection methodologiesextend beyond just computational complexity and hardware requirements.Many of these algorithms have not been fully tested across diverse distur-bance conditions. While the UL 1699B standard provides a set of standard-ized measurements to evaluate arc faults and minimize unwanted tripping,it does not adequately cover a wide range of real-world scenarios. For exam-ple, the standard does not account for interference from noise sources suchas converter noise or power line communication (PLC) signals from rapidshutdown systems. These additional disturbances can compromise detectionaccuracy, either leading to false positives or missed detections.As a result, inverter manufacturers are often compelled to outsource thedevelopment of arc fault detection solutions to third-party vendors to meetregulatory requirements. However, these outsourced solutions are frequentlysuboptimal, as they are not fully tailored to the specific power converter de-signs, resulting in poor integration and inconsistent performance [26].Given these limitations, this thesis proposes a new approach to arc faultdetection that aims to balance several critical factors: regulatory compli-ance, cost-effectiveness, robustness, and computational efficiency. The goalis to develop a solution that meets the UL 1699B standard while also ad-dressing its limitations. Specifically, this thesis will focus on extending thetesting scenarios beyond those prescribed by UL 1699B to create a morecomprehensive detection algorithm capable of handling a wider range ofnoise sources and disturbances.By incorporating a broader range of real-world conditions, the proposedalgorithm seeks to minimize false tripping and improve detection accuracy.At the same time, efforts will be made to reduce the computational burden,making the solution suitable for deployment on low-power, cost-sensitive mi-crocontrollers commonly used in PV systems. This approach ensures thatthe detection algorithm is not only compliant with safety standards but alsopractical for manufacturers aiming to keep production costs low.5In conclusion, this thesis aims to deliver a robust arc fault detectionsolution that bridges the gap between regulatory requirements, real-worldoperational challenges, and the need for cost-effective, efficient implementa-tions in PV systems.1.5 Thesis OutlineThe present work is organized as follows:Chapter 2 presents the main components of a PV system and providesa detailed explanation of the arc fault phenomenon. It also examines var-ious hardware strategies for measuring arc signatures, along with multipledetection algorithms.Chapter 3 discusses the experimental setup, including the code re-quirements for conducting the tests, searching for false trips, the necessaryhardware, and the analog front-end design for current measurements.Chapter 4 presents the lowest computationally intensive algorithms forarc fault detection, evaluates their effectiveness, and introduces the proposedtechnique (WIK) for arc fault detection along with its strategies to improveperformance and robustness.Chapter 5 provides concluding remarks and suggests potential futureimprovements.6Chapter 2Literature Review2.1 Photovoltaic SystemsPhotovoltaic (PV) systems normally consists of numerous solar panels con-nected together, DC-DC converters which regulates the voltage coming outof them, inverters to transmit the generated power to the grid, and batter-ies or any energy storage device to provide a back up. A typical system isshown in Figure 2.1.Solar Modules AC LoadLoadInverterChargerConverterSolar chargerConverterDC Bus AC BusBatteryFigure 2.1: Typical system configuration of a PV system with batterycharger.PV installations for commercial and residential use can vary substan-tially according to the topology they use, the size of the system, the requiredpower, and the location of the installation. The main types include stringinverters, microinverters and DC optimizers.String inverter systems are one of the most common configurations forboth residential and commercial applications. In these systems, multiplesolar panels are connected in series to form a string or strings, and the com-7bined DC voltage is then sent to a single inverter. The latter converts thishigh DC voltage into AC, that is then injected into the grid to be utilized.The key advantage of string inverters is their lower cost, but they tend toperform poorly if one panel in the string is shaded or faulty, and thereforethey are ideal for installations without any obstacles that could cast shadeon the array [27].One way to overcome this issue is to deploy a microinverter system,which provides a more suitable solution for installations with shading orcomplex rooftops, as now each solar panel is paired with its own small in-verter. Because this design allows each panel to function independently andinject its own AC into the grid, any shadowed panel won’t compromise theentire installation, maximizing the energy yield. Although they are initiallymore expensive compared to string inverters, their greater performance insome scenarios might compensate for their cost [28].A solution between the previous two is the DC optimizer system, whichcombines the advantages of string inverters with panel-level optimization[29] . As with microinverters, the DC optimizers are attached to each solarpanel, but instead of AC, they output to a single DC bus, which is thenconnected to a central string inverter. This strategy improves the overallsystem efficiency by individualizing each panel and solving the shading issue,but with lower hardware requirements since they don’t directly export tothe grid [30]. Consequently, they are more complex than traditional stringinverter systems but less expensive than microinverter solutions. In termsof arc fault detection, string inverters are usually more exposed to this faultsince there is only one device capable of detecting the arc signature. Withmicroinverters, not only are arcs far less common because the DC panelvoltage is lower than that of a string inverter, but their proximity to thepanel also makes it easier for them to detect arc signal and shut down. Asimilar reasoning applies to DC optimizers: despite sharing a high DC volt-age prone to arc faults, they are all close to the panels and monitor togetherto detect them.Depending on the application, these systems can be further classifiedinto grid-tied systems, off-grid systems, or hybrid systems. Grid-tied sys-tems, the most common type, are connected to the power grid, and exportto it the excess energy produced by the solar panels, generating revenues[31]. However, whenever the array is not generating enough energy, thesystem draws electricity from the utility. On the contrary, in those remote8locations without access to a electric grid , off-grid systems are the deployedsolutions. These systems operate completely independent of the grid andrequire a battery storage, and sometimes a backup generator, to supply elec-tricity to the installation when the panels produce insufficient power [32].Lastly, hybrid inverter systems combine the previous two solutions, andhave grown popular in the last few years due to the new technologies andadvancements in batteries, in particular lithium-based ones. These systemsare equipped to handle the conversion of solar power, energy backup, andthe grid connection for exporting or importing according to the power needs[33] . The disadvantages of these systems are their higher cost and com-plexity compared to grid-tie solutions, but cheaper than off-grid since therequirements for battery storage are less.2.2 The Power Converter In PV SystemThe output of a photovoltaic panel is characterized by its current-voltage(I-V) curve, that displays how current and voltage interact under specificirradiance and temperature conditions (typically at 1000 W/m2 and 25°C)[34]. That curve illustrates high current and low voltage during short-circuitconditions (Isc) and high voltage with low current at open-circuit (Voc). Theoperating point, determined by the load connected to the panel, falls some-where along that curve and defines the panel’s power output. The maximumpower point (MPP), where the product of current and voltage reaches itspeak, represents the maximum output the panel can achieve, and is crucialfor sizing the associated converters. Since sunlight and environmental fac-tors constantly change, the location of the MPP moves as well, requiringcontinuous tracking to optimize the panel’s performance.The DC-DC converters attached to the panels regulate the output cur-rent and voltage from them, in order to meet the requirements of the load,such as the grid or a battery system. These devices are responsible foradapting the varying voltage coming out of the panel to a stable and appro-priate one, and the type used depends on the system’s requirements. Whilebuck converters and boost converters are the most common topologies, inthose cases where more flexibility is required, buck-boost, SEPIC, and Cukconverters are employed, as they can step down or up the output voltage [35].9Regardless of the topology used, all converters attached to a panel mustensure they operate them at their maximum capacity via a Maximum PowerPoint Tracking (MPPT) algorithm in their control logic. This class of algo-rithms continuously regulates the operating point of the PV panel to trackthe MPP on the I-V curve, avoiding suboptimal points and reduced powerproduction. Although there are plenty of techniques to achieve this goal,one of the most used is called Perturb and Observe (P&O) [36]. By intro-ducing a perturbance, if the power increases, the voltage is further adjustedin the same direction, and vice versa. Other techniques, like fuzzy logic [37]or neural network-based algorithms [38] offer more sophisticated approachesto elevate the efficiency of the system, at the cost of more complexity.The type of DC-DC converter used in a solar panel system, along withtheir MPPT logic, has a direct impact on the occurrence and severity of arcfaults within PV installations. Each kind of converter introduces differentlevels of voltage and current ripple that depend on its design, the passiveand active components used and the switching characteristics. For example,excessive ripple can stress electrical components [39] and connections, thatovertime lead to degradation of the insulation materials and connectors [40],increasing the probability of arc fault formation.From a frequency-domain perspective, the switching frequency and thetransients, associated with the used topology, also generate electrical noiseand spikes that could compromise some detection algorithms of arc faults.Another case is the MPPT algorithm: if it changes the operating point toofrequently, it could potentially affect some detection strategies as well, sinceit increases the floor noise of the current signals.2.3 Arc Faults In PV ArraysAccording to the Underwriters Laboratories (UL) Standard UL1699 [22] ,an arc fault is described as a sustained luminous electrical discharge acrossan insulating material, often leading to partial melting of the electrodes,as seen in Figure 2.2. It happens due to the breakdown of the insulationin the electrical circuit, loose electrical connections, moisture in the air, orweakening of the insulation. The high heat generated by the arc fault caneasily ignite nearby flammable objects (like insulating plastics), making it amajor cause of electrical fires.10Figure 2.2: DC Arc fault between two copper bars. Here the air is ionizedand becomes a conductor.DC arc faults are intricate, unpredictable electrical phenomenon in-fluenced by environmental factors. Consequently, physical variables suchas ambient temperature, pressure, humidity, wind speed, electrode move-ment, nearby insulation, thermal convection, and others alter the arc fault’simpedance characteristics, making it challenging to determine consistentphysical constants across all environmental and electrical conditions [41][13].To understand the relationship with solar panels, it is important to firstdefine the fundamental structure of a solar array, as illustrated in Figure 2.3.The PV cells are connected together to form a solar module, which are thenconnected in series to form a solar string, increasing the DC operating levelof the whole system. These solar strings can also be connected in parallel toincrease the DC current level, consequently increasing the power generationcapability [42].As mentioned in the introduction, there are two main types of arc faultsin PV systems: series and parallel, with the latter also including groundingarc faults. Parallel and grounding arc faults tend to generate large faultcurrents because of the significant potential difference, making them easierto detect with standard protection devices like breakers or fuses [43]. Onthe other hand, series arc faults, since they introduce an impedance in serieswith the circuit, the current will be lower (less than the normal operatingcurrent) and will not trip an overcurrent device.11Series SeriesPV ModulePV Cell PV StringPV ArrayParallelFigure 2.3: Process for assembling a PV array.Parallel arcs develop between conductors from different strings, two con-ductors in the same string, or between a conductor and a grounding point.These arcs are typically caused by insulation breakdown due to factors likeanimal interference, mechanical damage, or aging. This occurs becausemany cables and wires in PV systems are exposed to the elements with-out protective covers [44]. Parallel arc faults, excluding grounding faults,are less common in PV systems compared to series arc faults [16]. As aresult, most PV system standards and regulations focus on detecting andprotecting against series arc faults.Series arcs can occur in small gaps between connected terminals, such asbusbar-ribbon connections in PV modules or connections in a combiner box.Factors like lack of maintenance, aging, weather effects (e.g., corrosion fromrain), mechanical damage caused by wind, animal interference, or improperwiring can create poor joints. These bad joints reduce the cross-sectionalarea, increase connection resistance, and significantly raise heat loss. Thisextra heat causes thermal stress, speeding up the deterioration of connec-tions, eventually leading to loose joints [45] . Therefore, a small gap mayform between two terminals without disrupting the current flow. When theelectric field across the gap exceeds around 3 V/µm (depending on environ-mental conditions surrounding the gap), the air ionizes, forming arc plasmaand a series arc. Oxygen feeding into the plasma sustains the arc discharge,and the gap size for series arcs is usually less than a few millimeters.Because of the design of PV systems and the nature of PV modules, therecan be thousands of connectors and a large amount of cabling in the system.Each connection point has the potential to create an arc fault, therefore thechances of such fault events rises substantially, particularly series arc faults.Additionally, since the power converter operates with an MPPT algorithm,12the fault current can return to normal levels even if the arc fault remainspresent, making it more difficult to detect DC arc faults.2.3.1 The Arc CharacteristicsAlthough several models have been developed to describe the behavior ofan arc [41], in general three main types of models are used to explain them:the steady-state model (V-I), the high-frequency component model, and thetransient model. Each of these models simulates a critical aspect neces-sary for analyzing arc fault responses. Depending on the application, thesemodels can either be applied individually or used together for a more com-prehensive analysis.PV SourcePerceived PV SourcePV SeriesResistanceArc FaultLoadArc Fault DetectorIdetFigure 2.4: Model of an arc fault as a dynamic series resistance between thepanel and the load.[41]2.3.2 Steady State V-IThe series arc fault is often considered a high impedance fault because thearc channel exhibits a significant amount of resistance that cannot be ig-nored, and is seen by the converter as an additional resistive element inthe network, as seen in Figure 2.4. Therefore, V-I equations are used todescribe the nonlinear resistive behavior of the arc. These equations aretypically developed through empirical methods, fitting a curve based on arcvoltage and current from many testing points. Most of these equations sim-plify the V-I characteristic into two variables and approximate it using a13Varc(V)Iarc (A)Low Current“Constant Power”RegionTransition point lineHigh Current“Constant Voltage”RegionIncreasing GapFigure 2.5: V-I curve for an arc fault for different gaps.[41]hyperbolic-tangent function that depends on the arcing current. Based onthe experimental setup, several V-I equations with similar forms have beenpropose [41].Looking at the V-I curve of a sustained arc fault, we find two partic-ular regions: a constant power and a constant voltage region, as shown inFigure 2.5. In the constant power region, the relationship between voltageand current is inverse, causing the arc fault to act like a nonlinear negativedifferential resistor. Whereas in the constant voltage region, although thevoltage does actually rise slightly with high arcing currents (hundreds ofamps), the arc fault behaves as a positive resistor. As a result, the arc faultcan be treated as a nonlinear impedance, with a point between these tworegions known as the transition current or point.2.3.3 High Frequency ResponseThe high frequency components present during an arc fault have their originin the randomness of the arc current itself, and it is caused by the plasmadischarge in the arcing channel. The coulomb and molecule collision in theplasma conduit is basically a random process, and therefore creates a Gaus-sian probability distribution of the arc’s ac components. As a result, thehigh frequency spectrum can be represented with the following equation [46]:14f(x) = 1√2πσexp(−(x− µ)22σ2)(2.1)where µ is the mean, and σ2 is the variance of the noise (µ is assumedto be 0 in the noise modelling). Other colored wideband noises has beenstudied as well for representing the signature. For example, J.C. Kim etal. [47] proposed a modified pink noise model to better simulate the arcfaults in different physical states. In pink noise the power spectral densityis inversely proportional to the frequency (1/f), and the author argues thatit is better at representing the high-frequency components of the arc faultfrequency spectrum compared with a Gaussian white noise.2.3.4 Transient ResponseThe way the arc is initially created determines how its transient is going tolook. One common method, used in one of the first revisions of UL 1699B,involved placing fine steel wool between two electrodes with a fixed gap.When energized, the steel wool melts, ionizing the air and initiating a shortarc transient, evidenced by a sudden drop in current and a rise in volt-age across the electrodes. A newer method introduced by the standard[22],which replaces the steel wool, involves generating the arc by gradually sep-arating two contacting electrodes. This transient has two stages: an initialstep change in current and voltage, followed by an almost stationary phasewhere the arc grows, modeled by exponential functions [48].2.4 Arc Fault DetectionIn AC, arc faults extinguish and reignite many times per second due to thezero crossing of the voltage waveform, exhibiting a very distinctive trait: a"zero-off dead zone" of the current waveform, sometimes called a "shoulder",as seen in Figure 2.6. Therefore, many detection algorithms for this type offault rely on this behavior. On the other hand, since DC arc faults lack zerocrossing points, they do not have such an identifiable feature, which makesthem both sustainable and difficult to detect.There are many other physical quantities that can be exploited in orderto effectively detect an arc, such as arc sound, temperature, irradiance, etc.156020Voltage (V)Time (s)0 0.005 0.010 0.015 0.020 0.025 0.030 VoltageCurrentCurrent (A)5-5-15-20-6015Figure 2.6: Typical AC arc fault current and voltage.[49][24]. However, because the location of the arc fault is always unknown, de-tection based on these magnitudes is more difficult in practical applications.To measure them, sensors must be installed close to or in proximity of thearc, which makes them inconvenient in most cases and also susceptible toother noise sources.Hence, for detection purposes, the high-frequency components mentionedin the last section play a key role. They provide an opportunity to detectthe existence of an arc fault by monitoring either current or voltage mea-surements. In this way, sensors can be placed in a convenient location (e.g.,beside or inside a converter) and remotely detect the arc through the prop-agation of its high-frequency components through the system. As a result,both magnitudes have been used extensively by extracting different featuresfrom them. Nevertheless, in a PV system, the noise injected by the arc faultinto the voltage signal is attenuated by the input capacitors that might bepresent, such as those in the power converter. In the current signal, the noiseis also dampened by parasitic inductances of long wires, although their effectis not as considerable and can be negligible [50]. For comparison, lookingat Figure 2.7(a), the current signal exhibits a +20 dB increase on averagearound 10 kHz, while the voltage signal in Figure 2.7 (b) shows a mere in-crease of +2 dB.2.4.1 Disturbances In DC Arc FaultsTo design a robust detection algorithm capable of distinguishing DC arcfaults from normal operating conditions, it is crucial not only to extract16Figure 2.7: Difference in voltage and current noise.those signatures that define an arc, but also to identify other disturbancesarising from regular operations. Such perturbations can cause the algorithmto either fail to respond or make wrong decisions, creating an unwanted trip.As shown in Figure 2.8, both internal and external disturbances have thepotential to hide or modify the arc’s features.In PV systems, the long cables act as an antenna, picking up radio-frequency noise, particularly in the range between 100 kHz and 500 MHz[50]. The inductance introduced by long cables also acts as a low-pass filter,decreasing the noise levels of the arc. Moreover, the way the system andPV array are configured also modifies the noise profile [51]. In addition,it has been observed that noise above 100 kHz is mostly linked to weakconnections, distant RF coupling from the room’s electronics or surround-ing electromagnetic fields, crosstalk between the positive and negative DCwires, resonance, or parasitic capacitances to ground [52].On the other hand, in the low-frequency spectrum, some perturbationscould also exhibit arc fault-like behavior, such as the step changes causedby turning converters on and off, partial shading, moving clouds, or wind-induced vibrations [53]. The grid’s fundamental frequency and its harmonics17External disturbancesourcesFundamental ACcomponentHigh frequency attenuationdue to filter effectWind-inducedVibrationMoving Clouds TelecommunicationHuman activitiesInverter Noise RF Noise due to cable effectMPPToperationInternal disturbance sources 1Hz 10Hz 100Hz 1KHz 10Khz 100Khz 1MhzFigure 2.8: Typical sources of disturbances in DC arc fault detection.[10]could also propagate into the DC line depending on the converter’s topology,especially if they are transformer-less. Additionally, the MPPT algorithmintroduces step changes into the current waveform whenever the duty cycleof the pulse-width modulation (PWM) signal is modified. These last ob-servations, along with those mentioned above, are some of the reasons whythe range between 1 kHz and 100 kHz is recommended for detection anal-ysis [50] . As a result, the switching frequency and its harmonics of mostconverters are major contributors in this range and need to be consideredin the detection algorithms.2.5 Detection TechniquesAs previously mentioned, current measurements are more commonly usedto extract arc features, and the techniques for identifying them generallyfall into three main categories: time domain, frequency domain, and time-frequency domain. Any feature or combination of features obtained fromthese methods could be sufficient for successfully detecting an arc. Eventhough arc faults are relatively straightforward to identify in the frequencydomain, more sophisticated detection strategies have been developed toavoid unwanted tripping. For example, methods employing artificial intelli-gence use a combination of multiple of those features to make a non-lineardecision regarding the presence of an arc fault. Other strategies like themodel-based approaches are primarily employed for developing and validat-ing detection algorithms, instead of direct arc fault detection.182.5.1 Statistical AnalysisThe waveform of the current signal contains a large amount of arc fault in-formation in the time domain, such as spike pulses, zero current, etc. Severalstatistical features can be used for arc fault detection from this domain, suchas the standard deviation, variance, RMS value, mean, and the extreme val-ues of the input signal. Jinjie Li et al. [54] also add to this list more featureslike skewness, kurtosis, crest factor, shape factor, impulse factor, kurtosisfactor, and margin factor, at the cost of increased computational burden.The difference between the maximum and minimum, over a certain lengthof time, is quite a simple and effective feature to use, but it can be compro-mised by the MPPT when there is a quick change in irradiance.Most time-domain signal characteristics are combined with some formof frequency-domain analysis to create a more reliable detection algorithmwith multiple identification criteria. Nonetheless, there are methods thatdo not rely on the frequency domain, instead using a statistical magnitudethat inherently includes the chaotic nature of the arc. For example, anotherstatistical approach that uses arc current entropy [55] helps to effectivelydiscern arc faults from normal events such as MPPT operation and inverterswitch-on. It is based on the modified Tsallis entropy, which gives insightinto the degree of disorder and signal intrinsic characteristics (SIC), and ithas to be computed twice, requiring around 24N Flops of computationalload.2.5.2 Fast Fourier TransformThe Fourier transform is one of the traditional ways to extract frequency-domain information of a signal from its time domain. A Discrete FourierTransform (DFT) is the mathematical technique for achieving this purposefrom discrete samples, and involves the following computation, where x(n)represents the signal, N the number of samples, and X(k) the resulting spec-trum.XN [k] =N−1∑n=0x[n]× e−j( 2πN )kn (2.2)19When using DFT to analyze digital signals, the algorithm assumes thatthere are repeating patterns hidden in the data, along with other random,non-repeating parts, which are referred to as noise. However, since the pre-vious calculation involves several mathematical operations (O(n2)), the FastFourier Transform (FFT) is used instead, accomplishing the same result withfar fewer operations (O(nlogn)). The Radix-2 algorithm, based on butterflycomputations, is one of the most popular techniques to compute the FFT,requiring a total of 5Nlog2N operations [56]. This algorithm is so widelyused that some microcontrollers, like the C2000 family from Texas Instru-ments, even have embedded hardware specifically designed to facilitate andreduce the computational burden of the FFT.In earlier detection methods, DC arc fault detection relied heavily onfrequency domain analysis of the current signal, and FFT was the preferredtool for calculating the power of the spectrum. The sampling frequency ofmost FFT-based algorithms ranges from 200 kHz to 250 kHz, allowing obser-vation of the power distribution in the most suitable section of the spectrum(0 to 100 kHz or 125 kHz, respectively) for arc detection [51]. Most methodssum the power in the energy spectrum during arcing and compare it to thesum in non-arcing states, or against a predefined threshold based on thenon-arcing spectrum, to reach a decision. Others do the same but instead ofthe whole spectrum they sum the power over a reduced range, for examplebetween 40-80 kHz [57] or 30-100 kHz[58]. Nevertheless, these strategiesmight fail against some electromagnetic inferences.Consequently, to further increase accuracy, instead of using only oneband of the spectrum, the range is divided into multiple bands, and eachone is compared against different thresholds [59]. A more sophisticated vari-ant of this approach involves sorting the sub-bands to reduce the impact ofswitching noise from power converters [60]. By sorting the amplitude ofeach frequency bin in ascending order, one could ignore the higher inten-sity ones (that include the switching noise) and use only those clean bandswhere an increase in the noise is effectively coming from the arc fault. Thislast approach significantly improves the signal-to-noise ratio, but it has notyet been validated under other transient conditions like partial shading orinverter setup.In the previous methods, the spectrum is compared with predefinedthreshold values, which is a limitation since they will be different for ev-ery system. This led S. Chae et al. [61] to propose an adaptive threshold20approach to solve this issue. The algorithm basically looks for potentialarc points, and proceeds to calculate thresholds according to the mean andstandard deviation of the frequency content from previous windows. Withthis strategy, an arc fault is confirmed when the magnitudes exceed thethreshold for a certain number of consecutive periods. This makes the dy-namic adjustment of the threshold an excellent option for adding flexibilityto different systems and operating environments. Although it can distin-guish arc faults from many normal operations, the method might struggleduring inverter startup (a typical scenario in PV systems), as changes in thefrequency domain could resemble arc faults, leading to false trips.2.5.3 Short Time Fourier TransformShort time Fourier transform (STFT) adds the time dimension to the regularFFT analysis, and therefore represents the signal in terms of time, frequency,and amplitude. As opposed to FFT, which solely gives information aboutfrequency domain, the STFT is able to provide both frequency and timeinformation of signals, providing a better understanding of how the spectrumchanges overtime. In practice, the method for calculating STFTs involvessplitting a longer time signal into shorter sections of equal length, use anadequate windowing function and then performing the Fourier transformindividually on each shorter section. The windowed STFT of a signal x(i)is then defined asSTFT[I](n, k) = e−j2πN nMkN−1∑m=0I(m+ nTs)h(m)e−j2πN mk (2.3)where STFT [I](n, k) is a matrix in a two-dimensional form, n and k arethe time and frequency variables of each axis and h(m) is a time windowfunction with only the real value part. Since the windowing is necessaryto avoid frequency leaking on the spectrum, that leaves some informationleft out of the analysis between the sample buffers, as shown in figure 2.9 a.Hence, one solution to overcome this is to take windows that overlap witheach other, as illustrated in Figure 2.9 b. However the amount of overlap-ping should be selected carefully since it increases the computational burdenof having to compute more FFTs as more overlapped is used.Another drawback of the STFT is that it has a fixed resolution, mean-ing that the width of the windowing function affects how the signal is repre-sented. As a consequence, a wide window yields higher frequency resolution,21Window AmplitudeFFT1 FFT2FFT1 FFT3FFT2 FFT4Figure 2.9: Short Time Fourier Transform and the overlapping method toavoid losses.FrecuencyTimeTimeFrecuencyFrequency ResolutionTime Resolution}}High Time ResolutionHigh Frecuency Resolutiona) b)Figure 2.10: Comparison of STFT resolution for different windows. A nar-rower time window a) yields a lower frequency resolution, and vice versa b).which can help to identify some disturbances in the spectrum such as switch-ing frequencies, but has poor time resolution (Figure 2.10 a). In contrast,a shorter time window provides lower frequency resolution that could maskthose frequencies of interest since their energy overlaps between bands, butit gives better time resolution which helps to detect transient events(Figure2.10 b).In [18], to improve the reliability of the detection algorithm, the authorcombines a statistical method and short-time Fourier transform (STFT),with a sample rate of 200 kHz, to recognize PV series arc faults from differ-ent detection perspectives. In [62], it is also observed that the STFT witha Hamming window performs better than real-time FFT, achieving a moreobvious separation between the normal and fault detection variable values.22FFTSTFTTimeTime TimeWavelet tranformFrequencyFrequencyFrequencySignal WaveFormFigure 2.11: Comparison of FFT , STFT and Wavelets frequency resolution.2.5.4 Wavelet TransformThe wavelet transform is a multi-resolution analysis that can decompose asignal into different time-domain signals, each one of them containing infor-mation from a specific frequency bandwidth. While the STFT has a fixedtime-frequency resolution, in wavelet transform each decomposed signal hasa different resolution, since its windowing function is adjustable. Therefore,this transformation can achieve higher resolution in both the time and fre-quency domains, using multiple detection windows at different bands. Acomparison of the distinctive time-frequency resolutions for FFT, STFT,and wavelet spectrograms is shown in Figure 2.11.A wavelet is a brief, wave-like signal with an amplitude that starts andends at zero, and has one or more zero crossings in the middle. Dependingon the type of mother wavelet used in the wavelet transformation, differentemphasis will be placed in the frequency domain. Figure 2.12 shows some ofthe most common ones. The performance of detection algorithms is highlydependent on the selected mother wavelet, affecting its complexity and ac-curacy. It has been found that Daubechies give a good compromise betweenthose two [44], because of their sharp cutoff frequency that reduces the over-lap between bands, and are among the most used. Daubechies, simplifiedas db, have a number associated to them that serves as a reference of theirperformance, therefore a db9 will me more computationally intensive andhave a sharper cutoff frequency than a db5.When working with wavelet transforms, there are two analysis that can23Db3Haar Db5Figure 2.12: Different types of mother wavelets.Original signalWavelet Packet DecompositionHH HH H H HGG GG G G GA3AA2 A1 D1 D1 D1 D1D3DA2 D2 D2A DAA D1AA AA DA DDADA1 DDA1D1 D1DDDDA1AAπ/8 π/4 3π/8 π/2 5π/8 3π/4 7π/8 πFrequencyADOriginal signalDiscrete Wavelet TransformHHHGGGA3A2A1D3D2D1A1 D1 D2 D3π/8 π/4 3π/8 π/2 5π/8 3π/4 7π/8 πFrequencyDAD1Figure 2.13: Graphical representation of discrete wavelet transform andwavelet packet decomposition for a level 3 coefficients.be conducted to a signal: a Discrete Wavelet Transform (DWT) or a WaveletPackage Decomposition (WPD). The main difference between the two is thatDWT only decomposes the lower frequency band (also called approximatecoefficients) at each level, while the WPD decomposes both the lower fre-quencies and the higher frequencies bands (also referred as detail coefficients)of the signal. Therefore, the later provides a more detailed decompositionand information, but requires almost double the computational load. A bet-ter representation of the decomposition from both techniques can be seen inFigure 2.13.Having multiple signals with different frequency content offers a widerange of combinations to study for arc fault detection. In [44], using a sam-ple rate of 1 MHz and DWT with db9, the frequency band from 7.8 to62.5 kHz was analyzed in the voltage signal across the load (rather thanthe current measurement), proving to be more accurate than using the FFT24spectrum. A 1-level DWT decomposition with a db wavelet and a 200 kHzsample rate was used to effectively perform a high-pass filter and extract thepower spectrum between 50 and 100 kHz [63]. This spectrum was later com-pared against a threshold, calculated from suspected non-arc state framesduring the inverter startup.A mixed criterion, using one or multiple packets (or frequency bands)in combination with other methods, has also been explored. For example,in [64], the author combined the reversal current maximum with the energyinformation and modulus maximum extracted from the range between 126and 250 kHz. Although this approach showed a good performance with alow rate of false trips, it required a high sample rate of 2 MHz and a 4-levelDWT with db4. In another method [65], the frequency band between 0 and25 kHz (including the DC offset) was normalized by the 25-50 kHz band overa specific time window, using a 200 kHz sample rate and a 2-level WPD withdb8. The resulting normalized signal was then used to trigger arc detectionwhenever it surpassed a threshold. A similar approach [66], though with alower sample frequency of 100 kHz, computed the ratio between the high-frequency band (781.25 Hz to 50 kHz) and the low-frequency band (0 to781.25 Hz), and compared this ratio against a threshold to detect arcs.DWT and WPD techniques are normally more computationally efficientthan FFT or STFT. However, they still require some prior knowledge of thePV system, in order to adjust the threshold and select the relevant frequencybands for the detection algorithm.2.5.5 Artificial Intelligence And Machine LearningOne of the drawbacks common to all the methods previously discussed isthat, for a particular PV system, they require the selection of the bestfeatures and thresholds to provide efficient arc detection. This process isnormally tedious since it involves analyzing multiple features in various sce-narios and configurations, and considering different system constraints, suchas computational burden and cost.As a result, machine learning techniques and artificial intelligence (AI)have progressively been utilized in the field of arc fault diagnosis. By au-tomated feature learning and mining techniques, the challenge of manuallyselecting the relevant features from the different domains is minimized. Its25application is primarily focused on two areas: first, integrating with thethree aforementioned methods, where a machine learning classifier is usedto reduce and categorize the computed high-dimensional features; second,developing an end-to-end learning model that directly takes time-domain orfrequency-domain data (or both) as input to automate the feature extrac-tion and their classification.Artificial intelligence techniques, like pattern recognition and deep learn-ing, automatically analyze signals aiming to identify abnormal behaviors,such as arc faults. In recent years deep learning has become a widely usedmethod, particularly for AC arc fault detection where it has achieved goodresults. For example Convolutional Neural Networks (CNN), one of themost popular methods in deep learning, looks for hidden features in signals,which helps to improve the performance of the detection algorithms. Con-sidering that in PV systems, series arc fault features are relatively weak insome domains, manually extracting those hidden fault features proves tobe extremely difficult and time consuming. Therefore, CNN can be used toconduct a meticulous data mining and extract relevant fault features. Theseselected features not only help to detect arc faults but also provide a tool tofurther understand the arcs characteristics, and in some cases take advan-tage of unexplored features. In [23] , it is shown that a basic CNN modelcan achieve outstanding results when trained on large-scale datasets. Nev-ertheless, in practice, arc fault samples are difficult to acquire, since manydifferent scenarios that resemble a real application have to be recorded,which sometimes makes it impractical, and the final quantity of samples isinsufficient . In cases of small sample sizes, the accuracy is reduced when themodel lacks sufficient depth, and when the model reaches a certain depth,it tends to overfit.Machine learning techniques focus on automating feature extraction andclassification processes, from features obtained previously from the time orfrequency domain. Supervised learning methods, such as decision trees, neu-ral networks and support vector machines, are trained from labeled datasetsto create rules. These rules, which include thresholds or weights, are thenapplied to real-time extracted features to classify normal and arc fault con-ditions. This strategy helps to facilitate the definition of an appropriatethreshold in those cases where it isn’t so straightforward. For example, in[67], the author uses SVM to identify the optimal threshold value basedon features extracted from the current measurements using DWT with db3wavelet, reliably detecting arc fault. Figure 2.14 shows the visual repre-26H1H2HwFigure 2.14: Graphical representation of support vector machines (SVM),showing the line that best separates two classes.sentation of a SVM threshold, or the separation line, between two differentlabeled sets. Similarly, in [68], seven features in both time and frequencydomains were extracted and two of them in each domain were selected totrain a Bayesian SVM, yielding a high accuracy in the detection of arc faults.However, the author stated that the performance hasn’t been proven yet tobe suitable for other PV systems.Unsupervised learning techniques, like clustering or K-Nearest-Neighbors(KNN), identify unusual patterns in data that has not been labeled. Thosepatterns can then help to filter out those features that do not correlate muchwith an arc fault, and could potentially lead to overfitting. For example,a combination of clustering and supervised learning was conducted in [54].In that study, a total of 34 features involving the time domain, frequency(FFT) and time-frequency domain (DWT), were extracted from the currentsignal. These features are further reduced to 9 through ML techniques, byfiltering out the weakly correlated features, and are finally fed to a stochas-tic configuration network (SCN) to be used for the arc fault detection. Thedownside of this strategy is the huge amount of high quality datasets neededfor training, as well as a significant computational requirements for runningthe detection algorithm in real time.In summary, machine learning techniques greatly facilitate the featureextraction procedure and its threshold definition for arc fault detection, butrequire special attention to not overfit and to avoid weak features. Theirperformance is strongly correlated with the quality and quantity of theirtraining datasets, which most of the time is not feasible. Moreover, theirdecision rules will still be fixed once deployed in the real world, which puts27an inherent constraint in its detection capabilities, leading to unwanted tripsor worse, to miss an arc fault. AI, in contrast, can include some form ofreinforcement learning that can help establish an adaptive threshold ac-cording to the environmental conditions. However continuous learning willrequire an intensive computational load, which in most cases is not possibleto achieve with industry-standard microcontrollers or not financially viablefor a residential product.2.6 Summary And Challenges In DC Arc FaultDetectionIn this chapter, we have explained how DC arc faults are generated in PVsystems and their most important features. As has been seen, their detectionfaces significant challenges due to the absence of very distinctive behaviorslike zero crossings found in AC systems, making detection more challeng-ing. The high-frequency noise generated by arc faults can be attenuatedby the system’s components or masked by external electromagnetic inter-ference, complicating accurate identification. Environmental factors furtheraffect the arc’s characteristics, leading to inconsistent detection thresholds,which can cause false tripping or, even worse, failure to trip. Additionally,the complexity of PV system configurations, including long cables, numer-ous connectors, and types of inverters, introduces more points of failure,complicating the propagation and detection of arc signals. These challengeshighlight the need for robust detection algorithms that can operate efficientlyin varied conditions, minimizing false alarms.The computational constraints of microcontrollers commonly used inPV systems limit the implementation of sophisticated detection algorithms,as these devices often lack the processing power, memory, and energy effi-ciency required for advanced real-time analysis. Many common strategiesrely on FFT or high-order wavelet transforms, which often demand signif-icant processing power. Others use machine learning techniques, which,though promising, require large, high-quality datasets that are difficult tocollect. As a result, designers are forced to balance algorithmic complexitywith performance, often opting for simpler, less resource-intensive methodsthat may compromise detection accuracy or speed, thereby increasing therisk in a PV installation. These limitations highlight the need for innovativestrategies that can optimize computational resources.28Therefore, the objective of this work is to find an efficient arc fault detec-tion algorithm that minimizes the hardware components and the computa-tional complexity of the detection algorithm, while achieving high accuracywithout sacrificing the effectiveness of arc fault detection or overall systemreliability29Chapter 3System Design andExperimental Setup3.1 Standards and Safety RegulationsFrom previous chapters, it has been highlighted that an arc fault can posesignificant safety risks to a PV system, as it can lead to potential fires. AsPV systems become more affordable, they are becoming more widespread,which has naturally resulted in regions setting national guidelines for thesesystems, in line with international safety norms. In Canada, arc fault de-tection in PV systems is regulated primarily under CSA C22.2 No. 292:18,which was recently updated in 2022 by the CSA Group (formerly the Cana-dian Standards Association). Most of its content, such as principles, testingmethods, and performance criteria, is based on UL 1699B, published byUnderwriters Laboratories (UL), which is used in the U.S. These standardsspecify the testing procedures and requirements that DC arc fault protectivedevices (DC-AFPDs) must comply with.UL 1699B requires that every arc fault circuit interrupter (AFCI) or arcfault detector (AFD) successfully detect arc faults in less than 2.5 seconds,or within a time such that the energy of the arc doesn’t exceed 750 Joules,which is defined by:Tresponse = IArc ∗ VArc/750 (3.1)where Iarc and Varc represent the current and voltage of the arc fault,respectively. The standard contemplates two types of tests. The first oneconsists of the AFD being able to effectively detect and extinguish an arcwithin the time constraints mentioned above, for different power scenarios.The second test involves testing the equipment for unwanted trips to assesswhether the detection device avoids giving false alarms in different scenarios,including startups, step-irradiance changes, and switching actuation.303.1.1 Arc Fault Detection TestsFor testing the arc fault in the case of a converter with one MPPT and onlyone string, like the one used in this work, a setup like the one shown inFigure 3.1 is required. These tests involve creating manual faults with anArc Fault Generator, which is placed in different locations across the string:at the beginning, in the middle, and at the end of the string. Its purpose isto examine if the AFD can identify the arc fault under different noise sig-natures, which vary according to the position where they are created, underthe nominal power ratings of the device.PV Array Power ConverterFigure 3.1: Location of arc faults for testing according to UL 1699b.3.1.2 Unwanted Tripping TestsFalse tripping tests are conducted by connecting the power converter andthe PV array as required for its normal operation, while also adding a DCdisconnect switch between the converter’s input and the array, as shown inFigure 3.2. Moreover, it also shows the three loading conditions under whichthe AFD should not trip:On-Off Transitions: In this test, the power converter shall be turned onfor five minutes and off for at least five minutes, for a total of three cycles,without the AFD indicating an arc fault.DC Switch Operation: While the converter is in standby, the DC switchshould be closed, allowing the system to export energy for 30 seconds fromthe PV source. Immediately after, the switch should be opened for five min-utes, after which the sequence is repeated two more times without the AFDtripping.31PV Array Power ConverterT(min)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Converter OFFConverter ON 5min 5min5min PV Switch Off100% irradiance50% irrandiancePV switch On5min 30sec30secTest StateFigure 3.2: Unwanted trip testing according to the UL standard with thesequences to be performed.Irradiance Step Changes: While the system is being operated at its fullrated power for five minutes, a cover should be placed on the array to lowerthe nominal current to half of the rated value. After 30 seconds in thisreduced power state, the cover should be removed, allowing the power toreturn to full capacity for another five minutes. The test is then repeatedtwo more times without the device giving false arc fault alarms.3.2 Decoupling Network and Line ImpedanceAs mentioned in the previous chapters, the frequency response of differentarray configurations can influence the arc signatures captured by the arcfault detectors. Therefore, in order to systematize the test scenarios, theUL standard requires the use of a decoupling network and a (string-model)line impedance, as depicted in Figure 3.3. While the first simulates the DCbehavior of the modules, the line impedance network simulates the high-frequency response.32 PVArray PVArraySecond Half of StringHalf String ModelMiddle of StringEnd of StringStart of String Half String Model First Half of StringDecoupling Network Module and Line Impedance POWER CONVERTER Dc Side Ac SideC1C2C3L2L1L3L4L5R3R4C5C6C4R1R2C1C2C3L2L1L3R1R2L4L5R3R4C5C6C4AFDFigure 3.3: Hardware setup required for arc fault tests.The main purpose of a decoupling network is to ensure that a homoge-neous impedance is seen by the devices under test, so they are not influencedby the array setup. Moreover, it isolates the circuits so that high-frequencynoise or transient signals generated by one part of the system do not prop-agate to other parts of the circuits. This is particularly required if, insteadof an array, a DC source is used. On the other hand, the purpose of theline impedance is to emulate 80 meters of total conductor length and itslow-pass filter behavior. This model can also have two different cutoff fre-quencies according to the value of capacitor C4, as shown in Figure 3.4.This allows testing the corner cases of the frequency response by dampeningthe arc signature when the higher value of the capacitor is chosen.In the case of the unwanted tripping tests, analogous circuits are re-quired, as shown in Figure 3.5. However, for these tests only one lineimpedance model is necessary, since it represents the full string response.Again, different values of C4 are available, which have a similar response asthe one shown in Figure 3.4. All the values required for these circuits arespecified in the standard and are shown in Table 3.1.330 25 50 75 100 125Frequency [kHz]10−610−410−2100102AmplitudeUL Network Frequency ResponceC=150nFC=20uFFigure 3.4: Frequency response of the UL Network for different C4Component Full String Half StringC1 Minimum 20 uF Minimum 20 uFC2, C3 22 nF 22 nFC4 150 nF and 10 uF 300 nF and 20 uFC5, C6 1 nF 500 pFL1 12 mH 12 mHL2, L3 Minimum 60 uH Minimum 60 uHL4, L5 50 uH + 0.7 uH/meter (above 80 meters) 25 uHR1, R2 Rtot / R3 Rtot / R3R3, R4 Maximum 1 Ohm Maximum 1 OhmTable 3.1: Components required for the decoupling and line impedance net-works for arc faults and unwanted trips according to UL1699BFull of StringFull String ModelC1C2C3L2L1L3R1R2L4L5R3R4C5C6C4DecouplingNetworkModule and Line ImpedancePOWER CONVERTER Dc Side Ac SideAFD PVArrayFigure 3.5: Hardware setup required for unwanted tripping tests34InsulatingClampsStationaryElectrodeMovingElectrodeFixed BaseSlidingBlockArc generatorStepper MotorFigure 3.6: Arc fault generator diagram.3.2.1 Arc Fault GeneratorArc faults are generated whenever there is a gap between two conductorswhere a DC current was already flowing. Previously, the UL 1699B stan-dard established that an arc should be generated by placing steel wool in anair gap between two electrodes that were part of the PV cables. Then, byclosing the circuit, current would start flowing through the steel wool, whichwould eventually burn out, causing the physical connection to open and anarc fault to be generated in the gap. However, this method was difficultto carry out, so the standard proposed a different method consisting of astationary electrode and a moving electrode, as shown in Figure 3.6. Theseelectrodes, made of copper, begin in contact with each other (shorted) andare then separated at a controlled rate to the specified gap, as stated inTable 3.2.Test no. Min Iarc (A) Sep. rate (mm/s) Gap (mm)1 2.5 2.5 0.82 7.0 5.0 0.8Table 3.2: Current and gap requirements for arc faults.353.3 Analog Front-End3.3.1 DesignThe performance of arc fault detection algorithms is strongly influenced bythe quality of the signals they process. The analog front-end circuitry playsa crucial role in maintaining a high signal-to-noise ratio in the current mea-surements, which is essential for the algorithms to function effectively. Mostdetection systems use some type of current sensor combined with either low-pass or band-pass filtering, depending on the specific detection strategy.In the literature, various current sensors have been employed, includingpulse current transformers [16], Hall-effect sensors [69], Rogowski coils [70],and tunnel magnetoresistances (TMR) [71]. The choice of sensor dependson the frequency range of interest, as well as the requirements for filteringand the analog-to-digital converter (ADC). For instance, Rogowski coils andTMR sensors can operate at frequencies above 1 MHz, but their main draw-back is the need for high-bandwidth op-amps for filtering and high samplingrates from microcontrollers, both of which increase system costs.BufferingFigure 3.7: Proposed arc fault detection strategy.In this study, an analog front-end was designed using both a Hall sensorand a current transformer, each of comparable cost, to evaluate the per-formance of both types of sensors. The sensor outputs are fed through an8th-order band-pass filter, whose output is then processed by the ADC insidea microcontroller (TI), as seen in Figure 3.7. The band pass filter employsa quad op-amp (AD8604) in a configuration that combines a 6th-order Mul-tiple Feedback low-pass filter with a 2nd-order Sallen-Key high-pass filter.The values of the components were selected for a bandpass of 10KHz and100KHz, and the circuit can be seen in Figure 3.836Figure 3.8: Analog front end circuit used in the measurement of the arcsignatures, which employs a current transformer and a 8th order bandpassfilter.3.4 Experimental Testing3.4.1 Detection System SetupTo conduct the tests, and in accordance with the guidelines of the UL stan-dard, an experimental setup was designed, as shown in Figure 3.9. An arrayof four panels, divided into two pairs, was used as the PV input source (max-imum power point @ 130V / 9.24A) and connected to the system throughdecoupling and impedance networks. Depending on the connection configu-ration, the arc generator could be placed at the beginning, middle, or end ofthe string, while the arc fault detector was positioned along the positive line,near the converter. During the tests, the waveforms were recorded using adigital oscilloscope to capture the most relevant signals, including the PVcurrent, the input measurement on the AFD board (as seen by the DSP),the arc voltage, and the input voltage to the converter.A DC-DC converter was connected to the PV array, in order to extractpower from the solar panels. This device was designed for a maximum inputvoltage of 200V and a nominal input current of 15 Amps, and it is controlledby an MPPT algorithm based on the perturb and observe method. One ofthe advantages of this converter is its high efficiency and high switching fre-quency (close to 140 kHz). This frequency helps minimize noise interferencein the arc detection device, as it lies above the frequency range used forarc fault current measurements. The converter’s output is connected to anelectronic load configured for constant voltage regulation at 400V, emulat-37 ULNetworkConverterAFDE-LoadRSDPLCArc GenFigure 3.9: Experimental setup diagram with the most relevant elements,and the 3 possible positions of the arc generator.ing the input of an inverter exporting to the grid. This setup ensured thesystem operated at full capacity during the experiments.3.4.2 Other ComponentsThe other critical components of the setup included an F280039C Launch-Pad DSP board from Texas Instruments, used to validate the arc fault de-tection (AFD) algorithms and power the analog front-end circuitry. A rapidshutdown (RSD) PLC signal transmitter was also included to emulate areal-world application scenario, even though UL-1699B does not specificallyrequire this signal in the circuit. Given that rapid shutdown systems willbecome mandatory for this type of system configuration, it was decided toinclude it for better realism. Moreover, the heartbeat signal of the RSDconsists of two tones at 131 kHz and 143 kHz [72], making it essential toensure these signals do not interfere with the detection algorithm or causefalse trips.3.4.3 Analog front End PerformanceWith the setup in place and the converter exporting power from the panels,the copper rods are separated in order to generate an arc fault. This way,the performance of the proposed analog front end could be assessed and acomparison was conducted between the resulting frequency response to theone from the raw DC measurement of the PV current.380 1 2Time [s]46Amplitude[A]PV DC Current signal0 1 2Time [s]−0.50.00.5Amplitude[V]Current after bandpass1 2Time [s]0255075100125Frequency[kHz]Spectrogram1 2Time [s]0255075100125Frequency[kHz]Spectrogram−100 −80 −60 −40Power/Frequency [dB/Hz]−100 −80 −60 −40Power/Frequency [dB/Hz]Figure 3.10: Comparison of the frequency response between the AC and DCmeasurement of the arc1 2Time [s]0255075100125Frequency [kHz]Spectogram of PV current1 2Time [s]0255075100125Frequency [kHz]Spectogram after bandpass100 80 60 40Power/Frequency [dB/Hz]100 80 60 40Power/Frequency [dB/Hz]MPPT NoisePLC SignalFigure 3.11: Performance of the analog front end against disturbances39In Figure 3.10, we can see the bandpass filter correctly emphasizes thefrequency band between 20 kHz and 100 kHz, magnifying the arc signa-ture in that spectrum while also attenuating the noise that was alreadypresent before the arc began, which is manifested as a darker area in thespectrum. This attenuation before the arc, along with the magnification ofthe arc signature afterward, effectively increases the signal-to-noise ratio ofthe measurement, which greatly facilitates the arc fault detection algorithm.To analyze the robustness of this filter, another experiment was con-ducted, this time with the addition of the rapid shutdown PLC signal anda minor modification to the MPPT algorithm to make it faster and moreaggressive. The result of this experiment, seen in Figure 3.11, shows thatthe PLC signal is indeed attenuated, especially the aliasing component ofthe 143 kHz tone (reflected into 107 kHz), as well as the converter noise inthe low-frequency band. This result further confirms the capability of thisanalog front end to mitigate some of the most relevant noises that couldpotentially confuse the detection algorithm.3.4.4 UL Network Frequency ResponseAs mentioned in section 3.2, the purpose of the UL Network is to emulateseveral arc scenarios by changing either the position or the characteristicimpedance of the line. Therefore, permutations of different scenarios weremade, either by increasing the capacitance of the line (C4) or by placingthe arc generator in another position on the strip. Figure 3.12 depicts howthe increase in the capacitor in the line attenuates the arc signature morecompared to a smaller capacitor. Moreover, when the capacitance is reducedand the arc signature’s signal-to-noise ratio is higher, it also saturates thecurrent measurement at the output of the operational amplifiers. It can alsobe seen that, without the UL network and by connecting the equipment di-rectly to the array, the current measurements fall roughly between the twoother corner cases. This further confirms the UL Network’s role in replicat-ing the most challenging scenarios regarding the frequency response.400.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.50.00.5Amplitude[V]UL Network with C = 150 nF0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram0.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.250.000.25Amplitude[V]UL Network with C = 20 uF0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram0.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.250.000.25Amplitude[V]UL Network bypassed0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram−100−80−60−40Power/Frequency[dB/Hz]−100−80−60−40Power/Frequency[dB/Hz]−100−80−60−40Power/Frequency[dB/Hz]Figure 3.12: Arc frequency signature for different line’s impedanceLastly, Figure 3.13 shows the spectrum of the arc signature when thefault is generated at the beginning, middle, and end of the strip, followingthe instructions of the UL Standard. In this experiment, it can be seen thatthe arcs at the beginning and end of the strip have a similar frequency re-sponse, as they are relatively close to the converter and the arc detector. Onthe other hand, an arc generated in the middle of the strip is slightly atten-uated by the impedance network in between, although this reduction is notas significant as a change in the line’s characteristic impedance shown before.410.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.50.00.5Amplitude[V]Begin of UL Network0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram0.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.50.00.5Amplitude[V]Middle of UL Network0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram0.0 0.5 1.0 1.5 2.0 2.5 3.0Time [s]−0.50.00.5Amplitude[V]End of UL Network0.5 1.0 1.5 2.0 2.5Time [s]050100Frequency[kHz]Spectrogram−100−80−60−40Power/Frequency[dB/Hz]−100−80−60−40Power/Frequency[dB/Hz]−100−80−60−40Power/Frequency[dB/Hz]Figure 3.13: Frequency signature for different arc locations3.5 Summary of Hardware SetupIn this chapter, we have introduced the experimental setup requirementsand design, following the guidelines of the UL 1699B standard and the de-sired frequency response of the analog front end. The band-pass filter for thearc current measurement was designed to maximize the signal-to-noise ratioof the signature, and its performance and robustness to disturbances wereconfirmed through experimental testing. It could also be seen that, with thehelp of the UL Network decoupling and line impedance, we were able to im-itate the most difficult settings in arc fault detection. These measurementsplay a critical role in deciding which detection strategy is the most effectivefor arc fault detection, as will be shown in the following chapter.42Chapter 4Detection Strategy andExperimental ResultsMost arc fault detection techniques found in the literature are based onsignal processing of the current measurements through time or frequencydomain analysis. These domain features are typically selected based onthe analog front end and power converter for which the arc fault detector isdesigned. This study, in particular, focuses on developing the least computa-tionally intensive algorithm for arc detection that can achieve high accuracyand robustness while keeping the number of computations low.4.1 Arc Fault Tests4.1.1 Test RecordingsIn order to analyze the performance of each individual algorithm, an of-fline approach was chosen. This way, multiple arc faults were stored us-ing a digital oscilloscope (Tektronix MSO58), employing several probes forthe most relevant measurements, such as PV voltage, arc voltage, AC andDC currents, and the current measurement from the AFCI. The additionalmeasurements were necessary for detecting exactly when the arc fault wasgenerated, as well as the exact power being extracted from the solar panels,and identifying other relevant disturbances that could be present.Each of the tests was 4 seconds long and measured at 250K samplesper second (allowing analysis up to 125 kHz), in order to emulate the sam-pling rate of the microcontroller to be used. This way, a total of 1 milliondata points were stored in single frames, one for each of the aforementionedmagnitudes, for a particular test. The arc fault was initiated roughly inthe middle of those 4 seconds to capture the frequency spectrum beforeand after the arc. A total of 300 arc tests were performed across differenttimes of the day, weather conditions, disturbances, and configurations of the430 20000 40000 60000 80000 100000 120000Frequency [Hz]10−1310−1110−910−710−5Power/Frequency[V2/Hz]Power Spectral Density (PSD) of Arc SignaturesFFT for UL Network C = 150nFFFT for UL Network bypassedFFT for UL Network C = 20uFFigure 4.1: Power spectral density of the arc for various scenarios: the ULnetwork with two different values of capacitance, and the panels connecteddirectly to the converter.impedance network. Afterwards, around 100 non-arc tests were performed,following the appropriate setup and procedures according to the UL Stan-dard. Since these tests analyzed a longer time frame and conditions, eachrecording lasted between one minute and six minutes, again at 250K samplesper second.4.1.2 The Arc SignatureOne of the first steps before choosing the algorithm is to verify the exact be-havior of the arc signatures in the frequency spectrum. Taking into accountthe different scenarios and permutations of the UL Network introduced inSection 3.4.4, we began by computing the Fast Fourier Transform of the4-second measurements and taking a closer look at the Power Spectral Den-sity (PSD) of the arc signals. The results of this study can be seen in Figure4.1. Due to the influence of the analog front end, we observe a bandpass-likefrequency spectrum, with attenuation in the low and high frequencies. Itcan also be seen that, as expected from the analysis made in the last section,the PSD without the network (bypassed) lies between the power densitiesof the other two corner cases.444.2 Feature Analysis4.2.1 Methodology And Chosen FeaturesA graphical representation of the workflow is depicted in Figure 4.2. Withthe recordings stored, a database was created by subdividing each of themeasurements into buffers of 512 samples, which were then post-processedto extract each of the individual features in the time and frequency domain.In this step, a numeric value representing the magnitude of that feature forthat particular buffer was also associated with the system’s state: arc faultor normal.0.270 0.272 0.274 0.276Time [s] -0.250.000.25Amplitude [V]Zoomed version0.0 0.1 0.2 0.3 0.4Time [s]0.5-0.250.000.25Amplitude [V]Time-Domain Arc signature2.048 msbuffer buffer buffer buffer DatabaseFeature extractionAlgorithmtrainingPerformanceTestingFigure 4.2: Methodology for processing the arc measurementsUsing a training algorithm involving support vector machines and deci-sion trees, a threshold was defined (Figure 4.3 a), which was then used tocompute the performance of the feature, based on a simple decision stump(Figure 4.3 b). Consequently, the accuracy of each algorithm is defined bythe number of samples that were correctly labeled based on the threshold(Figure 4.3 c). For the features, a set from each different domain was selectedin order to cover the different aspects of the arc from multiple perspectives.ThresholdFeature signalFeature valueBuffer number [n]Feature > ThresholdNormal Arc FaultFalse TrueDecision StumpFeature valueTest numberNormal Arc Faulta) b) c)Figure 4.3: Performance analysis through decision stump.450 25 50 75 100 125Frequency [kHz]0.000.250.500.751.00AmplitudeDetail Coefficient 4CWT1 D4CWT3 D4CWT5 D40 25 50 75 100 125Frequency [kHz]0.000.250.500.751.00AmplitudeDetail Coefficient 3CWT1 D3CWT3 D3CWT5 D30 25 50 75 100 125Frequency [kHz]0.000.250.500.751.00AmplitudeDetail Coefficient 2CWT1 D2CWT3 D2CWT5 D20 25 50 75 100 125Frequency [kHz]0.000.250.500.751.00AmplitudeDetail Coefficient 1CWT1 D1CWT3 D1CWT5 D1Figure 4.4: Frequency response of the details coefficients of DWT for db1and db5. Db3 was added for further comparison.This study focused on the lowest-complexity algorithms for arc detec-tion. From the time domain, the variance, standard deviation, min-max,median and kurtosis were used. From the frequency domain, an STFTwas implemented and then subdivided in 5 different sub bands, each oneof them 25 kHz wide, as shown in Figure 4.5. Moreover, from the samedomain a discrete wavelet transform was performed, using the Haar (db1)and Daubechies 5 (db5) with a level 4 decomposition, which yields the detailcoefficient’s frequency response as seen in Figure 4.4.0 25 50 75 100 125Frequency [kHz]0.000.250.500.751.001.25AmplitudeMultiband Fast Fourier TransformFFT Band1 FFT Band2 FFT Band3 FFT Band4 FFT Band5Figure 4.5: Frequency response of the multi band STFT464.2.2 Accuracy AnalysisIn this section, each of the previously discussed features is demonstrated inoperation. Examples are provided to illustrate their time-domain behaviorduring an arc fault, along with an analysis of their overall detection perfor-mance across various fault scenarios. Specifically, Figures 4.6 through 4.7present the statistical features, Figures 4.8 through 4.9 display the multi-band FFT results, and Figures 4.10 through 4.12 showcase the performanceof wavelets db1 and db5.4.2.3 Summary of PerformanceTable 4.1 summarizes the information presented in the previous section. Ascan be seen, among the statistical features, the median is not correlatedwith the arc faults, while the variance, standard deviation, and min-maxare. Kurtosis, although not strongly correlated, had some information aboutother events that will prove useful for increasing robustness. Meanwhile, allthe time-frequency features extracted are correlated with the arc occurrence,with the exception of the lower frequency components (FFT Band 1 and de-tail coefficients 1). These latter components do not provide a strong featurevalue, and their thresholds could be susceptible to false trips. The tablealso shows the signal-to-noise ratio of the arc conditions versus the non-arcconditions. As expected from the arc signature analysis in Section 4.1.2,the features that emphasize the range between 30 kHz and 80 kHz have ahigher correlation with the arc fault. Specifically, the three FFT bands thatcover the range from 25 kHz to 100 kHz, and the detail coefficients D2, D3,and D4, exhibit the best signal-to-noise ratios. Among these, FFT Band3 (covering 50 kHz to 75 kHz) and detail coefficient D3 show the highestcorrelation overall.Furthermore, a detailed analysis of the computational complexity of eachalgorithm provides additional information that aids in selecting an appro-priate strategy. Some features, such as the FFT and the DWT db5, re-quire considerably more time to compute compared to certain statisticalmeasurements and the Haar wavelet, as seen in Table 4.2. This differenceis even more pronounced when using a microcontroller without a floatingpoint unit (FPU), such as the Texas Instruments MSP430 series or the Mi-crochip PIC24 series. In these cases, floating-point calculations can takeseveral clock cycles, potentially exceeding the buffer duration (2.048 ms)and making real-time protection impossible.470.0 0.8 1.6 2.4 3.2−1.0−0.50.00.5AmplitudeArc waveform - Test A0.0 0.8 1.6 2.4 3.2−1.0−0.50.00.5AmplitudeArc waveform - Test B0.0 0.8 1.6 2.4 3.20.000.030.060.09AmplitudeSTA Variance - Test A0.0 0.8 1.6 2.4 3.20.000.030.060.09AmplitudeSTA Variance - Test B0.0 0.8 1.6 2.4 3.2−0.12−0.08−0.040.00AmplitudeSTA Median - Test A0.0 0.8 1.6 2.4 3.2−0.12−0.08−0.040.00AmplitudeSTA Median - Test B0.0 0.8 1.6 2.4 3.2081624AmplitudeSTA kurt - Test A0.0 0.8 1.6 2.4 3.2081624AmplitudeSTA kurt - Test B0.0 0.8 1.6 2.4 3.20.00.10.20.3AmplitudeSTA StdDev - Test A0.0 0.8 1.6 2.4 3.20.00.10.20.3AmplitudeSTA StdDev - Test B0.0 0.8 1.6 2.4 3.2Time [s]0.00.51.01.5AmplitudeSTA MaxMin - Test A0.0 0.8 1.6 2.4 3.2Time [s]0.00.51.01.5AmplitudeSTA MaxMin - Test Ba) b)Figure 4.6: Statistical features during an arc, for two different scenarios.48Figure 4.7: Performance of statistical features across several test.490.0 0.8 1.6 2.4 3.2−1.0−0.50.00.51.0AmplitudeArc waveform - Test A0.0 0.8 1.6 2.4 3.2−1.0−0.50.00.51.0AmplitudeArc waveform - Test B0.0 0.8 1.6 2.4 3.20369Amplitude×10−7 FFT Band1 - Test A0.0 0.8 1.6 2.4 3.20369Amplitude×10−7 FFT Band1 - Test B0.0 0.8 1.6 2.4 3.20.000000.000150.000300.00045AmplitudeFFT Band2 - Test A0.0 0.8 1.6 2.4 3.20.000000.000150.000300.00045AmplitudeFFT Band2 - Test B0.0 0.8 1.6 2.4 3.20.01.53.04.5Amplitude×10−5 FFT Band3 - Test A0.0 0.8 1.6 2.4 3.20.01.53.04.5Amplitude×10−5 FFT Band3 - Test B0.0 0.8 1.6 2.4 3.20.00.81.62.4Amplitude×10−6 FFT Band4 - Test A0.0 0.8 1.6 2.4 3.20.00.81.62.4Amplitude×10−6 FFT Band4 - Test B0.0 0.8 1.6 2.4 3.2Time [s]0.00.30.60.91.2Amplitude×10−7 FFT Band5 - Test A0.0 0.8 1.6 2.4 3.2Time [s]0.00.30.60.91.2Amplitude×10−7 FFT Band5 - Test Ba) b)Figure 4.8: Frequency band features during an arc, for two different scenar-ios. 50Figure 4.9: Performance of frequency band features across several test. Onthe left, the samples for which the system was normal510.0 0.8 1.6 2.4 3.2−1.0−0.50.00.51.0AmplitudeArc waveform - Test A0.0 0.8 1.6 2.4 3.2−1.0−0.50.00.51.0AmplitudeArc waveform - Test B0.0 0.8 1.6 2.4 3.20.000.040.080.12AmplitudeCWT1 D1 - Test A0.0 0.8 1.6 2.4 3.20.0000.0010.0020.0030.004AmplitudeCWT5 D1 - Test B0.0 0.8 1.6 2.4 3.20.0000.0150.0300.0450.060AmplitudeCWT1 D2 - Test A0.0 0.8 1.6 2.4 3.20.00000.00080.00160.00240.0032AmplitudeCWT5 D2 - Test B0.0 0.8 1.6 2.4 3.20.000.150.300.45AmplitudeCWT1 D3 - Test A0.0 0.8 1.6 2.4 3.20.00.20.40.60.8AmplitudeCWT5 D3 - Test B0.0 0.8 1.6 2.4 3.20.000.040.080.120.16AmplitudeCWT1 D4 - Test A0.0 0.8 1.6 2.4 3.20.000.020.040.06AmplitudeCWT5 D4 - Test B0.0 0.8 1.6 2.4 3.2Time [s]0.000.250.500.75AmplitudeCWT1 Total - Test A0.0 0.8 1.6 2.4 3.2Time [s]0.00.20.40.60.8AmplitudeCWT5 Total - Test Ba) b)Figure 4.10: DWT db1 and db5 coefficients during an arc, placed togetherfor magnitude comparison 52Figure 4.11: Performance of the DWT db1 coefficients across several tests.53Figure 4.12: Performance of the DWT db5 coefficients across several tests.54Feature FP TN FN TP Accuracy SNR [dB]Variance 55 30383 0 63306 0.9992 17.02Median 715 29723 51620 11686 0.4973 0.00Kurtosis 7169 23269 29820 33486 0.5678 1.03StdDev 35 30403 1 63305 0.9994 14.20MaxMin 134 30304 0 63306 0.9989 07.96FFT_B1 23330 7138 2111 61195 0.8871 0.12FFT_B2 69 30369 3 63303 0.9989 16.02FFT_B3 47 30391 3 63303 0.9992 17.78FFT_B4 24 30414 3 63303 0.9995 10.00FFT_B5 11841 18597 3 63303 0.8746 4.77CWT1_D1 67 30371 0 63306 0.9991 10.79CWT1_D2 59 30379 0 63306 0.9991 10.00CWT1_D3 48 30390 0 63306 0.9993 19.50CWT1_D4 37 30401 0 63306 0.9994 16.76CWT1_Tot 42 30396 0 63306 0.9993 16.76CWT5_D1 19810 10628 6 63300 0.7946 3.01CWT5_D2 102 30336 0 63306 0.9987 4.77CWT5_D3 54 30384 0 63306 0.9992 20.00CWT5_D4 30 30408 0 63306 0.9995 16.02CWT5_Tot 42 30396 0 63306 0.9993 16.76Table 4.1: Performance summary of the time and frequency domain features.The features used for the strategy were the Haar coefficient 3 CWT1_D3(high SNR) and Kurtosis (proved useful to increase the robutness).Algorithm Operations Total Time (ms)Mult. Add. Total With FPU No FPUVariance 514 1534 2048 0.0231 0.255Stand.Dev 515 1534 2049 0.0231 0.255MinMax* - 1022 1022 0.0102 0.127 (0.0102)FFT (512) 10752 9216 20480 0.2530 2.455DB1 DWT* 2304 768 3072 0.0422 0.385 (0.0422)DB5 DWT 4608 3456 8064 0.1040 1.007Kurtosis 1538 2046 3584 0.0435 0.447Table 4.2: Computation complexity of some features, considering theirfloating-point operation requirements and total time (for a 100 MHz clock)with and without an FPU. Some algorithms (*) can be computed just asquickly without an FPU, using integer-only operations. The timing for bothwavelet transform only counts for a two level decomposition (D3 and D4).554.3 Detection StrategyFrom the previous section, it was concluded that the wavelet coefficients wereamong the features with the highest signal-to-noise ratio, with medium tolow computational complexity. Between the two wavelets, the performancedifference was not as significant as the increase in computational require-ments, as db5 required almost three times more operations than db1. Fur-thermore, db5 mandates the use of a floating-point unit, while the Haarwavelet can be computed using integer operations, as its coefficients aresimply [+1− 1], as seen in Figure 2.12.An analysis of disturbance rejection, conducted during the unwanted triptests specified in the UL Standard, provided further insight into the sensi-tivity of each feature. After careful selection and assessment, a feature waschosen, and additional improvements were made to enhance its robustness.4.3.1 Wavelet Decomposition And Moving MinimumThe selected detail coefficient used as the feature for arc fault detection wasthe Haar Level 3 (referred to as CWT_D3). This coefficient resulted in thehighest SNR with the minimum computational complexity. However, thistype of feature was extremely sensitive to fast transients, such as relay orswitch permutations. Due to the nature of these transients, a large spikein current is created, causing the frequency spectrum to rise and leading tofalse trips. A straightforward solution to this type of disturbance was theintroduction of a moving minimum, also referred to as a sliding window min-imum or minimum filtering. The minimum filtering equation for a slidingwindow of size W is given by:y[i] = mini≤j<i+Wx[j] (4.1)Where x[j] is the input signal or data series, y[i] is the output of theminimum filter at index i, and W is the window size. By applying a simpleminimum window with W = 3, transient spike disturbances can be effec-tively canceled out without compromising arc fault detection, as it onlyintroduces W − 1 buffer-time lengths (i.e., 4.048 ms in this example), asshown in Figure 4.13.56with Minimum Filtering with Minimum FilteringSpike disturbance4 msArc faultFigure 4.13: Wavelet transform and minimum filtering strategy is able tosuccessfully increase the robustness against transient disturbances4.3.2 The IIR FilterAlthough the UL 1699B standard does not specifically address the rapidshutdown PLC devices required by law in Canada and the U.S. in its un-wanted trip testing, it is a relevant source of disturbance to be analyzed inorder to assess its influence on the detection strategy. After several tests us-ing the APSmart RSD PLC device, which complies with the SunSpec PLCsignal protocol, a critical robustness compromise was found. Due to the na-ture of this signal, which uses FSK with a dual-tone to broadcast a messageto the receivers on the panel over a duration of 168.96 ms every 1070 ms[72], the minimal filtering was insufficient to properly mitigate this signalwithout compromising the detection algorithm, as seen in Figure 4.14a.57To further improve robustness and avoid false tripping due to signals ofthat nature, a first-order Butterworth low-pass filter is implemented. Thisfilter, which achieves a maximally flat frequency response in the passband,has a discrete transfer function expressed as:H(z) = b0 + b1z−1a0 + a1z−1(4.2)where b0, b1 are the feedforward coefficients, and a0, a1 are the feedbackcoefficients. To derive the filter coefficients, the cutoff frequency fc, thesampling frequency fs (250 kHz), and the normalized cutoff frequency ωcare computed using:ωc =2πfcfs(4.3)An intermediate parameter α is then defined as:α = sin(ωc)2 (4.4)With a0 normalized to 1, the remaining coefficients are calculated as:b0 =α1 + α, b1 =α1 + α, a1 =1− α1 + α (4.5)The resulting filter is characterized by the difference equation:y[n] = b0x[n] + b1x[n− 1]− a1y[n− 1] (4.6)This equation governs the behavior of the first-order Butterworth low-pass filter, where y[n] is the filtered output, x[n] is the current input, andy[n − 1] represents the previous output. After careful tuning, an IIR filterwith a cutoff frequency of 500 Hz was implemented to mitigate this distur-bance in most scenarios, as shown in Figure 4.14a. After applying the IIRfilter, the noise disturbances from the PLC signal are filtered out, and dur-ing an arc (Figure 4.14b), it introduced an additional, but not significant,delay.5818msFigure 4.14: IIR filtering effect on the detection algorithm during: a) PLCheartbeat signal and b) an arc fault. The IIR filter smooths and slowsdown the response of the algorithm, increasing robustness at the cost of anincrement on the tripping time.594.3.3 Robustness Improvement Through KurtosisDuring more extensive tests for unwanted trips, another relevant source ofdisturbance was discovered, related to the power converter’s performance.Under certain conditions of line impedance and low solar irradiance, theconverter exhibited a boundary situation where its MPPT control algorithmbecame aggressive enough to introduce a significant amount of noise into thecurrent line, which, from the detection algorithm’s perspective, was consid-ered an arc fault. Although reducing the cutoff frequency of the previousfilter mitigated this disturbance, it resulted in a significant increase in thesettling time. Consequently, in the most challenging scenarios, the trip timewas around 300 ms, almost 20 times longer than the previous average delay.The proposed mitigation strategy for this type of disturbance, built onthe previous approach, involved introducing a new feature: Kurtosis. Thisprobabilistic measure is defined as the fourth central moment divided bythe square of the variance. It is a measure of the tailedness of a probabilitydistribution relative to the normal distribution. Its mathematical expressionis given by:KF [n] =1NN∑i=1(xi − µσ)4− 3 (4.7)where N is the number of data points, xi are the data points, µ is themean of the data, and σ is the standard deviation of the data. The term −3adjusts the kurtosis so that it is 0 for a normal distribution. This value, afterbeing properly filtered by another low-pass IIR filter, was used to modulatethe feedforward coefficients in equation 4.5, such that:y[n] = b0z[n] + 1 · x[n] +b1z[n] + 1 · x[n− 1]− a0 · y[n− 1] (4.8)where y[n] is again the filtered output used for detection decision, x[n]the output of the minimum filtering applied to the Haar detail coefficient 3( D3[n] or CWT1_D3) and z[n] the output of the second IIR filter. Fig-ure 4.15 depicts the final detection algorithm for arc fault, with increasedrobustness against different type of disturbances.60Z-1Z-1a1b1b0Z-1Z-1a1b1b01ABAB ? >Th```K[n]NormalArcTFminCWT_D3[n]Modulated IIRIIRx[n]z[n]y[n]NFigure 4.15: Proposed arc fault detection algorithm using Wavelet trans-form, IIR filtering, and Kurtosis (WIK). This block diagram showcases thewavelet coefficient input and the Kurtosis-modulated low-pass IIR filter usedto increase robustness.4.3.4 Experimental ResultsThis algorithm was tested in every scenario in the database, including arcfaults and unwanted tripping tests, to confirm its effectiveness. In Figure4.16, two of the most challenging scenarios in the dataset are depicted: alarge input disturbance during the unwanted tripping tests and an arc faultwith the lowest signal-to-noise ratio. The proposed detection strategy suc-cessfully handled both of these scenarios, as well as all others in the testdatabase, without compromising detection sensitivity or adding a signifi-cant delay.To achieve this performance, cutoff frequencies of 500 Hz and 1000 Hzwere used for the modulated IIR filter and the Kurtosis IIR filter, respec-tively, with a minimizing window of N = 4. As a comparison, withoutKurtosis modulation, the required cutoff frequency and minimum windowto successfully pass these tests were 90 Hz and 12, respectively, and theresponse still appeared marginal, as seen in Figure 4.16a. The latter alsoshows how the probabilistic feature strongly reacts to the randomness ofconverter noise, generating a huge spike in its response, which, in turn, at-tenuates the feedforward coefficients in the primary IIR filter, effectivelylowering the noise’s influence on the detection variable.61Figure 4.17 shows another scenario illustrating the characteristic behav-ior of the kurtosis coefficient against uniform waveforms. When a signal likethe PLC heartbeat is introduced into the PV current, its energy distributiondiminishes and consequently deactivates the modulation and attenuation ofy[n]. Furthermore, it can also be observed from the aforementioned figuresthat the randomness of an arc fault was not enough to create a significantincrease in the kurtosis value. Since a slight increase in its value did not slowdown the IIR loop, the detection speed was barely affected. This behaviormade this statistical measurement ideal for enhancing the robustness of thesystem while simultaneously not affecting the performance and speed of arcdetection.Finally, Figure 4.18 shows how each of the strategies mentioned in thissection addressed specific types of disturbances in the unwanted trip sce-narios. With the raw measurements, the system experienced multiple falsepositives, a number that decreased as more functionalities were added, ef-fectively placing all those samples below the decision threshold. It is worthmentioning that although an increase in the influence of kurtosis in the pri-mary IIR filter can reduce transient noise, it will not attenuate the PLCsignals as seen in Figure 4.18 e and f. However, the arc fault detection willbe affected and slowed down.6236ms402msmarginal responseFigure 4.16: Detection strategy performance against a) converter noise and b) arcfaults. The increase in the kurtosis component during the converter’s disturbancenoise, which had a frequency signature comparable to that of an arc fault, helpsattenuate the detection coefficient, preventing false tripping. Moreover, the superi-ority of this strategy can be observed in comparison to an IIR filter, which nearlytripped due to the disturbance and was even slower in detecting the arc fault.63PLC signal6ms24msFigure 4.17: Kurtosis behavior in uniform signals and arc faults, compared withthe IIR filter. Although the kurtosis spikes whenever the PLC signal starts or ends,it quickly becomes negative and deactivates the further attenuation of the IIR filter.Meanwhile, during an arc fault, depending on the time the buffer is taken, it couldhappen that this probabilistic measurement barely increases, since the distributionof the signal did not change.64a) b)c) d)e) f)spikesPLCConverter transientsConverter transientsPLC200Z[n]+1150Z[n]+11 Z[n]+11Figure 4.18: False trip sources, mitigation and kurtosis influence. In a) only theraw wavelet component is used, and in most tests it trips. The introduction ofthe Min in b) mitigate the spikes, whille the addition of the IIR in c) lowers downall the response. The introduction of the Kurtosis-modulation further reduces therest of the spikes below the threshold in d). In e) and f) the kurtosis attenuation,yielding a decrease in the converter’s transient, but not on the PLC signal.65Algorithm Accuracy Robustness Relative complexity N. OpMinMax Low Low Low 2 kSta Medium Low Low 2 kVariance Medium Medium Low 2 kHaar DWT High Low Low 3 kWIK High High Medium 6.5 kDB5 DWT High Medium Medium 8 kFFT High Medium High 20 kTable 4.3: Comparison of Methods by Accuracy, Robustness, ComputationalRequirements, and Operations. The proposed method of Wavelet, IIR andKurtosis (WIK) achieves the highest accuracy and robustness, while main-taining a medium to low computational complexity.4.4 SummaryIn this chapter, we analyzed the most relevant low-computationally inten-sive detection algorithms found in the literature to assess their performance,given the setup, converter, and analog front-end circuit designed. Once themost suitable algorithm was selected, considering its sensitivity and com-putational complexity, a strategy was further developed to improve its per-formance and robustness. Table 4.3 compares the WIK arc fault detectionmethod against the most commonly used low-complexity detection algo-rithms, highlighting the advantages of this method for arc detection in anincreasingly competitive market that demands the most cost-effective solu-tions.While minimum filtering and IIR are well-known methods for increasingrobustness, this work effectively reduces the influence of converter noise evenfurther by using Kurtosis as a dampening strategy, without sacrificing de-tection performance. The novelty of this approach lies in the utilization of astatistical feature that is not correlated with the arc fault itself—primarilybecause it resembles white noise—but instead with other sources of noisedisturbances, which tend to have more outliers, such as converter noise. Byleveraging this behavior to attenuate the IIR filter in cases where those noisesources are significant, we can effectively prevent false tripping and furtherenhance the robustness of the algorithm.66The proposed strategy, which employed Kurtosis to modulate the IIR fil-ter response, was able to effectively detect every arc in the analyzed scenar-ios, with an average trip time of 16 ms and a maximum of 36 ms. Moreover,this strategy was robust enough to filter all disturbances detected duringthe unwanted trip tests, including spike transients, repeating signals (PLC),and converter-induced pulses. In contrast, the solution without Kurtosismodulation required a larger minimizing window and a frequency 5 timeslower to achieve fairly similar robustness, but this resulted in an averagetripping time of 60 ms and a maximum tripping time of 402 ms. Therefore,in cases where there is enough room for additional computations (since itnearly doubles them), this type of strategy is highly recommended.Feature Total Ops With FPU Without FPUTime (ms) % Time (ms) %Haar D3 (2) 3072 0.0422 46.04 0.0422 8.62Kurtosis 3584 0.0435 53.71 0.447 91.33Modulated IIR Filter 10 <0.0001 0.14 <0.001 0.02Kurtosis IIR Filter 6 <0.0001 0.10 <0.001 0.02Total Per 2ms buffer 6672 0.0857 4.18 0.4894 23.9Table 4.4: Summary of selected features (Haar wavelet D3 and Kurtosis)and the IIR filters, showing their operation counts and computation time.Considering a sample buffer of 512 samples (2ms) this corresponds to 4.18%(0.0857ms) of total time per buffer needed for the computation, in the bestscenario with a FPU.Table 4.4 summarizes the computational requirements for this strategy,highlighting the reduced number of total operations that make it feasible,as it only requires 4.18 % of the total computational power of a low-costindustry-standard microcontroller with an FPU, and 23.9 % without. Apotential improvement would be to compute the Kurtosis more efficientlyto further reduce the required computing power.67Chapter 5Conclusion5.1 SummaryThis thesis has thoroughly investigated the development of arc fault detec-tion (AFD) algorithms for photovoltaic (PV) systems, focusing on enhancingdetection reliability, robustness, and efficiency while ensuring compliancewith industry standards such as UL 1699B. The proposed method, basedon a combination of Discrete Wavelet Transform (DWT), Infinite ImpulseResponse (IIR) filtering, and Kurtosis modulation (referred to as the WIKstrategy) demonstrates an advancement in the field of AFD.One of the major contributions of this work is the inclusion of experi-ments that go beyond the traditional testing prescribed by UL 1699B. Bysubjecting the AFD algorithm to various real-world disturbance scenarios,such as converter noise and power line communication (PLC) signals, thereliability and robustness of the detection method were rigorously evaluated.These extended tests highlighted the limitations of relying solely on the UL1699B standard, which may not account for all potential noise sources en-countered in practical applications. The additional testing confirmed thatthe proposed strategy could handle these disturbances without compromis-ing detection accuracy or tripping unnecessarily, making it more robust thanprevious approaches.A key innovation of this research lies in the integration of Kurtosis asa means to enhance the robustness of the detection process. By leveragingKurtosis to modulate the IIR filter, the algorithm effectively reduced the in-fluence of some noise sources, such as converter-induced transients, withoutsacrificing detection performance. This statistical feature, when combinedwith wavelet decomposition, allowed for more precise differentiation betweenactual arc faults and other non-related noise sources, significantly reducingfalse tripping events.68In conclusion, the proposed WIK strategy has proven to be a highly ef-fective solution for AFD in PV systems, meeting safety requirements whileaddressing real-world challenges. The incorporation of additional testingscenarios and the innovative use of Kurtosis further underscore the robust-ness and practicality of this approach, making it well-suited for deploymentin cost-sensitive, low-power microcontroller environments. This work pavesthe way for more reliable and efficient arc fault detection, contributing tothe enhanced safety and sustainability of photovoltaic installations.5.2 Future WorkFuture research should focus on further analysis of the proposed WIK arcfault detection (AFD) technique, under different environmental conditionsand operational scenarios, especially alongside converters with lower switch-ing frequencies. Expanding testing to extreme environments and large-scalefield trials will be critical in assessing robustness and real-world applicabil-ity. Additionally, exploring adaptive detection strategies that combine oneor more features, such as support vector machines, could further improveperformance. Developing more cost-effective, low-power hardware for im-plementing the AFD algorithms will also be key to enhancing the safety andscalability of photovoltaic systems.69Bibliography[1] V. Tyagi, S. Kaushik, and S. Tyagi. 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Given a buffer of N samples, the Haar DWT calculates theapproximation and detail coefficients at each level by processing pairs ofconsecutive samples. For level 1, the approximation and detail coefficientsare computed as:Approximation1[n] =x2n + x2n+12 , Detail1[n] =x2n − x2n+12 (A.1)At each subsequent level, the approximation coefficients from the pre-vious level are further decomposed in the same manner. For level j, thecoefficients are:Approximationj [n] =Approximationj−1[2n] +Approximationj−1[2n+ 1]2(A.2)Detailj [n] =Approximationj−1[2n]−Approximationj−1[2n+ 1]2 (A.3)This process continues until the desired decomposition level is reached.At each level, the number of coefficients is halved, resulting in N/2j coeffi-cients at level j.To compute the Power Spectral Density (PSD) from the Haar DWT, thedetail coefficients at each level are squared to obtain the power:Pj [n] = (Detailj [n])2 (A.4)The total power for each level is then the average of these squared values:78Pj =1NjNj−1∑n=0(Detailj [n])2 (A.5)where Nj = N/2j is the number of detail coefficients at level j. Eachlevel corresponds to a specific frequency band, defined by:[fs2j+1 ,fs2j](A.6)This approach efficiently computes the PSD, providing insight into thesignal’s energy distribution across different frequency bands.79
Thesis/Dissertation
eng
Electrical and Computer Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Ordonez, Martin
Digital filters for PV arc fault detection
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