Time-Domain Impedance-based fault location for HVDC Transmission lines

Departamento de Engenharia Electrotecnica e de Computadores FEUP Faculdade de Engenharia Universidade do Porto Time-Domain Impedance-Based Fault Location for HVDC Transmission Lines Luis de Andrade de Freitas Electrical Engineer, Universidad Sim´on Bol´ıvar, Venezuela (2002) M.Sc., Universidad Sim´on Bol´ıvar, Venezuela (2008) Doctoral dissertation submitted to the Faculty of Engineering of the University of Porto Supervisor Prof. Maria Teresa Ponce de Le˜ao Ph.D. Co-supervisors Prof. Helder Leite Ph.D. Prof. Paulo De Oliveira Ph.D. Departamento de Engenharia Electrotecnica e Computadores Faculdade de Engenharia da Universidade do Porto October, 2013 Porto — Portugal c 2013 — Luis de Andrade de Freitas No portion of the work contained in this dissertation has been submitted in support of an application for another degree or qualification of this or any other university or other institute of learning This thesis was funded by a Ph.D. Grant SFRH/BD/33788/2009 Time-Domain Impedance-Based Fault Location for HVDC Transmission Lines Luis de Andrade de Freitas Departamento de Engenharia Electrotecnica e Computadores Faculdade de Engenharia da Universidade do Porto To my family Mary, Gaby and Leo Acknowledgments I would like to express my gratitude to Prof. Dr. Maria Teresa Ponce de Le˜ao for her invaluable ideas, advice, suggestions, guidance and encouragement since the beginning of this research project. This Thesis owes to her a sense of ambition and innovation that would have being impossible to attain without her leadership and support, providing the means to stablish a good friendship. I would like to acknowledge the MIT-Portugal Program, specially Prof. Dr. Jo˜ao Pe¸cas Lopes and Prof. Dr. Eduardo Oliveira Fernandes for providing me the opportunity to participate in this program to develop this research work. I’m also very thankful for the support provided by the Department of Electrical and Computer Engineering of the Faculty of Engineering of University of Porto (DEECFEUP), and the Power Systems Unit of INESC Porto (Instituto de Engenharia de Sistemas e Computadores do Porto). Specially, Prof. Dr. Jo˜ao Tome Saraiva and Prof. Dr. Manuel Matos. Generous funding was provided by the Portuguese Funda¸c˜ao para a Ciˆencia e a Tecnolog´ıa with a Doctorate Scholarship. Sincere thanks to Prof. Dr. Helder Leite at University of Porto and Prof. Dr. Paulo De Oliveira at Sim´on Bol´ıvar University in Venezuela, for serving as co-advisers of this research and for their time invested with valuable advice and guidance. I also wish to thank two important companies for their help: Eletrobras Furnas of Brazil, especially to Eng. Guilherme Sarcinelli Luz, and Eng. Ronaldo dos Santos for allowing me to use both actual fault records and model’s data from their transmission line Foz do Igua¸cu-Ibiuna. And from ABB Eng. Andre Balzi for providing technical and financial information about fault location equipment commercialized by them. Great appreciation goes to Prof. Elmer Sorrentino at Sim´on Bol´ıvar University for being my counsellor and guide throughout this journey. I don’t want to forget my great office mates at ”J” building of FEUP campus, for helping me sort through the administrative hurdles and for their friendship. Many thanks to C´elia Couto at MIT-Portugal Program. Colleagues and friends are also acknowledged for their support. Last but not least, to my wife: for your patience, for your love and help. Without you I would be nowhere. To my family. Summary In the last decades, High Voltage Direct Current (HVDC) systems have had extensive growth due to the great development that has occurred in AC-DC-AC conversion technology based on power electronics, and also for being strongly promoted as a great solution for the connection of renewable energy sources through long distances, both offshore and onshore. However, there are still problems in the operation and maintenance of HVDC systems that can be reviewed and updated. Such is the case of automated methods of fault location. All currently available commercial methods are based on traveling wave technologies. These methods can have good accuracy, but they also have some disadvantages, such as the need for expensive measuring equipment dedicated exclusively to this purpose, and problems for detecting high impedance faults or faults close to the line terminals. This thesis develops a method for fault location on HVDC lines based on line impedance estimation, as a proposal to complement the current methods in cases where commercial methods are not capable to give a satisfactory result. The reason to develop this method based on a different technology than traveling wave, is because it’s intended to prevent the problems that affect these type of technologies. The proposed method uses a mathematical model of the transmission line as a basis for estimating the line’s impedance. This model was specifically attained to use in this project, and it was deducted from the transmission line differential equations in the time-domain. For this deduction is not required any approximation, so it was obtained a model that brings high accuracy to the fault location method. The method’s behavior is evaluated from the technical point of view, using both actual fault records and simulated fault records. The results are compared with results obtained by traditional methods in order to verify the performance of the different methods. The proposed method aims to assist in the operation process of HVDC systems, providing a robust fault locator, with high accuracy, and low cost. This method is intended to replace the current traveling wave-based methods, or at least complement them in cases where traditional methods have not performed well. ix 8. L. de Andrade and M. Ponce de Le˜ao, Direct Current Power Systems, In Proceedings of CIGR´ E Smarts Grids: Next Generation Grids for New Energy Trends International Symposium, Lisbon, Portugal, p. 8, April 2013 9. L. de Andrade, Y. Blanco and M. Ponce de Le˜ao, Using Power Systems Simulation Software for Fault Analysis, In Proceedings of Encontro Regional Ibero-americano do CIGRE, Foz do Igua¸cu, Brasil, p. 8, May 2013 Acronyms ABB Asea Brown Boveri Group AC Alternating Current ANN Artificial Neural Networks ASCII American Standard Code for Information Interchange ASEA Allm¨anna Svenska Elektriska Aktiebolaget BBC Brown Boveri & Cie BHEL Bharat Heavy Electricals Ltd. BM Bergeron’s Model CIGR´ E International Council on Large Electric Systems (in French: Conseil International des Grands R´eseaux ´ Electriques) CIRED Congr`es International des R´eseaux ´ Electriques de Distribution COMTRADEIEEE Standard Common Format for Transient Data Exchange CT Current Transformer DC Direct Current DG Distributed Generation DM Developed Transmisson Line Model EMTP Electro-Magnetic Transients Programs EU European Union FDTD Finite Difference Time Domain Method G.E. General Electric GPS Global Positioning System HVDC High Voltage Direct Current IEEE Institute of Electrical and Electronics Engineers IGBT Insulated-Gate Bipolar Transistor LCC Line-Commutated Converters PT Potential Transformer PV Photovoltaics SCADA Supervisory Control and Data Acquisition SEL Schweitzer Engineering Laboratories Inc. SO System Operator T&D Transmission & Distribution UHVDC Ultra High Voltage DC USA United States of America VSC Voltage-Source Converters xvii List of Symbols +Denote the Positive-sequence Component 0Denote the Zero-sequence Component αAttenuation Constant βPhase Constant Γ Reflection Coefficient γLine Propagation Constant γRG Line Propagation Constant with Low Frequency Components of the Frequency Domine Coeficients (γRG =√RG) ϵoAbsolute Magnetic Permeability in a Vacuum (8.85 ×10−12) µoAbsolute Dielectric Permittivity of Vacuum (4π×10−7) πRatio of a Circle’s Circumference to its Diameter (3.14159) τTotal Travel Time from one end of the Line to the Other (τ=l/v =l√LC) ωLine Frequency CCapacitance Per Unit Length cSpeed of Light in Vacuum (≈3×108m/sec.) dDistance Between the Measurement Point and the Fault Point FFault Point f1(x, t), f2(x, t) Denote a General Function Relative to xand t GConductsnce Per Unit Length ICurrent I1Current Measured in x= 0 at t=t1 I2Current Measured in x= 0 at t=t2 IFFault Current IRe Residual Current jImaginary Unit (√−1) K1, K2, Ka, Kb, Kc, KdConstant of the General Solution of Differential Equations LInductance Per Unit Length lTotal Length of the Line xix R Denote the Receiver Line-end RResistance Per Unit Length Ra, RbVariable Resistances Used in a Bridge Circuit RTTotal Line Series Resistance S Denote the Sender Line-end Smode Signal Vector in Mode Domine Sphase Signal Vector in Phase Domine tTime Variable. Denote any Time Inside the Time Interval Analized t1wavefront Arrival Time 1 t2wavefront Arrival Time 2 VVoltage vVelocity vtTravelling Wave Velocity V1Voltage Measured in x= 0 at t=t1 V2Voltage Measured in x= 0 at t=t2 VFFault Voltage XAxis on which the Distance Variable xMoves xDistance Variable. Denote any Point Inside the Transmission Line YTotal Shunt Admittance of the Line yShunt Admittance Line Per Unit Length ZTotal Series Impedance of the Line zSerie Impedance Line Per Unit Length ZoLine Characteristic Impedance ZaImpedance of the Medium a ZLC Line Characteristic Impedance with High Frequency Components of the Frequency Domine Coeficients (ZLC =√L C) ZRG Line Characteristic Impedance with Low Frequency Components of the Frequency Domine Coeficients (ZRG =√R G) Contents Summary ix Resumen xi Resumo xiii Publications xv Acronyms xvii List of Symbols xix Tables xxv Figures xxviii 1 Introduction 1 1.1 HVDC Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 TheBeginnings............................... 3 1.1.2 DC System Decline Causes . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 DC Application at the Beginning of the AC Era . . . . . . . . . . . . 5 1.1.4 Converters Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.1.4.1 Firsts High Voltage Converters . . . . . . . . . . . . . . . . . 6 1.1.4.2 Converters Applied Commercially . . . . . . . . . . . . . . . 7 1.2 HVDC Projects Around the World . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.1 Current HVDC Projects . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.2 The Next HVDC Projects . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 Justification and Statement of the Problem . . . . . . . . . . . . . . . . . . . 13 1.3.1 Motivation ................................. 13 1.3.2 Objectives.................................. 15 1.4 ResearchApproach................................. 16 1.4.1 Problem Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.4.2 MethodDevelopment ........................... 16 xxi CONTENTS xxii 1.4.3 MethodValidation............................. 17 1.5 Thesis Proposals and Contributions . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Supplementary Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6.1 Direct Current Power Systems . . . . . . . . . . . . . . . . . . . . . . 19 1.6.1.1 DC Advantages . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6.1.2 Economic Considerations . . . . . . . . . . . . . . . . . . . . 21 1.6.1.3 DC Grids Challenges . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 BibliographyChapter1 ................................. 28 2 Fault Location Analysis for Transmission Lines 33 2.1 Fault Location Origins and Definition . . . . . . . . . . . . . . . . . . . . . . 34 2.2 FaultLocationBenefits .............................. 36 2.3 Traveling Wave Based Fault Location . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.2 One-end and Two-ends Methods . . . . . . . . . . . . . . . . . . . . . 39 2.3.3 Comparative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Impedance-Based Fault Location . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.1 Principles of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.2 One-end Measurement Methods . . . . . . . . . . . . . . . . . . . . . . 49 2.4.3 Two-ends Measurement Methods . . . . . . . . . . . . . . . . . . . . . 50 2.4.4 Other Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4.5 Comparative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.5 FinalRemarks ................................... 55 BibliographyChapter2 ................................. 57 3 Transmission Line Model 61 3.1 Line Model Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2 Frequency-Domain Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.1 LongLineModel.............................. 64 3.2.2 ShortLineModel.............................. 67 3.3 Time-DomainModel................................ 68 3.3.1 Bergeron’sModel.............................. 68 3.3.2 Other Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.4 FinalRemarks ................................... 72 BibliographyChapter3 ................................. 74 4 Proposal for Impedance-Based Fault Location for HVDC 77 4.1 Time-Domain Distributed Parameters Transmission Line Model . . . . . . . . 79 4.1.1 Line Model Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 CONTENTS xxiii 4.1.1.1 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 81 4.1.1.2 Model Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.1.2 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.1.2.1 ACLineTests .......................... 87 4.1.2.2 DCLineTests .......................... 90 4.1.3 Final Remarks of the Model . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1.3.1 OtherComments......................... 94 4.2 Fault Location Method Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.2.1 FaultDetection............................... 96 4.2.2 Impedance-Based Fault Location Method . . . . . . . . . . . . . . . . 98 BibliographyChapter4 .................................100 5 Working Examples 103 5.1 FurnasHVDCLine.................................103 5.1.1 Furnas Transmission System . . . . . . . . . . . . . . . . . . . . . . . 103 5.1.2 The HVDC Fault Process . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.1.3 The HVDC Fault Location Equipment . . . . . . . . . . . . . . . . . . 106 5.2 FaultLocationTest ................................107 5.2.1 Method Performance to Actual Faults . . . . . . . . . . . . . . . . . . 109 5.2.2 Accuracy Test Using Simulation Data . . . . . . . . . . . . . . . . . . 111 5.2.3 Sensitive Test to Fault Resistance . . . . . . . . . . . . . . . . . . . . 116 BibliographyChapter5 .................................120 6 Conclusions & Future Research 123 6.1 Contributions and Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.2 Future Lines of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 A Test HVDC line Model 127 A.1 Description of the HVDC System . . . . . . . . . . . . . . . . . . . . . . . . . 127 A.2 Control and Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 130 A.2.1 ProtectionSystem .............................130 A.2.2 MasterControl...............................131 A.2.3 Controller Block Inputs and Outputs . . . . . . . . . . . . . . . . . . . 131 A.3 ModelTest .....................................133 B COMTRADE Standard 135 B.1 Standard Files Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 B.1.1 Configuration Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 B.1.2 DataFiles..................................136 B.1.3 HeaderFiles ................................136 B.2 SamplingRate ...................................136 CONTENTS xxiv B.3 IllustrativeExample ................................137 B.3.1 .cfgFileFormat ..............................138 B.3.2 .datFileFormat ..............................140 List of Tables 1.1 Summary of main HVDC projects. . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Summary of main HVDC projects under construction. . . . . . . . . . . . . . 12 2.1 Traveling wave-based fault location methods summary. . . . . . . . . . . . . . 41 2.2 Transmission line parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Simple impedance equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 Impedance-based fault location methods summary. . . . . . . . . . . . . . . . 52 2.5 Results range for the sensibility tests. . . . . . . . . . . . . . . . . . . . . . . 55 4.1 Test average errors with 765 kV line records. . . . . . . . . . . . . . . . . . . 88 4.2 Test average errors with 230 kV line records. . . . . . . . . . . . . . . . . . . 88 4.3 Transmission line parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.4 Test average errors with the long line records. . . . . . . . . . . . . . . . . . 91 4.5 Test average errors with the short line records. . . . . . . . . . . . . . . . . . 91 5.1 HVDC Transmission line parameters. . . . . . . . . . . . . . . . . . . . . . . . 112 5.2 Equivalent AC system data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.3 Fault location average errors test. . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.4 Fault location test errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 xxv 4 CHAPTER 1. INTRODUCTION distance transmission of AC electricity in the world when Willamette Falls Electric Company installed experimental AC generators from Westinghouse in 1890. In 1896, the first AC generation and transmission system was finished in the Niagara Falls using Westinghouse equipment [9]. The race between AC and DC systems was faced by great personalities of the time, in what would become the first standards war (Figure 1.2) [10]. Much has been written about the so called ”war of currents”, but this conflict was more a media fight than a conflict that had real importance in the selection of the winning system. Final decisions on the type of system to be applied always ended up being based on technical reasons, and AC systems of the time offered greater advantages than DC systems given the needs and available technology of the time. Figure 1.2: The three man faced in the first standards war. From left to right: T. Edison, N. Tesla and G. Westinghouse. N. Tesla’s work contributed greatly to demonstrate the benefits of the use of AC systems, like the invention of the induction motor in 1888 [11]. Increasingly, promoted by industrialists such as George Westinghouse, the advantages of AC electric utility service became obvious, and by the end of the 19th century DC systems began an inevitable decline. The advent of the transformer, tree-phase circuits, and the induction motor promoted the strengthening of AC electric systems as the world standard. The transformer made possible the use of different voltage levels for generation, transmission, distribution, and use -particularly important for the high-voltage power transmission over long distances-. The 1890s DC systems required wire for each voltage level, making a city’s streets look like a spider web of wire. With the use of three-phase networks it was possible to ensure a smooth, non-pulsating flow of power and also bring an easy way to interrupt current on high-voltage equipment. The induction motor is rugged, cheap, and serves the majority of industrial and residential purposes. Also, the advent of steam turbines, which are best at high speeds, gave a great advantage to AC generators since the commutators of DC motors and generators impose limitations on the voltage, size, and especially in the speed of these machines. The victory of AC over DC was almost complete. But some vestiges of DC distribution can be found in the electric traction system (trolley bus, railways or subway). Also, some cities continued to use DC well into the 20th century. For example, in Europe, Helsinki had 1.1. HVDC HISTORICAL BACKGROUND 5 a DC network until the late 1940s, Stockholm lost its dwindling DC network as late as the 1970s, and London had some loads on DC as late as 1981. In USA, certain locations in Boston still used 110 volts DC in the 1960s. In 2007, the last DC circuit, a vestige of 19th century DC system of New York City was shut down [12]. 1.1.3 DC Application at the Beginning of the AC Era Despite the general acceptance of AC systems, some people never forgot the obvious advantages of DC, so they proposed not to replace AC but to complement it with DC, introducing a DC link on AC systems. This is how the HVDC systems came about. All HVDC systems are composed by four mains parts, as shown in Figure 1.3: AC System AC System Figure 1.3: General scheme of a bipolar HVDC system. •Transformers: responsible for bringing the AC system voltage to values that are manageable by the converters. •Converters: are the devices that make the connection between AC and DC systems. A converter is basically an assemblage of controlled switches that commutes the different AC phases with the DC system as the AC phases vary. Therefore, the HVDC requires at least a converter at the sending end (called rectifier), and other at the receiver end (called inverter). •Conductors: the systems can be classified according the number of conductors they have: mono-polar (with one conductor, usually of negative polarity), bipolar (with two conductors, one positive and other negative), or homo-polar (with two or more conductors all having the same polarity, usually negative). •Protection and control: both always at the level of the converters which bring a high potential of control over voltage, current, power (active and reactive), and frequency. The HVDC systems have many advantages over its AC counterpart, like: •Greater capacity per equivalent conductor and simpler line construction. •Each conductor can be operated as an independent circuit. •Reduction of transmission losses and no skin effect. •Improvement of the stability system. •No problem with reactive power and voltage regulation. 6 CHAPTER 1. INTRODUCTION •No Ferranti effect problems. •No need of synchronous operation. But also HVDC systems have some disadvantages like: •Converters generate harmonics. •Converters require greater reactive power. •Converters have little overload capability. Based on these advantages and disadvantages, many applications were found for HVDC, the most important are shown below: •For transmitting large amounts of power over long distances. •For interconnecting AC systems having different frequencies or where asynchronous operation is desired. •For cables crossing bodies of water. 1.1.4 Converters Evolution The converters are one of the most complex and important devices in a HVDC system. Since a DC transmission scheme requires currents to be converted from AC to DC or vice versa, the feasibility and advantageousness of DC transmission depended on the development of suitable converters. The converters in a HVDC system have proved to be reliable but expensive. They also constitute a bottle neck to the power transmissible since valves have little overload capability. 1.1.4.1 Firsts High Voltage Converters Three of the most serious attempts to develop a converter suitable to DC transmission are the transverter, the electrolytic, and the atmospheric-arc converter. The transverter, developed by W. Highfield and J. Calverley in 1920 [13], was an electromechanical switch that consisted essentially of polyphase transformers commutated by synchronously rotating brush gear. It performed the three basic operations of voltage transformation, phase multiplication, and commutation, and could be used either as a rectifier or as an inverter. Several experimental transverters were built; the largest of which was rated at 2 MW 100 kV DC but none has been used commercially. The electrolytic rectifier was patented by G. Carpenter in 1928 [14]. Based on an electrochemical method where two different metals are suspended in an electrolyte solution, and direct current flowing one way through the solution sees less resistance than in the other direction. Despite several attempts, this device was not produced for high voltage applications because of the low breakdown voltage and the risk of electric shock. The atmospheric-arc converter, devised by E. Marx in 1932, is a switching device in which an arc between two like water-cooled main electrodes are ignited by a high-frequency spark between auxiliary electrodes in the path of the main arc, and is extinguished after a zero 1.1. HVDC HISTORICAL BACKGROUND 7 current by a blast of air that is continually released on the arc’s path. A 5 km experimental line using atmospheric-arc converter was successfully operated in Germany with 16 MW and ±40 kV. The main difficulty encountered was that the main electrodes were consumed regularly requiring periodic replacement. 1.1.4.2 Converters Applied Commercially The first commercial converter technology that came to be was the mercury-arc valves [15]. It was based on the early works of P. Cooper Hewitt in 1903 [16], but it was U. Lamm2in 1933 who develop a commercial high voltage mercury-arc valve [17]. A mercury-arc valve consists of an evacuated chamber containing a pool of mercury at the bottom forming the cathode. The anode is a carbon electrode at the top of the chamber. When the mercury pool is heated an arc can be struck within the chamber which conducts electrons from the cathode to the anode but not in the other direction. Hence, the device operates as a rectifier. The mercury-arc rectifier was used for power transmission and industrial processing between 1930 and 1975, when it was replaced by thyristor valves. With the advent of the thyristor the converters evolution moved from electrochemical to solid state technology. It was developed in 1956 by engineers at General Electric (G.E.) led by R. Hall [18], but the firsts high voltage applications were in the middle of 1970s. The thyristor quickly replaced the mercury-arc valves as standards converters because of lower maintenance costs, simpler converter stations, and easier control system. The thyristor is a silicon solid-state semiconductor device with four layers of alternating N and P type materials. They act as bi-stable switches, conducting when their gate receives a current pulse, and continuing to conduct as long as the voltage across the device is not reversed. In HVDC applications, many devices are placed in series/parallel configurations to achieve the desired voltage and current ratings. The thyristor rectifier was used from 1975 to 2000 when it was replaced by Insulated-Gate Bipolar Transistor (IGBT). IGBT is a three-terminal silicon semi-conductor device, noted for high efficiency and fast switching. The IGBT is a Voltage Source Converter (VSC), meaning that it can be switched off as well as on by gate control. This seemingly small difference has completely revolutionized HVDC systems. The use of IGBT instead of thyristors is not a development comparable with the transition from mercury-arc valves to thyristor valves, but a rupture that required a complete change of the layout and design philosophy of the converter stations, and that greatly expanded the range of applications of HVDC. IGBTs allow the implementation of VSC instead of LCC. A main advantage of VSC converter stations is a high degree of flexibility: VSC has the inherent capability to control not only active but also reactive power. The IGBT is a fairly recent development, first appearing in the 1980s. Third-generation devices were available in the late 1990s and quickly gained a reputation for excellent ruggedness and tolerance of overloads. In HVDC applications many devices are placed in series/parallel configurations to achieve the desired voltage and current ratings. 2Lamm is sometimes called “The Father of HVDC lines” due to its contribution to the current DC systems configuration. In 1933 he worked for ASEA. 8 CHAPTER 1. INTRODUCTION 1.2 HVDC Projects Around the World 1.2.1 Current HVDC Projects It’s difficult to quantify how many HVDC projects there are in the world, mainly at the moment of delimiting what HVDC means. The scope of this work only quantifies the projects of a commercial nature (not developed with research purposes) that include every element of a previous HVDC project (back to back projects are not included since they don’t have conductors). Also, this work only refers to the beginnings of each project, future updates or extensions of a same project are not included. Finally, all the projects that have been in operation have been accounted for disregarding if they have been dismantled (projects under construction are not included). There are 65 HVDC projects that interconnect power systems around the world [19]. Most of these projects are found in Europe (33.9%), Asia (32.3%), and America (24.6%), other projects have been built in Oceania (6.1%), and Africa (3.1%). Most European HVDC projects involve submarine cables, while Asia is dominated by overhead lines. Although the commercial application of HVDC has existed since 1954, 58.5% of the projects have been developed in the last 20 years. This increase in the construction of HVDC systems in recent years is due mainly to the growth of the electrical network in Asia. Figure 1.4 shows the distribution of the HVDC projects throughout the continents and how these have increased in recent years, especially in the Asian region. 1952 1962 1972 1982 1992 2002 2012 Africa Oceania America Asia Europe u uu u u u u u u uu uu u u uuuu u u uu u uu uu uu uu uuu u u u u u uu u u u u uu u u u u u u Figure 1.4: HVDC projects distribution. In the manufacturing field of HVDC systems, the most important companies in charge of this task are ABB, Siemens, and Alstom. In the beginning, G.E. was an important manufacturer of HVDC systems, but in the mid 1990s the HVDC division at G.E. was absorbed by Alstom. Other manufacturers like Hitachi, Toshiba, and BHEL, among others, have had an important role in the construction of certain projects. The first HVDC applications were built using mercury-arc converters. The initiative in exploring the HVDC applications were taken by G.E., in 1936 they used a 27 km line with 5.25 MW and 30 kV to connect the Mechanicville hydroelectric plant with the G.E. factory in New York [20]. This line was also the first that proved a feature of HVDC systems: frequency conversion (from 60 Hz to 40 Hz). Although it is the first application of a complete HVDC system, it’s not considered the first commercial application since it supplied the G.E. factory. The Gotland I3project is considered the first truly commercial HVDC scheme in the 3Gotland is between V¨astervik Converter Station (57o43’41”N 16o38’51”E) and Ygne Converter Station (57o35’13”N 18o11’44”E). Today is on service after many upgrades. 1.2. HVDC PROJECTS AROUND THE WORLD 9 world. It was built by ASEA (now part of ABB), operated at 20 MW at ±100 kV, and consisted of 96 km of underwater cable between V¨astervik and Ygne in Sweden. This site is the most significant heritage site in the development of HVDC systems because it showed the progress made by mercury-arc technology (Figure 1.54). (a) (b) Figure 1.5: Mercury-arc converter diagram shown in Lamm’s patent (a) that was also used in the Gotland I project (b). In spite of the achievements of this project, HVDC did not immediately become a commercial success. Just until the 1960s more HVDC projects appeared. The most important of these projects was the Volgograd-Donobass5line [21] and was developed in 1965. It was a 473 km overhead line with 720 MW at ±400 kV built by the Russian government. It was the largest and with the highest voltages during these times. During these years the Sardinia6HVDC system was also built in Italy between Sardinia and the mainland [22], which was the first HVDC system in the Mediterranean. It was a 413 km underwater cable with 200 MW at 200 kV constructed by English Electric (now part of Alstom). It was built in 1967 based on mercury-arc valves, but in 1993 it was upgraded with thyristor valves and it was added a third terminal towards Corsica, France, becoming the first multi-terminal HVDC system in the world. In 1970 was built the Pacific Intertie7overhead line with 1440 MW, ±400 kV, and 1362 km of length [23]. It was the first HVDC of USA and was built by G.E. and ASEA. After some upgrades, it now has 3100 MW and ±500 kV. In 1975 was built the Cahora-Bassa8overhead line with 1920 MW, ±563 kV, and 1456 km 4Photo source: ABB web site 5Volgograd-Donobass is between Volzhskaya Converter Station (48o49’34”N 44o40’20”E) and Mikhailovskaya Converter Station (48o39’13”N 38o33’56”E). The scheme is today in a bad state and only operated with a voltage of 100 kV. Nevertheless, it is being modernized. 6Sardinia is between Suvereto Converter Station (43o03’10”N 10o41’42”E) and Codrongianos Converter Station (40o39’07”N 8o42’48”E). Today is operational after many upgrades. 7Pacific Intertie is between Celilo Converter Station (45o35’39”N 121o6’51”W) and Sylmar Converter Station (34o18’39”N 118o29’21”W). Today is operational after many upgrades. 8Cahora-Bassa is between Songo Converter Station (15o36’41”S 32o44’59”E) and Apollo Converter Station (25o55’11”S 28o16’34”E). Today is on service after some upgrades. 10 CHAPTER 1. INTRODUCTION in length between Mozambique and South Africa [24]. It was the first HVDC system in Africa. This project was a breakthrough in technology for several reasons: it was the second to use thyristor valves (the first was the Kingsnorth in England, but had half the voltage and a third of the power), and it was built in cooperation by three important manufacturers: BBC (now part of ABB), Siemens, and AEG (now part of Alstom). The Cahora-Bassa was also the most powered, with the highest voltage, and longest HVDC system of the world for almost a decade until the construction of the Itaipu project. Itaipu9was built in Brazil in 1986 [25]. It was an overhead line with 3150 MW, ±600 kV, and 800 km of length built by ASEA. It was the first HVDC system in South America and was built in order to connect the Itaipu dam (the biggest hydroelectric dam between 1984 and 2008) to S˜ao Paulo city (Figure 1.610). Figure 1.6: Foz do Igua¸cu converter station. The Itaipu hydroelectric plant can be seen in the background. The first uses of IGBT valves in high voltage were in 2000 in Australia. The project called Directlink11 was an underground cable with 180 MW, ±80 kV, and 59 km built by ABB [26]. This project demonstrated the great advantages in control that IGBT technology can bring to HVDC systems, but this technology is still limited to lower level applications. The state-of-the-art in high level HVDC is the Ultra High Voltage DC (UHVDC), and the largest project in this area is the Xiangjiaba-Shanghai12 in China [27]. It was built by ABB in 2011. Nowadays is the most powered, with the highest voltage, and longest HVDC 9Itaipu is between Foz do Igua¸cu Converter Station (25o27’58”S 54o32’33”W) and Ibi´una Converter Station (23o40’02”S 47o06’19”W). Today is on service. 10Photo source: ABB web site 11Directlink is between Mullumbimby Converter Station (28o34’15”S 153o27’8”E) and Bungalora Converter Station (28o15’20”S 153o28’20”E). Today is on service. 12Xiangjiaba-Shanghai is between Fulong Converter Station (28o32’47”N 104o25’04”E) and Fengxia Converter Station (30o55’32”N 121o46’16”E). 1.2. HVDC PROJECTS AROUND THE WORLD 11 system of the world. It has 6400 MW, 800 kV, and 2071 km. Table 1.1 shows a summary of the most important HVDC projects to date. Figure 1.7 shows how the voltage levels of the projects have increased since Gotland to recent years. Table 1.1: Summary of main HVDC projects. Project Name Location Year Characteristics MW kV km Gotland Sweden 1954 20 ±100 96 Volgograd-Donbass Russia 1962 720 ±400 473 N. Z. Inter Island N. Zealand 1965 600 ±250 609 Sardinia Italy 1967 200 200 413 Pacific Intertie USA 1970 1440 ±400 1362 Nelson River Canada 1973 1854 ±463 890 Cahora-Bassa MZ-ZA 1975 1920 ±533 1456 Hokkaido-Honshu Japan 1979 300 250 167 Itaipu Brazil 1986 3150 ±600 785 Quebec-N. England Canada-USA 1990 2250 ±450 1500 Directlink Australia 2000 180 ±80 59 East-South Intercon. India 2003 2000 ±500 1450 Celilo USA 2004 3100 ±400 1200 Norned NO-NL 2008 700 ±450 580 Yunnan-Guangdong China 2010 5000 ±800 1418 Xiangjiaba-Shanghai China 2011 6400 800 2071 1952 1962 1972 1982 1992 2002 2012 900 800 700 600 500 400 300 200 100 0 Voltage [kV] Gotland Volgograd-Donbass Nelson River Cahora-Bassa Itaipu Xiangjiaba-Shanghai   r r r r r r Figure 1.7: Evolution of voltage levels in HVDC projects. 12 CHAPTER 1. INTRODUCTION 1.2.2 The Next HVDC Projects The growing needs of electrical systems, such as the load increases, the interconnection of large networks, the integration of renewable energy sources, and changes in operation and management of the systems, bring a high development potential for HVDC systems. The coming years will see the construction of projects that will go over 2500 km in length, that will surpass 7000 MW or that will break the ±1000 kV barrier [28]. Throughout the world, projects are being planned that were unthinkable 15 years ago. These projects plan to connect large generation centers with mega-cities over thousands of kilometers. Like in China [29], Brazil [30], and India, that expect to harness the vast hydroelectric potential they posses. Another important reason for the undertaking of these projects is the connection of large electric markets, such as USA where it’s planned to take advantage of price differentials between the three great markets of the region [31]. Also in Europe a major project is in development that aims to connect all electrical markets of the EU and also to take advantage of the wind energy potential of the North Sea, creating a HVDC network with the largest underwater HVDC cables of the world [32]. Table 1.2 shows the most significant HVDC projects expected in the coming years: Table 1.2: Summary of main HVDC projects under construction. Project Name Location Year Characteristics MW kV km Rio Madeira Brazil 2013 3150 ±600 2500 Jinping-Sunan China 2013 7600 ±800 2090 Tres Amigas USA 2014 5000 300 — North-East Agra India 2015 6000 ±800 1728 NorthConnect Norway-UK 2020 1400 — 711 In the early 20th century, AC systems were imposed over DC systems due to the benefits they offered and because these benefits could not be reproduced by DC systems with the available technology of the time. Some of these benefits have to do with the ease of changing voltages and current interruption. These benefits allowed AC systems the transmission of energy over long distances, but with the growth of electrical networks, these AC systems are operated to their limit and DC systems have proven to be of great help to solve the problems that large electrical systems have, including distance limitations. The natural descendants of DC systems of the early 20th century are the current HVDC systems. The HVDC systems have evolved considerably since their inception in the mid 20th century based on mercury-arc technology to become an ideal solution for large block transmission over long distances. This ensures a great future for the HVDC systems and a great development potential for large electrical systems. 1.3. JUSTIFICATION AND STATEMENT OF THE PROBLEM 13 The development of power electronics has enabled the growth that HVDC systems have had in recent years, and have helped to show the great value that DC systems have for modern networks. As more than one hundred years ago, today’s DC technology remains a fundamental part of several modern electrical systems. 1.3 Justification and Statement of the Problem The power system’s behavior has become increasingly difficult to analyze and predict for the utility industry because of the large scale and the complexity of modern systems. In the most important electrical systems of the world such as Brazil, Canada, China, India, USA and many European systems [30, 32–38], the longest lines are also the most important, because they carry large amounts of energy from generation centers to consumption places, making these lines vital to the correct operation of their systems. Traditionally, AC transmission lines have been used in the development of these large systems, but the last year has seen rapid advances in power electronics and control technology, that allow the use of HVDC lines. The characteristics of the HVDC lines make them ideal for applications in systems interconnection and transmission of large blocks of energy. But even with all the potential advantages of HVDC system applications, they are still lines that require special attention when problems arise. Inability to quickly locate and remove faults on a HVDC line could destroy the stability of the power system and lead to serious social and economic consequences. 1.3.1 Motivation When a major power system disturbance occurs in HVDC lines, protection and control actions need to take place to prevent power system degradation and restore the system to a normal state within a minimum time. But in most cases, the service outages of these lines inevitably lead to the loss of large blocks of loads. So, a quick repair to recover the line service is vital for the system’s operators. The operators must deal with a very complex situation where they perform a series of procedures to achieve breakdown service. These procedures always carry a significant expenditure of time. Once the fault has been cleared and the HVDC lines isolated by the protection systems, most of the following processes are carried out by the maintenance crews. They need the most sophisticated equipment and methods to locate and repair the fault in an economically viable way and as quickly as possible. One of the first steps in the repair of the faults always is locating the fault. Therefore, in these cases it is extremely difficult to determine directly by line inspections where a fault occurred, because they are used as an interconnection between different power systems over long distances by overhead lines or by cables crossing bodies of water. Most HVDC lines inevitably cross through complex terrain or in deep sea, and work under harsh weather conditions, so the time required to physically check the lines is much greater than the faults in the sub-transmission and distribution systems. However, researches about fault location techniques for transmission lines show that accurate and fast methods are of great significance and of practical engineering value [39, 40]. Prompt and accurate fault location in a HVDC system can accelerate the system’s restoration, reduce the outage time, 20 CHAPTER 1. INTRODUCTION centers to consumption centers, over long distances and at high voltage levels. But twenty first century needs have already exceed the operating limits of AC systems. The increase in the amount of transmitted power and greater distances covered by existing electrical systems are beyond the capabilities of the secure and stable operation of AC technology. Recent developments in power electronics applied to converters have made current HVDC systems to provide a better solution than AC systems for the transmission of large blocks of power over long distances, so it’s safe to assume that the roles played by AC and DC systems in the early twentieth century have been inverted during the last few years. These demonstrates that the same reasons that led to the adoption of AC systems as the global standard are the same reasons that now bring back DC systems, and just as more than 100 years ago, is not unreasonable to consider today a drastic change of paradigm in the design of electrical systems. DC systems of early twentieth century were unable to meet the needs of its time due to two main reasons: its inability to generate, transmit, and distribute power at different voltage levels, and its difficulty to interrupt high levels of current in DC. With the advent of power electronics, these problems were solved. The converters are a powerful tool for the control and protection of HVDC systems [13] and are an easy, safe, and fast way to cut power when needed. Also, this technology can be applied to change in voltage levels with AC/DC converters equipment. The development of such equipment began for low voltage applications, but there are some studies that show its feasibility for high voltage applications and without magnetic-core transformers [14]. 1.6.1.1 DC Advantages The most common arguments in favor of HVDC are: •Investment cost: It is undeniable that the transmission of large amounts of power over long distances is more cost efficient in DC than AC. This is not so clear in the case of shorter distances, but there are still certain considerations that must be taken into account and that are discussed in more detail below. •Long distance water crossing: In a long AC transmission cable, the reactive power flow will limit the maximum transmission distance due to the large cable capacitance. With HVDC there is no such limitation so, for long cable links, HVDC is the only viable technical alternative. •Lower losses: An optimized HVDC transmission line has lower losses than AC lines for the same power capacity. The losses in the converter stations have of course to be added, but since they are only about 0.6% of the transmitted power in each station, the total HVDC transmission losses come out lower than the AC losses in practically all cases. •Controllability: One of the fundamental advantages with HVDC is that it is very easy to control the active power in the link. •Stability: It is sometimes difficult or impossible to connect large AC systems due to stability reasons. In these cases, HVDC is the only way to make possible an exchange of power between the two networks. Also, DC systems are more stable and reliable 1.6. SUPPLEMENTARY RESEARCH 21 during faults than AC systems because when a DC system adopts a bi-polar dual-loop configuration, any fault can take one loop out of service, while the other loop can still operate by switch conversion to avoid power interruption in a large area. •Magnetic pollution: Magnetic fields from HVDC lines are negligible in comparison to corresponding magnetic fields from AC lines. •Environment: The latest developments in renewable energy are in DC. Improved energy transmission contributes to a more efficient use of existing power plants. Also, the land coverage and the associated right-of-way cost for a HVDC overhead transmission line is not as high as for an AC line, this reduces the visual impact. It is also possible to increase the power transmission capacity for existing rights of way. There are, however, some environmental issues that must be considered for the converter stations, such as: audible noise, visual impact, electromagnetic compatibility, and use of ground or sea return path in mono-polar operation. 1.6.1.2 Economic Considerations A long HVDC transmission line costs less than a long AC line for the same transmission capacity. However, the terminal stations are more expensive in HVDC because they must perform the conversion from AC to DC and vice versa. On the other hand, the average costs of transmission (overhead lines and cables), and land acquisition/right-of-way costs are lower in HVDC, just like operation and maintenance costs. Initial loss levels are higher in the HVDC system, but they do not vary with distance. In contrast, loss levels increase with distance in a high voltage AC system. Above a certain distance, the so called ”breakeven distance” (Figure 1.9), the HVDC alternative will always give the lowest costs. The break-even-distance is a lot smaller for submarine cables than for an overhead transmission line, and this distance depends on several factors, such as transmission medium and different local aspects (permits, cost of local labor, etc). - 6 """""""""""""" " Cost Distance Break-even AC Losses AC Line AC Terminals DC Losses DC Line DC Terminals Total AC Cost Total DC Cost s ? 6 ? 6 ? 6 ? 6 ? 6 ? 6 Figure 1.9: Cost comparison between AC and DC lines In Figure 1.9 is easy to see that for short distance lines, the cost of building in AC is less than the cost of building in DC. This is a fact that may hinder the establishment of DC systems. The major costs in a DC line project are the converters located at each line-end. Even so, with the continuous development that has occurred in recent times in converter technology, this cost is expected to decline in the coming years. 22 CHAPTER 1. INTRODUCTION The DC-DC converters are another vital equipment and a cost that should be taken into account. It is becoming accepted that a DC-DC converter will have considerably higher costs and losses than a comparable AC transformer. Another important issue to consider in the DC grid are DC breakers, without this type of equipment would not be possible to pass from two or three terminal HVDC lines to an entire DC grid. A lot of work was done in this area [47], and some manufacturers (especially in Europe) have shown interest in addressing this challenge; where certain proposals have emerged [48] and even the first commercially available DC breaker was manufactured [49]. Nevertheless, because of a range of advantages associated with DC transmission, DC networks may compete with established AC grid topologies. In the case of distribution systems, several studies have been carried out over the use of a DC distribution system and they show the feasibility of this type of systems, both in isolated topologies [50] and linked to larger networks [51]. Just like in transmission grids, the converters are the most expensive equipment in distribution grids but, since the converters are composed by a series of power electronic valves, when the voltage is lower, fewer valves are needed, so the price decreases; therefore, in distribution networks the total cost is lower than in transmission networks. The load is a factor that deserves attention in distribution systems. In most systems, the loads are of two main types: electronic devices, and motors. All electronic equipment works in DC and converters are required in order to connect to AC networks. Motors work in AC, but the vast majority use voltage based speed control, which involves using AC-DC-AC converters. If these controls were connected directly to DC, the AC-DC conversion would not be necesary. Therefore, a DC distribution grid would eliminate the need of converters sets for each load, reducing the cost, complexity, and possibly increasing the efficiency. But beyond this, the choice between AC or DC systems should not be made based only on the costs associated with building the system. There are other operational factors that must be taken into account in the decision making process. The great control of the converters is a powerful tool in the operation of DC systems and the full control of power flow that enables efficient power trading between regions. Whereas in a meshed DC system it might not be possible to directly control currents in all lines. With the use of DC systems, energy markets could reach a precision that is not possible with AC systems. Due to the growing need for energy in populations, AC electrical systems have become more vulnerable to blackouts. These blackouts have increased in recent years around the world, affecting vast areas and millions of people14. •The 2003 blackout in the northeast of USA, and east Canada affected an estimated 45 million people in 8 USA states, and 10 million people in Ontario, caused by a fallen tree branch. •The 2003 blackout in Italy affected a total of 56 million people between the north of this country and the south of Switzerland. •The 2005 blackout in Indonesia was a cascading outage across Java and Bali, affecting some 100 million people. •The 2008 blackout in Venezuela affected more than 10 million people, caused by stability problems in the transmission system. 14Source of people affected by blackout estimation by Reuters 1.6. SUPPLEMENTARY RESEARCH 23 •Over 5 million people were affected in 2001 when cascading outages hit parts of California, Arizona, and northwestern Mexico. •The 2012 blackout in Brazil affected as many as 53 million people across 11 states caused, by a cascading problem in the transmission system. •The 2012 India blackout was the largest outage in history. The outage affected over 620 million people and was spread across 22 states in northeast India. Because converters are so controllable, each HVDC line can be operated independently, avoiding stability problems in DC systems, making them safer and virtually immune to large blackouts. The costs incurred by each of the large blackouts of the last years, greatly exceeds the difference in costs of construction between AC and DC systems [52, 53]. 1.6.1.3 DC Grids Challenges Wider use of DC grids will definitely add several important features for handling future sustainable power generation, but it also involves challenges. To a limited extent, these are of a technical nature. The challenges mainly concern adoption of international regulations in order to manage these new grids15. When DC grids grow into meshed grids, there will be a need for control and protection schemes as well as for powerful breakers. The basic technologies in these fields are known although further development and verification is needed to fully meet all future needs and regulatory demands. The feasibility of three-terminal HVDC systems has been clearly demonstrated with already operational projects around the world. Also, standards will be called for in the future to provide greater harmony of HVDC grids, to this end, a work group has been established within CIGR´ E [54] made up of both manufacturers and users. The work group is researching reliability of DC grids, and various grid configurations like radial and meshed grids are being reviewed. Because a grid has more branches than nodes, methodologies for power flow control are also being looked into. Current conditions of electrical systems around the world present an unique opportunity in the decision making process to establish how the systems of the future are going to be, not only in countries with emerging economies but also in countries with already mature economies. In countries with emerging economies like China, Brazil, and India, the electrical systems are still being expanded or even under development, so their design is open to great changes of paradigm in their construction. The expansion of mature electrical systems is quite difficult because of the many permit and land requirements for the building of new lines. There are projects like the one in Europe where the plan is to build a DC grid that connects the European continent, North Africa, and even parts of the Middle East, in order to share the hydro, wind, and solar resources scattered throughout this vast area. Beyond the likelihood of expansion, mature systems currently present another unique opportunity to foster the change of paradigm in electrical systems. The electrical systems in Europe and the USA base their infrastructure in large projects built with the available 15Like ENTSO-E, which already has a working group addressing this. 24 CHAPTER 1. INTRODUCTION technology of the mid-twentieth century, and are approaching the end of their useful life and must be replaced in the coming years. This will require a huge investment from these countries to support the needs of their population. So this requires the answer to an important question: If such a large investment should be made, why is not made on a system with the best features and benefits that current technology has to offer? It is undeniable that DC systems are at least one of the possible roads to take for the construction of the electrical systems of the future, and as such they should be taken into account and evaluated. 1.7 Organization of the Thesis Originally, it was intended to write this work as a continuous idea, each development of the argument being logically derived from what had come immediately before. This proved to be an impossible ideal. The scope of research areas indicated a number of boundaries where chronological development of this work was not possible. Therefore, it was decided to divide the analysis into sections of chronological development where each section retains its own chronological order, and at points that will reference would be made from more than one section in the future. Figure 1.10 shows a diagram with the organization of the topics covered by this research. A brief review of the issues addressed in this work is made below. These are the subjects required for the development of this book. Also there is a justification of the order in which this book is structured: Introduction: This part shows a first approach to the problem of fault location, and justifies their importance for electrical systems in general, and in particular HVDC systems. It is also the framework of the problem and considers how they will be addressed in order to propose a solution. To understand the context in which the work is carried out, a review of the evolution of HVDC systems is made, as well as the prospects that exist for short-term development. This theme conforms the Chapter 1 of the book. The main topics of this part are: •HVDC systems background •Justification and statement of the problem •Research approach •Thesis proposals and contributions Fault location review: This section addresses one of the two main themes of the work: the fault location methods. Shows the importance these methods have for the power system operation. A review of existing methods is made and the basis of their operation are explained. All fault location methods could be classified in two types: impedance-based, and traveling wave-based fault location. The section seeks to study these methods in two ways, one theoretical and other practical. In the theoretical part, a general definition of fault location is presented and a critical analysis of different methods is made. In the practical section, a comparative analysis between two of the most widely used methods is made. 1.7. ORGANIZATION OF THE THESIS 25 Introduction Fault Location Review Line Model Review Line Model Development Method Development COMTRADE Standard Method Test Test HVDC line Model Conclusion q q) ? ? ? ?  - - Figure 1.10: Thesis’ organization diagram. The objective of these tests is to deepen the understanding of the different methods by making comparisons between their performances, so as to observe their behavior and test the strengths and weaknesses of each method. This theme conforms the Chapter 2 of the book. The main topics of this part are: •Origins, definition and benefits •Traveling wave-based fault location review •Impedance-based fault location review •Principles of operation of the methods •Comparative analysis of the methods Line model review: This section addresses the second main theme of the work, the transmission line models. Since the fault location method proposed in this work needs to estimate the voltage and current profiles along the line based on a mathematical model, it is necessary to know the models of transmission lines currently available. 26 CHAPTER 1. INTRODUCTION This section addresses the problem of transmission lines modeling, and shows the basic differential equations that describe the lines’ behavior. A review of the different methods used to solve these equations is also made and they are grouped into two types of modeling: frequency-domain, and time-domain models. This theme conforms the Chapter 3 of the book. The main topics of this part are: •Line model differential equations •Frequency-domain models •Time-domain models Line model development: This part begins the development of the proposal presented in Chapter 1. This part shows the development of a new time-domain distributed parameters transmission line model. Since HVDC lines have no frequency, frequency-domain line models can not be applied. Moreover, the existing time-domain line models are based in solutions that use lumped parameters, therefore, the model’s accuracy is lost. The model deduced here has a structure similar to other time-domain models, but in a more complex way that provides greater accuracy. This is because approximations are not used to solve differential equations. This model was developed specifically to use in the fault location method proposed in this work. This theme conforms the first part of Chapter 4 of the book. The main topics of this part are: •Line model deduction •Model analysis •Illustrative examples Method development: This section presents, in a structured manner, all the knowledge presented so far. The principles of operation of the fault location method proposed is explained, and its structure is shown. Also, it explains the selected algorithm for this method, as well as the different stages that is composed of. The work developed here proposes the implementation of an impedance-based method for locating faults in two-terminal HVDC lines, using the time-domain line model in order to estimate the voltage profile over the line during the fault. This theme conforms the second part of Chapter 4 of the book. The main topics of this part are: •Method scheme •Fault detection •Impedance-based fault location method Method test: Fault records of a HVDC line will be analyzed with the developed method in order to validate the method’s performance. The results will be compared with two commercially available methods. Tests with records of actual and simulated faults were carried out in order to prove the method with the highest number of possible variations. This theme conforms the Chapter 5 of the book. The main topics of this chapter are: 1.7. ORGANIZATION OF THE THESIS 27 •HVDC line used •Actual fault process and commercial fault location equipment •Method’s performance to actual faults •Method’s accuracy test •Fault resistance sensitive test Conclusion: This section provides a summary of the research, and argues quantitative and qualitative conclusions for this work. This part is pretended to give closure to the research and provides an assessment of its results. This theme conforms Chapter 6 of the book. The topics covered are: •Conclusions •Contributions and findings •Future lines of research COMTRADE standard: Supplementary information can be obtained here to understand the theme developed in Chapter 4. This part addresses the issue of the IEEE Standard Common Format for Transient Data Exchange (COMTRADE). This standard is intended for use by digital computer based devices which generate or collect transient data from electric power systems. The standard should facilitate exchange of the transient data for the purpose of simulation, testing, validation, or archival storage. This theme conforms the Appendix B of the book. The topics of this section are: •COMTRADE standard files summary •Sampling rate •Illustrative example Test HVDC line model: Supplementary information can be obtained here to understand the theme developed in Chapter 5. In this part is done a detailed explanation of the HVDC line model used for the simulation of faults required for the tests. It explains the block diagrams used for modeling of the line and converters systems. It also explains the block diagrams of the control and protection systems that act during the faults. This theme conforms the Appendix A of the book. The topics covered in this part are: •Description of the HVDC system •Control and protection systems 28 BIBLIOGRAPHY CHAPTER 1 Bibliography Chapter 1 [1] IEA, “Co-generation and renewables: Solutions for a low-carbon energy future,” International Energy Agency, 2011. [2] EWEA, “Wind in power: 2012 european statistics,” tech. rep., The European Wind Energy Association, Feb. 2013. [3] GWEC, “Global wind report 2012,” tech. rep., Global Wind Energy Council, Apr. 2013. [4] O. Peake, “The history of high voltage direct current transmission,” in 3rd Australasian Engineering Heritage Conference (U. of Otago, ed.), p. 8, 2009. [5] G. Asplund, L. Carlsson, and O. Tollerz, “50 years of HVDC. part I: From pioneer to world leader,” ABB Review, no. 4, pp. 6–8, 2003. [6] E. Kimbark, Direct Current Transmission. New York: Wiley Interscience, 1971. [7] L. de Andrade and T. Ponce de Le˜ao, “A brief history of direct current in electrical power systems,” IEEE History of Electro-technology Conference, p. 6, 2012. [8] C. Sulzberger, “Thomas edison’s 1882 pearl street generating station,” IEEE Global History Network, 2003. [9] R. Belfield, “The niagara system: The evolution of an electric power complex at Niagara falls, 1883-1896,” Proceedings of the IEEE, vol. 64, no. 9, pp. 1344–1350, 1976. [10] T. McNichol, AC/DC the Savage Tale of the First Standars War. San Francisco: Jossey-Bass, 2006. [11] N. Tesla, “A new system of alternate current motors and transformers,” in Transactions of the American Institute of Electrical Engineers, vol. V, pp. 308–327, 1888. [12] R. Lobenstein and C. Sulzberger, “Eyewitness to DC history: the first and last days of DC service in New York City,” IEEE Power and Energy Magazine, vol. 6, no. 3, pp. 84–90, 2008. [13] W. E. Highfield and J. E. Calverley, “Improvements in and relating to electric converting apparatus,” 1921. [14] G. Carpenter, “Liquid rectifier,” United States Patent Office, vol. USA, US1671970, 1928. [15] A. Moglestue, “From mercury arc to hybrid breaker 100 years in power electronics,” ABB Review, no. 2, pp. 70–78, 2013. [16] P. Cooper Hewitt, “Method of manufacturing electric lamps,” United States Patent Office, vol. USA, US682692, p. 7, 1901. [17] U. Lamm, “Gaseus discharge converter,” United States Patent Office, vol. USA, US2006053, p. 3, 1935. BIBLIOGRAPHY CHAPTER 1 29 [18] R. Hall, “Power rectifiers and transistors,” Proceedings of the IRE, vol. 40, no. 11, pp. 1512–1518, 1952. [19] W. G. on HVDC and FACTS, “HVDC projects listing,” IEEE Transmission and Distribution Committee, 2008. [20] G. Breuer, M. Morack, L. Morton, and C. Woodrow, “D-C transmission: An american view-point,” Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers, vol. 78, no. 3, pp. 504–512, 1959. [21] N. Chuprakov, A. Milutin, A. Posse, and V. Shashmurin, “Initial period of operation of the D.C. transmission line between Volgograd and Donbass,” IEE Conf. HVDC Transmission, 1966. [22] V. Ciallella, P. Grattarola, A. Taschini, C. Martin, and D. Willis, “Testing and operating experience of the Sardinia-Italian mainland D.C. link,” CICGRE Session, 1968. [23] R. Cresap, W. Mittelstadt, D. Scott, and C. Taylor, “Operating experience with modulation of the pacific HVDC intertie,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-97, no. 4, pp. 1053–1059, 1978. [24] W. Bayer, K. Habur, D. Povh, D. Jacobson, J. Guedes, and D. Marshall, “Long distance transmission with parallel AC/DC link from Cahora Bassa (Mozambique) to South Africa and Zimbabwe,” 1996. [25] C. Peixoto, “Itaipu 6300 MW HVDC transmission system feasibility and planning aspects,” Symposium on Incorporating HVDC Power Transmission Into System Planning, pp. 211–236, 1980. [26] B. Railing, G. Moreau, J. Wasborg, D. Stanley, J. Miller, and Y. Jiang-H¨afner, “The directlink VSC-Based HVDC project and its commissioning,” 2002. [27] A. Kumar, V. Lescale, U. ˚ Astr¨om, R. Hartings, and M. Berglund, “800 kV UHVDC from test station to project execution,” 2009. [28] R. Nayak, R. Sasmal, Y. Sehgal, M. Rashwan, and G. Flisberg, “Technical feasibility and research & development needs for ±1000 kV and above HVDC system,” in CIGRE Conference, p. 10, 2010. [29] K. Zha, X. Wei, and G. Tang, “Research and development of ±800kV/4750A UHVDC valve,” in Second International Conference on Intelligent System Design and Engineering Application, pp. 1466–1469, 2012. [30] J. Graham, A. Persson, and G. Biledt, “The integration of remote hydroelectric plants into the brazilian network using HVDC transmission,” in CIGRE Conference, p. 9, 2006. [31] M. Reynolds, D. Stidham, and Z. Alaywan, “The golden spike: Advanced power electronics enables renewable development across NERC regions,” IEEE Power and Energy Magazine, vol. 10, no. 2, pp. 71–78, 2012. 36 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES starting the visual inspection, so that the work area can be delimited to a small section of the line. For the location, these techniques are based on the impact that faults have on other well-defined points on the same line. In these other previously defined points, different types of data are collected and analyzed to conclude that only an event with certain characteristics may have such effects on the measuring point. The location of this event is the fault location. Many methods have been developed about fault location in transmission lines and many articles have been published about each of these methods (sections 2.3 and 2.4). The researches discussed below are all pioneers in their respective work areas and all are representative samples of developments that have occurred in the different fault location methods. 2.2 Fault Location Benefits Once the fault is cleared, the adopted fault locator is enabled to detect the fault’s position. Then, the maintenance crews can be informed of that location in order to fix the resultant damage. Later, the line can be re-energized again after finishing the maintenance task. Since transmission line networks spread for some hundreds of kilometers in different environmental and geographical circumstances, locating these faults based on the human experience and the available information about the status of all breakers in the faulted area is not efficient and time consuming. These efforts can effectively help to sectionalized the fault (declare the faulted line section), rather than to locate precisely the fault’s position. Temporary faults are self-cleared and do not affect permanently the supply’s continuity, however, the location of such faults is also important. In this case, the fault’s location can help to pinpoint the weak spots on the line as well as hidden problems. As a result, the plans of maintenance schedules can be fixed to avoid further problems in the future. Fast and effective maintenance processes lead to improve the power availability to the consumers. This consequently enhances the overall efficiency of the power grids. These concepts of (availability, efficiency, quality, etc) have an increasing importance nowadays due to the marketing policies resulting from deregulation and liberalization of power and energy markets. All the mentioned benefits of savings in time and effort, improved availability, and assistance to maintenance plans can be reviewed from a economical perspective. There is no doubt that time and effort saving, increasing the power availability, and avoiding future accidents can be directly interpreted as a cost reduction or a profit increase. This is an essential concept for competitive marketing. 2.3. TRAVELING WAVE BASED FAULT LOCATION 37 2.3 Traveling Wave Based Fault Location In general, these methods are founded on the work of Carson [4, 5] and are based on measuring the time that takes the wavefront to propagate from the point where a discontinuity occurs in the line to the measuring terminals. If the speed by which the wave travels is known, then is possible to calculate how much distance the wavefront has traveled. The general principles of operation of these methods are explained below. 2.3.1 Principles of Operation A traveling wave is a wave observed traveling through a medium. This is basically any space containing matter in any given state. When moving, the crest of the wave will move from particle to particle from the incidence of energy transfer. An ideal traveling wave has the moving crest (called wavefront), followed by a drop. This creates a sine wave pattern. The ideal example of a traveling wave is an ocean wave. When any fault occurs in transmission lines, a traveling wave appears. It means that fault current is divided into two separate currents, and each of these currents goes to each side of the transmission line. Those currents are shaped as a wave, they quickly achieve their peak value but their decrease lasts much longer. Traveling waves spread along the transmission lines at almost light speed. Because of the resistance of the lines, their peak value of current decreases as they move. When a traveling wave comes to any crossing, it divides itself into several smaller waves and each of them proceeds to another branch. The value of the current in each branch depends on the total impedance in that branch. If the impedance is smaller, the current is higher and vice versa.              @ @@ @@ @@ @@ @@ @@ @ @ @@ @@ @@ @@ @@ @@ @ ? 6 6 ?? 6 11−Γ Γ ZaZb Figure 2.3: Reflection and refraction phenomena of waves in a one dimensional medium. Figure 2.3 shows a unit step function reflected and refracted at a change in surge impedance of a distributed-constant line. For a simple discontinuity of this sort, the reflection coefficient (Γ) is given by: Γ = Zb−Za Za+Zb (2.3) 38 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES When Zaand Zbare the impedance of the medium aand b. The behavior of the traveling wave in a transmission line will be discussed in more detail in chapter 3. Traveling wave based fault location methods are based on the velocity of the traveling wave, assuming is constant for each transmission line, and can be calculate by vt=1 √LC . Since the time it takes the wavefront to propagate from the fault point to the terminals may be measured, and the travel speed is known, then is possible to calculate how much distance the wavefront has traveled. Two different methods can be used to calculate the travel distance: reflectometry and interferometry. Both methods are widely used in the optics field. The reflectometry method is based on the phenomenon of reflection of the wave. i.e., the change in direction of the wavefront at an interface between two different media so a part of the wavefront returns to the medium from which it originated until the fault point. This process is repeated continuously as shown in Figure 2.4. Then, the fault distance from a measurement point can be calculate by equation (2.4). - S R (-) (-) (+) (+) t1 (-) (+) t2 d s s d=1 2(t2−t1)( 1 √LC ) (2.4) Figure 2.4: Reflectometry Lattice diagram. . Where dis the distance between the measurement point and the fault point, t1and t2are the first two consecutive wavefront arrival times measured, and Land Care the inductance and capacitance of the line by length unit, respectively. Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is a diagnosis of the original state of the waves. This works because when two waves with the same frequency are combined, the resulting pattern is determined by the phase difference between the two waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Therefore, when a fault starts, two traveling waves are generated, one to each line end. The waves leave the fault point with the same phase, but they arrive at the line ends with a phase difference because of the difference of the distance between each line end and the fault point, as shown in Figure 2.5. By combining these waves is possible to calculate the difference. Then, the fault distance from a measurement point can be calculate by equation (2.5). Where dis the distance between the fault point and the point where t1was measured, t1and t2are the wavefront arrival times measured at both measurement points, lis the total length of the line, and Land Care the inductance and capacitance 2.3. TRAVELING WAVE BASED FAULT LOCATION 39 - S R t1(-) (-) (+) (+) t2 (-) (+) d s s d=1 2[l+ (t1−t2)( 1 √LC )] (2.5) Figure 2.5: Interferometry Lattice diagram. . of the line by length unit, respectively. 2.3.2 One-end and Two-ends Methods The traveling wave based fault location was first proposed by R¨ohrig in 1931 [6]. Its use was implemented initially in the middle of the 20th century by Stevens and Lewis [7, 8] but they were gradually abandoned in the 1970s because of their high cost, poor reliability, and maintenance problems. In the middle of the 1980s, the interest for traveling wave-based methods was renewed by SEL Inc., and other research articles were published to employ this technique for fault location [9-11]. A technique for locating faults using information from only one end of the line is developed in [9, 10]. This method uses successive reflections generated by faults (reflectometry technique). In many cases, there are large impedance mismatches when a fault starts, this generates transient waves that travel through the line and are reflected between the fault and the line ends. From measurements of the first two consecutive transient arrival times, the fault location can be calculated. Because the method only uses information from one line end, the key is the observation of the relative polarity of the two wavefronts generated by the fault and propagated towards each line end. So is possible to differentiate the wavefront originating from one line end and those reflected from the opposite end. On the other hand, in [11] is developed a technique by Dewe et al. for location using information from both ends of the line. By having information available at both ends, the analysis is facilitated. In this method, the analysis is based on the time difference in the arrival of the fault-generated wave at each end of the line (interferometry technique). The simultaneous processing of information from both ends is achieved by a very accurate data acquisition technique with the time reference signals provided by a global positioning system receiver. Since then, others traveling wave-based methods were developed, where the traveling wave-based method and other known methods were combined to facilitate the detections and fault analysis. Like the method proposed by Magnago et al. in [12], that uses the wavelet transform to improve the wavefront detection, because it allows time localization of different frequency components of a given signal. 40 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES After the 1990s, with the developments of communication systems and digital signal processing techniques, the traveling wave-based fault location techniques got more and more applications in different AC transmission systems. But these methods are mostly used for HVDC lines than for AC systems. In fact, fault location methods implemented on HVDC lines are all based on traveling wave without exception. Some examples of these are [13–15]. In [13] is proposed by Murthy et al. a method for fault location in HVDC lines using wavelet transforms. The ability of the wavelet transform to locate both time and frequency makes it possible to simultaneously determine the sharp transitions of signals and the location of their occurrence. Other method is proposed by Ping et al. in [14], combining the single-end and two-ends methods. With this combination, the aim is to complement the results of both methods. This will reduce the amount of cases where each separate method is not enough or has problems in locating the fault. And in [15] is proposed by YoungJin et al. a combination between a traveling wave with cross correlation methods for locations on HVDC cable lines. To detect the wavefront, it’s used the cross correlation method, based on the similarity between the first wavefront (used as the template signal) and a subsequent wavefront, both measured at the same line end. If two signals have the same shape, the correlation result would be maximum. All these traveling wave-based methods have a fast response and high accuracy. However, they are also facing some insurmountable technical problems: •The detection of the wavefront is the key to traveling wave fault location. If the wavefront cannot be captured successfully, or the wavefront does not exist at all at the occurrence of a fault, the fault location will fail. For instance, when the line is grounded through a large resistance, the transient traveling wave signals are too weak to be detected, disabling the fault location under these circumstances. Moreover, if a fault is caused by a gradual change in the transition resistance, the traveling wave may also be too weak to be discovered, resulting in the failure of the fault location [9–12, 14–16]. •In these methods, is measured the time it takes the wavefront to arrive at the point where the device is installed, and the fault distance is the product of the time and the wave speed. Therefore, the accuracy of the fault location is dependent, to a great extent, on the wave speed, and since the wave speed is vt= 1/√LC (where Lis the inductance and Cis the capacitance of the propagation medium) these methods also depend on the line parameters [14– 16]. •Accuracy in fault location depends upon sampling frequency. Since the speed at which the wave travels over transmission lines is slightly lower than light speed, in order to achieve higher accuracy, a very high sampling frequency has to be used in traveling wave fault location methods. Therefore, more expensive and complex equipments are required [11, 16]. •The wavefront must be identified to locate the fault, which is often carried 2.3. TRAVELING WAVE BASED FAULT LOCATION 41 out by experienced professionals and cannot be implemented automatically by computers [1]. •Since the traveling wave fault location uses the signal high frequency components for the analysis, is vulnerable to interference of external signals [11, 14]. •If the fault occurs near a line end, is very difficult to identify the wavefront with information of this line end due to the high speed of the traveling wave [12, 13, 15, 16]. •Another difficulty arises for faults near the buses or for those faults occurring at near zero voltage inception angle because, if the voltage is zero when the fault starts, there is not an abrupt change of the line continuity and a wavefront is not produced [12, 13, 15, 16]. Table 2.1 shows a summary of all the fault location methods discussed here. Table 2.1: Traveling wave-based fault location methods summary. Reference One-end Two-ends Synchronized Unsynchronized Long line application Short line application Communication needed [7] l l l [8] l l l [9] l l l l [10] l l l l [11] l l l l [12] l l l l [13] l l l [14] l l l l [15] l l l l 2.3.3 Comparative Analysis Most of the literature indicates the need for high sampling rate of fault records as one of the main disadvantages of traveling wave methods, but do not show quantitative results to support it. 42 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES In order to evaluate this statement, this section presents a sensitivity analysis, comparing the results of two methods. For the test, two of the most widely accepted methods were used. First, a one-end method based on spectrum estimation [17], and then a two-ends method based on wavelet [12]. The test consists in analyzing a fault repeatedly but using records with different sampling rate. The records sampling rate varies from 2 kHz to 5 MHz. The test was performed for both selected methods in order to compare the results. Simulated faults were used for the analysis in order to study the sensitivity of these methods to variations in the frequency of sampling fault records. For this analysis, actual faults records could not be used, since different records of the same fault are required and also obtained in a wide frequency range. Likewise, is not enough to simulate changes in the records sampling rate by deleting samples, because the results would always be multiples of the original record and would not allow the integral study of all possible frequencies. The fault was simulated using MatLab R . The power system was based on two parallel 735 kV 60 Hz transmission lines with 500 km length and two different equivalents systems, one at each line end. The resistance and reactance of each equivalent system was respectively 5.3754 Ω and 53.754 Ω for the equivalent system S and 2.6877 Ω and 26.877 Ω for the equivalent system R. Both lines were modeled using the distributed parameter line model. Table 2.2 shows the transmission system data used in the line models. Table 2.2: Transmission line parameters. 735 kV Line Parameter Seq +, - Seq 0 Resistance (Ω/km) 0.01165 0.2676 Inductance (H/km) 0.8679e-3 3.008e-3 Capacitance (F/km) 13.41e-9 8.57e-9 The analyzed event was a monophasic solid fault at 200 km from bus S as is shown on Figure 2.6. The fault begins at 0.031 sec. after the simulation starts and the line is opened at 0.05 sec. after that. Both line ends are opened simultaneously. In order to make comparisons between records, the results are not shown in distance values (km), but referred to as percentage errors based on the total distances of the lines (%) as indicated in [18]. The fault distance was chosen to ensure that the incident and reflected wavefront don’t coincide when arriving at each line end and, therefore, they can be clearly distinguishable at the analysis, as shown in the Lattice diagram of Figure 2.7. In three-phase transmission lines, the traveling waves are coupled and a single wave velocity does not exist. In order to implement these methods in three-phase systems, 2.3. TRAVELING WAVE BASED FAULT LOCATION 43 Eq. Syst. S Eq. Syst. R R 500 km 200 km 300 km S Figure 2.6: Simulated power system model. S R (-) (-) (+) (-) (+) (-) (+) (-) Figure 2.7: Simulated fault Lattice diagram. the phase domain signals are first decomposed into their modal components [12]. In this study, all line models are assumed to be fully transposed, and therefore the well known Clarke’s constant and real transformation matrix is used: Smode =1 3  1 1 1 2−1−1 0√3−√3 Sphase (2.6) Where Sphase and Smode are the phase signal and mode signal components, respectively. Simulated records phase signals are first transformed into their modal components and the mode 2 is taken for analysis. The second mode (mode 2), also known as the aerial mode, is the most common mode used in this type of analysis since is present for any kind of fault. In order to illustrate the tests, Figure 2.8 and Figure 2.9 show the voltages and currents records for both line ends during the fault. As records show, the fault begins intentionally far from the wave peak and zero crossing, in order to achieve a higher break in the continuity of the medium as possible. Also, is possible to see how traveling waves appear in the phases without fault due to mutual coupling effect between phases. Currents from the S line-end were used for the analysis with spectrum estimation 44 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES method, and currents from both line ends were used for the analysis with wavelet method. Both methods are based on decomposing the fault records into the frequency components that exist in the signal. For this, the Fourier transform was used in the first method, and wavelet transform in the second method. 1.5 1 2 0.5 0 -0.5 -1 -1.5 0 -2 0.02 0.04 0.06 0.08 0.1 0.12 Time [sec.] Voltage [p.u.] 0 0.02 0.04 0.06 0.08 0.1 0.12 Time [sec.] 8 6 10 4 2 0 -2 -4 Current [p.u.] Figure 2.8: Voltages and currents signal for the S line-end. 1.5 1 2 0.5 0 -0.5 -1 -1.5 0 -2 0.02 0.04 0.06 0.08 0.1 0.12 Time [sec.] Voltage [p.u.] 0 0.02 0.04 0.06 0.08 0.1 0.12 Time [sec.] 8 6 4 2 0 -2 -4 Current [p.u.] Figure 2.9: Voltages and currents signal for the R line-end. With the Fourier transform is possible to see the different frequencies that compose the signal. Knowing which is the predominant frequency in the signal (besides the fundamental frequency), the time that takes the wavefront to travel from the line end to the fault point can be calculated and then the fault location is known. With the wavelet transform, is possible to know not only the signal frequency components but also at what time they appear. Comparing these times with those of the opposite extreme, is easy to know the fault location. Figure 2.10 and Figure 2.11 show two typical results obtained with each method for the same fault. These methods are applied repeatedly on the same fault, but using records with different sampling rate. The sensitivity analysis results of the methods against these variations are shown on the next section. Figure 2.12 shows the test results obtained with variations of the records sampling rate for the spectrum estimation and wavelet methods, and also shows the minimum theoretical error. All results are presented using the distance from the S line end as reference. 2.3. TRAVELING WAVE BASED FAULT LOCATION 45 0 50 100 150 200 250 300 350 400 450 500 0 100 200 300 400 500 600 700 800 900 Frequency (Hz) Figure 2.10: Fourier transform example for fault records. 200 400 600 800 1000 1200 D1 A1 Original Coefficients Time [msec.] Figure 2.11: Wavelet transform example for fault records. 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1 1.E+0 1.E+1 1.E+3 1.E+4 1.E+5 1.E+6 1.E+7 Spectrum Wavelet Minimum Frequency (Hz) Error (%) Figure 2.12: Records sampling rate variation test results. 52 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES Table 2.4: Impedance-based fault location methods summary. Reference One-end Two-ends Synchronized Unsynchronized Long line application Short line application Communication needed [20] l l l [21] l l l [22] l l l [23] l l l [28] l l l l [29] l l l l [30] l l l [31] l l l l [32] l l l l l [33] l l l l l [34] l l l l l [35] l l l l In order to evaluate this statement, a comparison of the results of two methods is presented. For the test, two of the most widely accepted methods were used, the one-end method [20], and the two-ends method [28]. In the analysis of asymmetrical faults where the sequence networks are used, the most common errors in transmission lines models are found in the ground conductivity (which are reflected in the zero-sequence network), and in differences in the conductors arrangement along the line (which are reflected in the positive and negative sequence networks). To be able to study the sensitivity to these kinds of errors, two different faults were analyzed. First, a monophasic fault, where the zero-sequence parameters were varied, and then a biphasic fault, where the positive and negative sequence parameters were varied. The records used for the tests come from actual faults occurred in two overhead transmission lines, the monophasic fault record comes from a 765 kV line with 225 km, and the biphasic fault record comes from a 69 kV line with 11 km. In order to make comparisons between them, the results are not shown in distance values (km), but referred to percentage errors based on the total distances of the lines (%) as indicated 2.4. IMPEDANCE-BASED FAULT LOCATION 53 in [18]. To facilitate the comparison, faults with some common characteristics were required: in both cases the fault was cleared quickly (between 3 and 4 cycles), also, in both cases the fault was located near the ”sender” end (the ”sender” and ”receiver” ends were determined with the pre-fault conditions of the line), the monophasic fault was located at 16.41% of the total length of the line and the biphasic one was at 14.91% of the total line length. The variations were made individually and over all parameters (resistance, inductance, and capacitance), for both the zero-sequence test and the positive and negative sequence test. In this test, the conductances of the lines were neglected. The variations were from -100% to 100% of the real values, i.e. each parameter varies from zero to twice the real value. In order to illustrate the tests made, Figure 2.14 and Figure 2.15 show the triphasic currents records for both ends of each fault. -100 -100 t [ms] t [ms] -50 -50 0 0 50 50 7 7 IA Source -1.724 kA IB Source 8.704 kA IC Source 1.087 kA IA Receiver 1.677 kA IB Receiver 2.181 kA IC Receiver -0.570 kA Figure 2.14: Triphasic currents for the monophasic fault. -200 -200 t [ms] t [ms] -150 -150 -100 -100 -50 -50 0 0 50 50 6 6 Ia Source -0.007 kA Ib Source -18.65 kA Ic Source 18.67 kA Ia Reciver 0.022 kA Ib Reciver -3.767 kA Ic Reciver 3.728 kA Figure 2.15: Triphasic currents for the biphasic fault. Figure 2.16a and Figure 2.16b show the test results obtained with variations of the zero-sequence parameters (monophasic fault), and positive and negative sequences 54 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES -10.0 -5.0 0.0 5.0 10.0 15.0 20.0 25.0 -100 -50 0 50 100 Inductance variation [%] -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 -100 -50 0 50 100 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 -100 -80 -60 -40 -20 0 20 40 60 80 100 One-end Two-end Resistance variation [%] Capacitance variation [%] Error [%]Error [%] Error [%] (a) Zero-sequence variation for the monophasic fault. -0.05 -0.03 -0.01 0.01 0.03 0.05 -100 -80 -60 -40 -20 0 20 40 60 80 100 One-end Two-end -10 40 90 140 190 240 -100 -80 -60 -40 -20 0 20 40 60 80 100 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 -100 -80 -60 -40 -20 0 20 40 60 80 100 Inductance variation [%] Resistance variation [%] Capacitance variation [%] Error [%]Error [%] Error [%] (b) Positive and negative sequence variation for the biphasic fault. Figure 2.16: Parameters variation test results. parameters (biphasic fault). All distances results are presented using the source end of each line as reference. In the first approach, is possible to observe that the one-end method has higher sensitivity to variations in positive and negative sequence parameters, while the twoends method is more sensitive to changes in zero-sequence parameters. Table 2.5 shows in more detail the range achieved by the errors of each method and in every sensitivity test. The results of the inductance variations are completely in line with the main statement, because the two-ends method proved to be less sensitive to the parameters variations of all sequence networks than the one-end method. In the case of resistance variations, the results do not confirm that statement, since the two-ends method proved to be more sensitive to the parameters variations of all sequence networks than the one-end method. This could be because, as mentioned 2.5. FINAL REMARKS 55 Table 2.5: Results range for the sensibility tests. aaaaa aResults One-end Two-ends Test aaaa aMax Min Max Min Seq. 0 Res. 0.077 -0.078 0.623 -1.070 Ind. 22.84 -6.216 8.687 -3.293 Cap. 0.038 -0.034 0.315 -0.315 Seq. +,- Res. 0.015 -0.015 0.645 -0.963 Ind. 238.97 -7.462 4.270 -0.049 Cap. 0.00 0.00 0.002 -0.002 above, the method described in [20] uses only the imaginary part of the equations that describe the fault’s resistance, whereas the method described in [28] uses the entire model line in the final resolution. For this reason, is expected that the twoends method is more sensitive to changes in the real components of the line model. In any case, these results are not alarming since errors obtained varying the resistances are always very small compared with those obtained varying the inductances. In the case of capacitance variations, the errors obtained were very small compared to the other two tests. Therefore, is noted that these methods do not have any sensitivity to changes in these parameters and this type of lines. But these results could be different if underground lines era analyzed, where the capacitance is more significant. 2.5 Final Remarks This chapter presents the different methods that exist for fault location, as well as different types of tests are performed using these methods. A comparative analysis is done between two of the traveling wave based methods. The analysis is based on the statement that the methods that use information from both line-ends are more robust than methods that use information from only one line-end. Although in general, this statement is well founded, this analysis showed that is not absolutely correct since the two-ends method proved to be more sensitive to the variations that the one-end method. In any case, these results are not alarming since differences between errors are very small, and also the two-ends methods have better results at higher sample rates which are the most common used samples for the traveling wave fault location methods. Also a comparative analysis is done between two of the impedance-based methods in order to prove the general behavior of these type of methods, and the statement that the two-ends methods are more robust than the one-end methods because they 56 CHAPTER 2. FAULT LOCATION ANALYSIS FOR TRANSMISSION LINES are less sensitive to errors in the line parameters. Although in general this statement is well founded, this analysis showed that is not absolutely correct and in some cases needs to be clarified in order to avoid confusions. The objective of these tests is to deepen the understanding of the different methods by conducting comparisons between their performances, so as to observe their behavior and test the strengths and weaknesses of each method. The highlight of these tests is to show the importance of really knowing the different fault location methods in order to select the one that best suits the available resources. As section 1.7 explained, the chapters of this work don’t follow a linear order because the research of different fields of knowledge was required for its development. After the review of the different fault location methods, the next chapter will address the problem of transmission lines modeling. The transmission line models are an integral part in fault location methods based on impedance measurement. The line models are the framework used for calculating the line’s impedance, from the voltage and current measurements obtained at the line-ends addressed in section 2.4. BIBLIOGRAPHY CHAPTER 2 57 Bibliography Chapter 2 [1] P. Gale, J. Stokoe, and P. Crossley, “Practical experience with travelling wave fault locators on scottish power’s 275 & 400 kV transmission system,” in Sixth International Conference on Developments in Power System Protection, pp. 192–196, 1997. [2] L. de Andrade and R. Guanipa, “Costs reduction in attention to transmission lines faults using faults location equipment,” I Congreso Venezolano de Redes y Energ´ıa El´ectrica, 2007. [3] H. L. Clark, An Elementary Treatise on Electrical Measurement. London: E. & F. N. Spon, 1868. [4] J. R. Carson, “Theory of the transient oscillations of electrical networks and transmission systems,” Transactions of the American Institute of Electrical Engineers, vol. XXXVIII, no. 1, pp. 345–427, 1919. [5] J. R. Carson, “Wave propagation in overhead wires with ground return,” Bell System Technical Journal, vol. 5, no. 4, pp. 539–554, 1926. [6] J. R¨ohrig, “Location of faulty places by measuring with cathode ray oscillographs,” Elektrotech. Zeits., vol. 8, pp. 241–242, 1931. [7] R. Stevens and T. Stringfield, “A transmission line fault locator using fault-generated surges,” Transactions of the American Institute of Electrical Engineers, vol. 67, no. 2, pp. 1168–1179, 1948. [8] L. Lewis, “Traveling wave relations applicable to power-system fault locators,” Transactions of the American Institute of Electrical Engineers, vol. 70, no. 2, pp. 1671– 1680, 1951. [9] M. Ando, E. O. Schweitzer, and R. A. Baker, “Development and field-data evaluation of single-end fault locator for two-thermal HVDC transmission lines part 1: Data collection system and field data,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-104, no. 12, pp. 3524–3530, 1985. [10] M. Ando, E. O. Schweitzer, and R. A. Baker, “Development and field-data evaluation of single-end fault locator for two-terminal HVDC transmission lines-part 2 : Algorithm and evaluation,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-104, no. 12, pp. 3531–3537, 1985. [11] M. Dewe, S. Sankar, and J. Arrillaga, “The application of satellite time references to HVDC fault location,” IEEE Transactions on Power Delivery, vol. 8, no. 3, pp. 1295– 1302, 1993. [12] F. Magnago and A. Abur, “Fault location using wavelets,” IEEE Transactions on Power Delivery, vol. 13, no. 4, pp. 1475–1480, 1998. [13] P. Murthy, J. Amarnath, S. Kamakshiah, and B. Singh, “Wavelet transform approach for detection and location of faults in hvdc system,” in IEEE Region 10 and the Third international Conference on Industrial and Information Systems, pp. 1–6, 2008. 58 BIBLIOGRAPHY CHAPTER 2 [14] C. Ping, X. Bingyin, and L. Jing, “A traveling wave based fault locating system for HVDC transmission lines,” in International Conference on Power System Technology, pp. 1–4, 2006. [15] K. Young-Jin, K. Sang-Hee, L. Dong-Gyu, and K. Hyung-Kyu, “Fault location algorithm based on cross correlation method for HVDC cable lines,” in IET 9th International Conference on Developments in Power System Protection, pp. 360–364, 2008. [16] T. Kawady and J. Stenzel, “Investigation of practical problems for digital fault location algorithms based on EMTP simulation,” in IEEE/PES Transmission and Distribution Conference and Exhibition, vol. 1, pp. 118–123 vol.1, 2002. [17] E. Styvaktakis, M. Bollen, and I. Gu, “A fault location technique using high frequency fault clearing transients,” IEEE Power Engineering Review, vol. 19, no. 5, pp. 58–60, 1999. [18] IEEE, “IEEE guide for determining fault location on AC transmission and distribution lines,” IEEE Std C37.114-2004, pp. 1–36, June 2005. [19] L. Crichton, “The distance relay for automatically sectionalizing electrical net works,” Transactions of the American Institute of Electrical Engineers, vol. XLII, pp. 527–537, 1923. [20] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, and T. Sakaguchi, “A new algorithm of an accurate fault location for EHV/UHV transmission lines: Part I - Fourier transformation method,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-100, no. 3, p. 8, 1981. [21] T. Takagi, Y. Yamakoshi, J. Baba, K. Uemura, and T. Sakaguchi, “A new algorithm of an accurate fault location for EHV/UHV transmission lines: Part II - Laplace transform method,” IEEE Transactions on Power Apparatus and Systems,, vol. PAS-101, no. 3, pp. 564–573, 1982. [22] L. Eriksson, M. Saha, and G. Rockefeller, “An accurate fault locator with compensation for apparent reactance in the fault resistance resulting from remore-end infeed,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-104, no. 2, pp. 423–436, 1985. [23] M. Djuric, Z. Radojevic, and V. Terzija, “Distance protection and fault location utilizing only phase current phasors,” IEEE Transactions on Power Delivery, vol. 13, no. 4, pp. 1020–1026, 1998. [24] GE Multilin, “DDFR distributed digital fault recorder instruction manual,” 2011. [25] SEL Inc., “SEL-734 advanced metering system instruction manual,” tech. rep., Schweitzer Engineering Laboratories, Inc., 2010. [26] ABB Inc., REL 512 Line Protection and Breaker Control Terminal Instruction Booklet, vol. V. 2.31. PA, USA: Substation Automation and Protection Division, 2003. [27] Siemens, “SIMEAS R. digital fault and power quality recorder manual,” tech. rep., Siemens AG, 2011. BIBLIOGRAPHY CHAPTER 2 59 [28] A. Johns and S. Jamali, “Accurate fault location technique for power transmission lines,” IEEE Proceedings Generation, Transmission and Distribution, vol. 137, no. 6, pp. 395–402, 1990. [29] A. Girgis, D. Hart, and W. Peterson, “A new fault location technique for twoand three-terminal lines,” IEEE Transactions on Power Delivery, vol. 7, no. 1, pp. 98–107, 1992. [30] D. Novosel, D. Hart, E. Udren, and J. Garitty, “Unsynchronized two-terminal fault location estimation,” IEEE Transactions on Power Delivery, vol. 11, no. 1, pp. 130– 138, 1996. [31] J. Izykowski, E. Rosolowski, P. Balcerek, M. Fulczyk, and M. Saha, “Accurate noniterative fault location algorithm utilizing two-end unsynchronized measurements,” IEEE Transactions on Power Delivery, vol. 25, no. 1, pp. 72–80, 2010. [32] M. Kezunovic and B. Perunicic, “Automated transmission line fault analysis using synchronized sampling at two ends,” IEEE Transactions on Power Systems, vol. 11, no. 1, pp. 441–447, 1996. [33] J. Joe-Air, Y. Jun-Zhe, L. Ying-Hong, L. Chih-Wen, and M. Jih-Chen, “An adaptive PMU based fault detection/location technique for transmission lines. I. theory and algorithms,” IEEE Transactions on Power Delivery, vol. 15, no. 2, pp. 486–493, 2000. [34] S. Brahma and A. Girgis, “Fault location on a transmission line using synchronized voltage measurements,” IEEE Transactions on Power Delivery, vol. 19, no. 4, pp. 1619– 1622, 2004. [35] G. Preston, Z. Radojevic, C. Kim, and V. Terzija, “New settings-free fault location algorithm based on synchronised sampling,” IET Generation, Transmission & Distribution, vol. 5, no. 3, pp. 376–383, 2011. [36] M. Saha, K. Wikstrom, J. Izykowski, and E. Rosolowski, “New accurate fault location algorithm for parallel lines,” in Seventh International Conference on Developments in Power System Protection, pp. 407–410, 1999. [37] H. Jung, Y. Park, M. Han, C. Lee, H. Park, and M. Shin, “Novel technique for fault location estimation on parallel transmission lines using wavelet,” International Journal of Electrical Power & Energy Systems, vol. 29, no. 1, pp. 76–82, 2007. [38] J. Izykowski and E. Rosolowski, “Accurate non-iterative fault location algorithm for three-terminal line,” in International Conference on Electrical and Electronics Engineering, pp. I–154–I–158, 2009. [39] L. de Andrade and E. Sorrentino, “Fault locator for parallel multi-terminal transmission lines with sources only at two terminals,” II Congreso Venezolano de Redes y Energ´ıa El´ectrica, p. 7, 2009. [40] G. Manassero, E. Senger, R. Nakagomi, E. Pellini, and E. Rodrigues, “Fault-location system for multiterminal transmission lines,” IEEE Transactions on Power Delivery, vol. 25, no. 3, pp. 1418–1426, 2010. 60 BIBLIOGRAPHY CHAPTER 2 [41] K. Sang-Hee, A. Yong-Jin, K. Yong-Cheol, and N. Soon-Ryul, “A fault location algorithm based on circuit analysis for untransposed parallel transmission lines,” IEEE Transactions on Power Delivery, vol. 24, no. 4, pp. 1850–1856, 2009. [42] C. Apostolopoulos and G. Korres, “A novel algorithm for locating faults on transposed/untransposed transmission lines without utilizing line parameters,” IEEE Transactions on Power Delivery, vol. 25, no. 4, pp. 2328–2338, 2010. [43] M. Saha, J. Izykowski, E. Rosolowski, and B. Kasztenny, “A new accurate fault locating algorithm for series compensated lines,” IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 789–797, 1999. [44] G. Preston, Z. Radojevic, and V. Terzija, “Novel parameter-free fault location algorithm for transmission lines with series compensation,” in 10th IET International Conference on Developments in Power System Protection. Managing the Change., pp. 1–5, 2010. [45] G. Mahdi and S. Javad, “An accurate and noniterative fault location algorithm for transmission lines in the presence of shunt connected FACTS devices,” IEEE Transactions on Power Delivery, 2011. [46] L. Yuan and M. Kezunovic, “Optimal estimate of transmission line fault location considering measurement errors,” IEEE Transactions on Power Delivery, vol. 22, no. 3, pp. 1335–1341, 2007. Chapter 3 Transmission Line Model No general model for arbitrary wave shapes or combinations of line parameters is known. Exact models have been produced for only a few special cases. In other cases, approximate solution procedures have been proposed. Consequently, there are many ways of obtaining a solution available [1]. Each has its own advantages and disadvantages relative to the others depending on the particular transmission system being analyzed and the nature of the signals being considered. A survey of these techniques, together with their advantages and disadvantages, will assist in appreciating how a particular transmission problem might be solved best. In general, transmission line models can be classified according to Figure 3.1. Transmission Line Models                                                      Steady State                Time-Domain Frequency-Domain          Single Line Multiple Line Lossless Line Lossy Line Transient State                              Time-Domain                          Lattice Model Finite Differences Operational Methods Bergeron’s Model          Single Line Multiple Line Fundamental Frequency Frequency Dependent Frequency-domain Figure 3.1: Classification of transmission line models It will be seen that solution techniques have been classified into two types. Frequencydomain and time-domain. Frequency-domain solutions are those in which time is removed as an independent variable from both the network equations and the initial 68 CHAPTER 3. TRANSMISSION LINE MODEL A= 1 + ZY 2 B=Z C=Y(1 + ZY 4) D= 1 + ZY 2 Note that here is also true that A=Dand AD −BC = 1. 3.3 Time-Domain Model This section describes general solution methods for finding the time responses of electromagnetic transients in arbitrary single or multiphase networks with lumped and distributed parameters. The time-domain model most widely used for transient analysis was proposed by Dommel in 1969 [4], and is based in solving equations (3.3) and (3.4) by neglecting the losses and using the method of characteristics. 3.3.1 Bergeron’s Model The method of characteristics is a mathematical method for solving hyperbolic partial differential equations and was originally given by Allievi in 1902 [5], and later developed by Schnyder in 1929[6], Angus in 1935 [7], and Bergeron in 1928 [8], where it was used as a graphical method of calculating transients in penstocks. Bergeron developed a particular proficiency with the graphical method and published a number of articles in the 1930’s. His applications range over a wide variety of topics including the propagation of surges on electrical transmission lines. An English translation of his work was published in 1961, and for this reason the model is called the Bergeron’s model, but it found application in a power system transients program by Dommel. It has generally been assumed that the method has application only for lossless transmission systems, this being stated as late as 1967 [9]. All the examples cited above have concerned lossless transmission systems. But Dommel used the method for a losses line, first using a lossless transmission line, and then giving a representation of a lumped losses element in the model. Equations (3.3) and (3.4) are not directly integrable. Therefore, losses will be neglected at this stage, i.e., R= 0 and G= 0. Consider a lossless line with inductance Land capacitance Cper length unit, then at a point xalong the line, voltage and current are related by: ∂V (x, t) ∂x =−L∂I(x, t) ∂t (3.25) ∂I(x, t) ∂x =−C∂V (x, t) ∂t (3.26) 3.3. TIME-DOMAIN MODEL 69 The method of characteristics to solve these equations is based on a transformation in the x−tplane which accomplishes the conversion of (3.25) and (3.26) into a pair of ordinary differential equations. Each of these two ordinary differential equations holds true along a different family of characteristic curves in the x−tplane, one family corresponds to the forward or incident wave, and the other to the backward or reflected wave. Then, the general solution, first given by d’Alembert[10] is: V(x, t) = Zo(f1(x−vt)−f2(x+vt)) (3.27) I(x, t) = f1(x−vt) + f2(x+vt) (3.28) with f1(x−vt) and f2(x+vt) being arbitrary functions of the variables (x−vt) and (x+vt). The physical interpretation of f1(x−vt) is a wave traveling at velocity vin a forward direction, and of f2(x+vt) is a wave traveling in a backward direction. Zoin (3.27) is the surge impedance (Zo=√L C), vis the wave’s velocity (v=1 √LC ). Multiplying (3.28) by Zo, and adding it to or subtracting it from (3.27) gives: V(x, t) + ZoI(x, t) = 2Zof1(x−vt) (3.29) V(x, t)−ZoI(x, t) = −2Zof2(x+vt) (3.30) Note that in (3.29) the expression (V(x, t) + ZoI(x, t)) is constant when (x−vt) is constant, and in (3.30) (V(x, t)−ZoI(x, t)) is constant when (x+vt) is constant. The expressions (x−vt)=constant and (x+vt)=constant are called the characteristics of the differential equations. The significance of (4) may be visualized in the following way: let a fictitious observer travel along the line in a forward direction at velocity v, then (x−vt) and, consequently, (V(x, t)+ZoI(x, t)) along the line will be constant for him. If the travel time to get from one end of the line to the other is τ=l/v =l√LC (lis the line’s length), then the expression (V(x, t) + ZoI(x, t)) encountered by the observer when he leaves node Sat time t−τmust still be the same when he arrives at node Rat time t, that is: VR(t−τ) + ZoIR,S(t−τ) = VS(t) + Zo(−IS,R(t)) (3.31) From this equation follows the simple two-port equation for IS,R IS,R(t) = 1 Zo VS(t) + IS(t−τ) IR,S(t) = 1 Zo VR(t) + IR(t−τ) (3.32) With equivalent current sources ISand IR, which are known at state tfrom the past state at time t−τ, 70 CHAPTER 3. TRANSMISSION LINE MODEL IS(t−τ) = −1 Zo VR(t−τ)−IR,S(t−τ) IR(t−τ) = −1 Zo VS(t−τ)−IS,R(t−τ) (3.33) Figure 3.5 shows the corresponding equivalent impedance network, which fully describes the lossless line at its terminals. Topologically, the terminals are not connected; the conditions at the other end are only seen indirectly and with a time delay τthrough the equivalent current sources I. ZoZo + + VS(t) IS,R(t) VR(t) IR,S(t) IS(t-τ) IR(t-τ) Figure 3.5: Equivalent impedance network for a lossless line. The simplicity of the method of characteristics rests on the fact that losses are neglected. This simplicity also holds true for the line without distortion, where R/L = G/C; the only difference is in computing IS(and analogous IR): IS(t−τ) = e−(R L)τ(−1 Zo VR(t−τ)−IR,S(t−τ)) (3.34) Unfortunately, power lines are not distortionless, since Gis usually negligible (or a very complicated function of voltage if the corona effect is to be taken into account). The distributed series resistance with G= 0 can easily be approximated by treating the line as lossless, and adding lumped resistances at both ends. Such lumped resistances can be inserted in many places along the line when the total length is divided into many line sections. In its present form, resistance was lumped as RT/4 at both ends, and RT/2 at the middle of the line (RTis the total series resistance); under these assumptions the equivalent impedance network of Figure 3.5 is still valid and only the values change (ISanalogous to IR): IS(t−τ) = (1 + h 2)(−1 Zo VR(t−τ)−IR,S(t−τ))+(1 + h 2)(−1 Zo VS(t−τ)−IS,R(t−τ)) (3.35) With h= (Zo−RT 4)/(Zo+RT 4) From equations 3.34 and 3.35 is possible to find a general solution for current at any point of the line (x), and at any time (t), but remembering that τis not for the entire line, i.e., τ=x/v, and also that e−(R L)τ≈1−Rx Zo+1 2(Rx Zo)2, then the current is: 3.3. TIME-DOMAIN MODEL 71 I(x, t) =(Zo+Rx 4)(VS(t−x/v)+(Zo+Rx 4)IS(t−x/v)) −(Zo−Rx 4) ·(VS(t+x/v)−(Zo−Rx 4)IS(t+x/v)) + Rx 2(1 + Rx 4Zo)2(VS(t)−Rx 4IS(t)) (3.36) The same deduction can be applied to find an equation for the voltage at any point of the line (x), and at any time (t): V(x, t) =1 2(Zo−Rx 4 Zo )2(VS(t−x/v)+(Zo−Rx 4)IS(t−x/v)) +1 2(Zo+Rx 4 Zo )2(VS(t+x/v)−(Zo+Rx 4)IS(t+x/v)) −(Rx 4Zo )2VS(t)−Rx 4(Zo+Rx 4 Zo )(Zo−Rx 4 Zo )IS(t) (3.37) which reduces the equations for the case of a lossless line, where R= 0 and G= 0, thus the equation can be integrated directly. Then lumped resistance is added in order to compensate the attenuation effect produced by losses. 3.3.2 Other Approximations Directly in time-domain some solutions have been developed, reducing the generality of the specifications, i.e., assuming that some parameters R, L, G, and Care small enough to be negligible. This simplifies (3.3) and (3.4), and solutions for certain border conditions can be found. These reductions represent specific applications of the transmission line. One of these approximations is L= 0 and G= 0 to describe underground cables. This type of approach is widely used to model systems of low frequency or DC [11]. Another solution is given in [9] which reduces the equations for the case of a lossless line, where R= 0 and G= 0, thus the equation can be integrated directly. The solution provides a useful model in time-domain, but is limited to short lines or short segments of long lines that can be approximated to models with small loss. Other solution is based on starting with the frequency-domain model to see the effect that different frequencies have in the line parameters and transfer it to time-domain doing some approximations [12, 13]. This approach results in a time-domain model equivalent to [9] but that can be used for studies that require frequencies other than the fundamental to be represented. Works for transmission line modeling in time-domain that do not apply simplifications to (3.3) and (3.4) have also been proposed, in order to find a direct solution to the problem. These works propose the use of different numerical methods for 72 CHAPTER 3. TRANSMISSION LINE MODEL solving the differential equation. Like using π-circuits [14], the modal method [15], the finite difference method (FDTD) [16], the finite element method [17], the timestep integration method [18] and others. All these works bring useful transmission lines models, but all these resolution methods require, in a greater or lesser extent, numerical approximations for solving the differential equation. This compromises in one way or another, the ability of models to accurately describe the transmission lines behavior. Other methods for transmission lines modeling based on traveling wave theory have been proposed, as in [19] who describes a model which is an extension of the Lattice diagram solution widely used for graphical solution of simple distributed-constant networks. In this method, the voltage and current signals are calculated as the sum of the different incident and reflected waves in each point of the line, and which are obtained with the wave’s velocity (vt) and the reflection’s coefficient (Γ). Finite difference approximations to derivatives or integrals lead to formulas from which accurate solutions are possible, but from which exact solutions can never be obtained. Consequently, for this case they have little to offer in comparison with the three previous solution techniques. They are however finding application in the general lossy transmission line case, particularly for multiple circuit transmission lines. Multiple circuit transmission lines can be handled as for steady state sinusoidal frequencies. Modal components are mostly used. For each frequency is carried out the transformation to modal components, the component solutions, and the inverse transformation . Unfortunately the transformation to modal components is usually frequency dependent. Consequently, a different transformation must be found for each component’s frequency. A few combinations of line parameters enable transformations to be found that are frequency invariant. 3.4 Final Remarks One feature revealed by this section is the abundance of simple and exact techniques available for solution of the lossless transmission problem. Another feature revealed by this section is the lack of any simple technique to handle the general lossy transmission problem. For this problem, solution in the frequency-domain requires numerical inverse transformation and sometimes numerical forward transformation. Solution in the time-domain requires calculation at many points. Both frequency and time-domain solutions can require the storage of large amounts of information and neither yield an exact solution. Thus, it’s common to use a lossless transmission line representation to reduce to workable proportions the complexity of problems involving traveling waves in power systems. Since power system transmission lines belong to the general lossy category, this represents a fairly rough approximation, and as power system voltage levels has increased, a need for more accurate representation has become apparent. Typically transient, like power system’s faults, involves non-linear circuit elements, changing system topology, and discontinuous signals. These are inherently more easily 3.4. FINAL REMARKS 73 handled by time-domain formulations. Frequency-domain methods are more suited to the solution of linear problems. Problems where non-linearities can be considered to be composed of discontinuous linear segments can be solved using frequency-domain methods, but at the expense of increased computational effort. Time-domain methods of solution fall into two categories. In the first, voltage and current increments are propagated throughout the system, these are the superpositionbased techniques (Lattice method). In the second, actual system voltages and currents are used directly (Bergeron’s model). The Bergeron’s Model is the most simple time-domain model and is used as a foundation for the most widely used models in power systems simulations. For more than 40 years, Bergeron’s Model has provided a widely accepted solution for line modeling. But in the last 40 years, electrical systems have changed greatly. The markets aperture and the introduction of renewable energy, have led systems to operate at the limit of safety. Under these conditions, it is increasingly important the accurate prediction of the system’s behavior. This justifies the search of more accurate line models. This approach will be further investigated in Chapter 4, in an attempt to find a accurate representation of a lossy transmission line in order to implement it in a impedance-based fault location method. 74 BIBLIOGRAPHY CHAPTER 3 Bibliography Chapter 3 [1] A. Ametani, “The history of transient analysis and the recent trend,” IEEJ Transactions on Electrical and Electronic Engineering, vol. 2, no. 5, pp. 497–503, 2007. [2] W. Thomson (Lord Kelvin), “On the theory of the electric telegraph,” Mathematical and Physical Papers, Cambridge Unv. Press, vol. 2, pp. 61–76, 1884. [3] O. Heaviside, “General solution of maxwell’s electromagnetic equations in a homogeneous isotropic medium, especially in regard to the derivation of special solutions and the formulae for plane waves,” Philosophical Magazine and Journal of Science, vol. 27, no. 164, p. 20, 1889. [4] H. W. Dommel, “Digital computer solution of electromagnetic transients in single-and multiphase networks,” IEEE Transactions on Power Apparatus and Systems, vol. PAS88, no. 4, pp. 388–399, 1969. [5] Allievi, “Teoria generale del moto perturbato dell acqua nei tubi in pressione,” Annali della Societ´a degli Ingegneri ed Architette Italiani, 1902. [6] S. Schelkunoff, “Druckst¨osse in pumpensteigleitungen,” Schweiz Bauzig, vol. 94, pp. 271–273 and 283–286, 1929. [7] W. Angus, “Simple graphical solution for pressure risc in pipes and pump discharge lines,” Journal of Eng. Institute of Canada, vol. 18, pp. 72–81, 1935. [8] L. Bergeron, Water Hammer in Hydraulics and Wave Surges in Electricity. New York: Wiley, 1961. [9] F. J. Branin, “Transient analysis of lossless transmission lines,” Proceedings of the IEEE, vol. 55, no. 11, pp. 2012–2013, 1967. [10] J. d’Alembert, “Recherches sur la courbe que forme une corde tendu¨e mise en vibration,” Histoire de l’acad´emie royale des sciences et belles lettres de Berlin, vol. 3, pp. 214–249, 1747. [11] A. Heaton and A. Issa, “Transient response of crossbonded cable systems,” Proceedings of the Institution of Electrical Engineers, vol. 117, no. 3, pp. 578–586, 1970. [12] J. Marti, “Accuarte modelling of frequency-dependent transmission lines in electromagnetic transient simulations,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-101, no. 1, pp. 147–157, 1982. [13] J. Marti, L. Marti, and H. W. Dommel, “Transmission line models for steady-state and transients analysis,” in Joint International Power Conference Athens Power Tech, vol. 2, pp. 744–750, 1993. [14] H. W. Dommel, EMTP Theory Book. Vancouver, Canada: Microtran Power System Analysis Corporation, 2th ed., 1992. BIBLIOGRAPHY CHAPTER 3 75 [15] J. Faria, “A new generalized modal analysis theory for nonuniform multiconductor transmission lines,” IEEE Transactions on Power Systems, vol. 19, no. 2, pp. 926–933, 2004. [16] P. Trakadas and C. Capsalis, “Validation of a modified FDTD method on nonuniform transmission lines,” Progress In Electromagnetics Research, no. PIER 31, pp. 311–329, 2001. [17] R. Lucic, I. Juric-Grgic, and V. Jovic, “FEM analysis of electromagnetic transients in linear networks,” European Transactions on Electrical Power, vol. 19, no. 6, pp. 890– 897, 2009. [18] M. Tang and J. Mao, “Transient analysis of lossy nonuniform transmission lines using a time-step integration method,” Progress In Electromagnetics Research, vol. 69, pp. 257– 266, 2007. [19] L. Barthold and G. Carter, “Digital traveling-wave solutions i-single-phase equivalents,” Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers, vol. 80, no. 3, pp. 812–818, 1961. 76 BIBLIOGRAPHY CHAPTER 3 Chapter 4 Proposal for Impedance-Based Fault Location for HVDC All currently available commercial equipment to locate faults in HVDC lines use methods based on traveling wave1. In general, these methods are based on calculating the time that takes an electromagnetic pulse to travel through the line under investigation. Most accurate methods use special equipment installed on one end of the line and send an electromagnetic pulse. This pulse travels without interruption throughout the line until it reaches the location where the fault is reflected, and then returns to the starting point. Knowing the time that takes the pulse to make the entire route and its speed, is easy to calculate the distance traveled finding the location of the fault. These methods require that the line is de-energized and only apply to permanent failures, and they require personnel and equipment in the field. Other methods of easier application, use for the analysis the data obtained during the occurrence of the fault. When a fault starts, it generates pulses that travel throughout the line, these pulses are recorded by measuring devices located on both ends of the line. The CT’s and VT’s of a HVDC system are usually installed behind an harmonic filtering circuit and their outputs can’t be used to detect traveling waves from the line. The transient voltage must be acquired by measuring the transient current through the earth wire of the surge using a coupling capacitor and an external transformer. The records can be decomposed into its waves with different frequencies to find the high frequency wave generated by the fault. With this information, and knowing the velocity of the wave, it’s possible to calculate the fault’s location2. These methods are faster and simpler to implement than those that require personnel and special equipment in the field. It can also be used with the line energized and in the analysis of transitory faults. But the great weakness of these methods is that not all faults produce pulses easily identifiable in the records. If the pulse produced by the fault 1The main manufacturers of these equipments are Manitoba HVDC Centre (https://hvdc.ca/), and ABB (www.abb.com/) 2This issue was addressed in more detail in Section 2.3 84 CHAPTER 4. PROPOSAL FOR IMPEDANCE-BASED FAULT LOCATION FOR HVDC I=−V1 e−(R L+G C)t(e−(R L+G C)x√LC +RC LG ) e−(R L+G C)t(e−(R L+G C)x√LC −e(R L+G C)x√LC ) sinh(xγRG) ZRG +I1e−(R L+G C)t(e−(R L+G C)x√LC −1) e−(R L+G C)t(e−(R L+G C)x√LC −e(R L+G C)x√LC )cosh(xγRG) +V2 e−(R L+G C)t(e(R L+G C)x√LC +RC LG ) e−(R L+G C)t(e−(R L+G C)x√LC −e(R L+G C)x√LC ) sinh(xγRG) ZRG −I2e−(R L+G C)t(e(R L+G C)x√LC −1) e−(R L+G C)t(e−(R L+G C)x√LC −e(R L+G C)x√LC )cosh(xγRG) (4.18) The expression e−(R L+G C)tis canceled, and the equation’s dividend can be expressed as follows: e−(R L+G C)x√LC −e(R L+G C)x√LC =−2 sinh(( R ZLC +GZLC)x) So, (4.17) and (4.18) are simplified as follows: V=−V1e−(R ZLC +GZLC )x −1 2 sinh(( R ZLC +GZLC )x)cosh(xγRG) +I1 e−(R ZLC +GZLC )x+LG RC 2 sinh(( R ZLC +GZLC )x)ZRG sinh(xγRG) +V2e(R ZLC +GZLC )x −1 2 sinh(( R ZLC +GZLC )x)cosh(xγRG) −I2 e(R ZLC +GZLC )x+LG RC 2 sinh(( R ZLC +GZLC )x)ZRG sinh(xγRG) (4.19) I=V1 e−(R ZLC +GZLC )x+RC LG 2 sinh(( R ZLC +GZLC )x) sinh(xγRG) ZRG −I1e−(R ZLC +GZLC )x −1 2 sinh(( R ZLC +GZLC )x)cosh(xγRG) −V2 e(R ZLC +GZLC )x+RC LG 2 sinh(( R ZLC +GZLC )x) sinh(xγRG) ZRG +I2e(R ZLC +GZLC )x −1 2 sinh(( R ZLC +GZLC )x)cosh(xγRG) (4.20) Finally, the solutions in (4.19) and (4.20) can be expressed in matrix form: [V I]=[A1B1 C1D1 A2B2 C2D2]    V1 I1 V2 I2    (4.21) 4.1. TIME-DOMAIN DISTRIBUTED PARAMETERS TRANSMISSION LINE MODEL 85 Where A1,B1,C1,D1,A2,B2,C2, and D2are: A1=−e−(R ZLC +GZLC )x−1 2 sinh(( R ZLC +GZLC)x)cosh(xγRG) B1=e−(R ZLC +GZLC )x+LG RC 2 sinh(( R ZLC +GZLC)x)ZRG sinh(xγRG) C1=e−(R ZLC +GZLC )x+RC LG 2 sinh(( R ZLC +GZLC)x) sinh(xγRG) ZRG D1=−e−(R ZLC +GZLC )x−1 2 sinh(( R ZLC +GZLC)x)cosh(xγRG) A2=e(R ZLC +GZLC )x−1 2 sinh(( R ZLC +GZLC)x)cosh(xγRG) B2=−e(R ZLC +GZLC )x+LG RC 2 sinh(( R ZLC +GZLC)x)ZRG sinh(xγRG) C2=−e(R ZLC +GZLC )x+RC LG 2 sinh(( R ZLC +GZLC)x) sinh(xγRG) ZRG D2=e(R ZLC +GZLC )x−1 2 sinh(( R ZLC +GZLC)x)cosh(xγRG) 4.1.1.2 Model Analysis As (4.21) shows, the results for (4.1) and (4.2) have the form f(x, t) = f1(x, t1) + f2(x, t2) which are exactly the results predicted by d’Alembert’s method [7], who first provides a solution to the wave propagation, and then was applied for transient phenomena transmission line analysis [8–11]. At first glance, it seems that the elements A1,B1,C1,D1,A2,B2,C2, and D2are not time-dependent because of the canceling of e−(R L+G C)tin (4.17), and (4.18). But is necessary to remember that x√LC is a time measurement and describes the time that takes the waves to travel from one terminal to the point xthroughout the line. The model deduced here has a structure similar to other well known time-domain models, such as the Bergeron’s model, but in a more complex way that provides greater accuracy. This is because approximations are not used to solve differential equations. In this model there are also factors similar to the propagation coefficient and characteristic impedance that are equivalent terms to the model in the frequencydomain [5, 6]. In the frequency-domain exists only one expression for the characteristic impedance because the frequency-domain provides the way to encompass the various 86 CHAPTER 4. PROPOSAL FOR IMPEDANCE-BASED FAULT LOCATION FOR HVDC line parameters as one impedance or admittance. But in this time-domain model are two characteristic impedances because the primary parameters come from different physical properties of the line. Since Rand Gdescribe the energy dissipation or line losses, they are included in a characteristic impedance, while Land Cdescribe the storage of energy in the fields around the line, they are encompassed by a second characteristic impedance. Other line models entirely deduced from time-domain, have also one of these two characteristic impedances, but no previous model has both terms. The presence of one or other characteristic impedance depends on the type of simplification used in the deduction of each different model. This model is able to take into account the full range of characteristic impedances and propagation coefficient, since ZLC ,ZRG, and γRG are not approximated values of characteristic impedances and propagation coefficient in frequency-domain, instead, they are time-domain decoupled representations of the characteristic impedances and propagation coefficient in frequency-domain. In order to illustrate the previous idea, the particular case of DC systems can be analyzed using (4.21). Thus, the terms where ZLC appears tend to decrease for long time intervals since it exists a limit to the energy stored in the fields of the line. Also, as the line losses are always present, the terms where ZRG appears do not decrease over time. This condition would be maintained as long as the voltages and currents do not vary. When variations occur in the system, the energy stored in the fields also changes, and the terms related to ZLC reappear, until the system is stabilized again in another operational point. Thus, the terms where ZLC appears can be associated with states where there are variations of voltage and current, while the terms where ZRG appears can be associated with the states where the voltage and current are constant. Take as example the case of a steady-state line: If steady-state phenomena are analyzed, some simplifications can be applied to the model, that is, when t→ ∞, then V1≈V2, and I1≈I2, therefore the matrix factors of (4.21) become: A1+A2= cosh(xγRG); B1+B2=−ZRG sinh(xγRG); C1+C2=−sinh(xγRG) ZRG ;D1+D2= cosh(xγRG) And (4.21) is simplified to: [V I]=[cosh(xγRG)−ZRG sinh(xγRG) −sinh(xγRG) ZRG cosh(xγRG)][V1 I1](4.22) Which is the typical transmission line model with distributed parameters presented in section 3.2.1 [5, 6]. Note that for this particular case, γRG =√RG and ZRG = √R/G, so the frequency system is ω= 0 which is an analysis for DC lines, and is consistent with the statement of section 4.1.1.2 concerning to the model’s application in low frequency conditions. It’s important to take into account that the term ”steadystate”, with conditions V1≈V2, and I1≈I2applies only to DC systems; for AC 4.1. TIME-DOMAIN DISTRIBUTED PARAMETERS TRANSMISSION LINE MODEL 87 systems the instantaneous values of voltages and currents are not equal over time. In AC systems ”steady-state” refers to the voltage and current phasors when they are stable over time, and not their instantaneous values. Also, if this steady-state approximation is applied to the Bergeron’s model derived in [8, 10], the result is: [V I]=[1−xR 0 1 ][V1 I1](4.23) Which is a simple model for short DC lines for steady-state approximation, but that is not used for long transmission lines. The following sections will be dedicated to a more detailed analysis of the model in order to validate its behavior. 4.1.2 Illustrative Examples In this section, actual transient-state records in COMTRADE format of different transmission lines will be analyzed with the model deduced here in order to validate the model’s behavior. The results will be compared to the Bergeron’s model which is the line model most widely used. Tests with records of AC and DC systems were carried out in order to show that the model is applicable to different types of lines. The tests consist in taking the voltage and current from transient event records of the sender line-end, and with this information, try to predict the events at the receiver end. This is done with the model deduced here and with the Bergeron’s model. Then, the results are compared with actual records of the receiver end in order to show which of the two models can predict more accurately the actual behavior of the lines. 4.1.2.1 AC Line Tests In order to use actual transient event records in COMTRADE format, two faults in AC lines were selected for this test. One fault in a long 765 kV line with 153 km, and another fault in a short 230 kV line with 44 km. The faults are single-phase and they occur outside the lines analyzed, i.e., faults occurred on the receiver end of parallel lines, so they are not fault records but contribution records to an external fault. The reason for selecting these records is to avoid the change in power flow that occurs in the receiver end. If the fault was within the line, this flow change would prevent the calculation of receiver end signals during the fault, and could not observe the model’s accuracy during different system conditions (pre-fault, fault, and post-fault). For AC systems testing, the signals instantaneous values were used. There are some circumstances that have not been taken into account that could affect the model’s accuracy during real faults analysis of an AC system. One is that the most common problems in real faults analysis are possible inaccuracies in the line’s parameters. In this test, any problems of this type would affect in the same way 88 CHAPTER 4. PROPOSAL FOR IMPEDANCE-BASED FAULT LOCATION FOR HVDC both models, and would not affect the final results because this test seeks to compare these results to each other. On the other hand, the model deduced here is based on a single-phase line, while AC systems are triphasic, and there are mutual effects from other phases; this problem is corrected using decoupled parameters, in other words, in order to implement this model in three-phase systems, the phase domain signals are first decomposed into their modal components [12]. In this study, all line models are assumed to be fully transposed, so a transformation matrix is used accordingly. Smode =1 3  1 1 1 2−1−1 0√3−√3 Sphase (4.24) Where Sphase, and Smode are the phase signal and mode signal components, respectively. Simulated records phase signals are first transformed into their modal components and the mode 2 is taken for analysis. The second mode (mode 2), also known as the aerial mode, is the most common mode used in this type of analysis since is present for any kind of fault. Tables 4.1 and 4.2 show the percentage of errors obtained when comparing the results of both models with actual measured values. These errors are in percentages (%) based on the nominal values of each line. They are an average of the instantaneous values of each stage that make up the records. Table 4.1: Test average errors with 765 kV line records. Voltage Error (%) Current Error (%) BM DM BM DM Pre-fault 12.541 2.637 5.298 2.470 Fault 14.506 3.061 6.502 3.960 Post-fault 12.072 3.695 5.788 3.333 Table 4.2: Test average errors with 230 kV line records. Voltage Error (%) Current Error (%) BM DM BM DM Pre-fault 1.492 1.480 3.139 3.106 Fault 0.730 0.727 2.771 2.693 Post-fault 1.360 1.345 3.079 3.041 4.1. TIME-DOMAIN DISTRIBUTED PARAMETERS TRANSMISSION LINE MODEL 89 Also, in order to illustrate the tests, Figure 4.2 and 4.3 are the results of voltage and current in the faulted phase of the records analyzed, these graphics show the results obtained with both models superimposed on the receiver end of the actual records. -700 -500 -300 -100 100 300 500 700 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Voltage (kV) (a) -4 -3 -2 -1 0 1 2 3 4 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 Record BM DM Current (kA) (b) Figure 4.2: 765kV line real record compared with Bergeron’s model (BM) and with the developed model (DM). (a) Voltage (b) Current. The largest errors were obtained in long line tests using the Bergeron’s model. In this test, the model presented here showed to be more accurate because it is better adapted for the modeling of long lines. In the short line test, the results obtained with both models are similar and they are more precise than in the long line test. This is because the approximations used in Bergeron’s model apply better to this type of line than with long lines. Even so, the model deduced here was slightly more accurate than Bergeron’s model. 90 CHAPTER 4. PROPOSAL FOR IMPEDANCE-BASED FAULT LOCATION FOR HVDC -200 -150 -100 -50 0 50 100 150 200 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 Voltage (kV) (a) -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 Record BM DM Current (kA) (b) Figure 4.3: 230kV line real record compared with Bergeron’s model (BM) and with the developed model (DM). (a) Voltage (b) Current. 4.1.2.2 DC Line Tests In the following item, simulated records of different DC lines are analyzed with the deduced model. The results are compared with Bergeron’s model. Like in the previous item, the tests consist in taking the voltage and current records of the line’s senderend, and with this information try to predict what is happening at the receiver-end. The results of both models are compared with the records produced to the receiverend in order to see which model can predict more accurately the actual behavior of the line. For this test, there were simulated transient events of two DC lines. A long line with 900 km and a short line with 150 km. The transient event used was the line being energized. The SimPowerSystem module of Simulink/MatLab R was used for the simulation with sample time steps of 0.5 ms. The resistance and inductance of each equivalent system were: 0.001 Ω, and 0.5 H respectively for the equivalent system S, and 30 Ω, and 0.5 H for the equivalent system R. Both lines were modeled using the 4.1. TIME-DOMAIN DISTRIBUTED PARAMETERS TRANSMISSION LINE MODEL 91 distributed parameter line model. Table 4.3 shows the transmission system data used in the line models.The energizing was simulated without any control so that the lines pass from zero to 1 p.u. (sender-end) in a natural way. This gives the opportunity to analyze two different system conditions: first, a transitional period when the line is energized, and then a steady-state period when the line reaches a value close to 1 p.u. (on the receiver end). Table 4.3: Transmission line parameters. Long Line Short Line Length (km) 900 150 Resistance (Ω/km) 0.011 0.011 Inductance (mH/km) 0.832 0.832 Capacitance (pF/km) 13.41 13.41 Conductance (pS/km) 27.668 27.668 Tables 4.4 and 4.5 show the percentage of errors obtained when comparing the results of both models with the receiver end values. They are an average of the instantaneous values of each period that make up the records. Table 4.4: Test average errors with the long line records. Voltage Error (%) Current Error (%) BM DM BM DM Transient 0.789 0.662 0.820 0.558 Steady-state 0.437 0.426 0.410 0.140 Table 4.5: Test average errors with the short line records. Voltage Error (%) Current Error (%) BM DM BM DM Transient 0.421 0.421 0.178 0.175 Steady-state 0.045 0.045 0.044 0.017 Also, in Figure 4.4 and 4.5 are presented the results for voltage and current for the lines energizing process, these graphics show the results obtained with both models superimposed on the receiver end records. 92 CHAPTER 4. PROPOSAL FOR IMPEDANCE-BASED FAULT LOCATION FOR HVDC -6 -4 -2 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Voltage (p.u.) (a) 0 0.2 0.4 0.6 0.8 1 1.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Record BM DM (b) Figure 4.4: Long DC line record compared with Bergeron’s model (BM) and with the developed model (DM). (a) Voltage (b) Current. The errors shown in tables 4.4 and 4.5 are much smaller than those of tables 4.1 and 4.2, because the tests with simulated data have a better control of the accuracy of the line parameters. In the long-line analysis (table 4.4), is possible to see that the model presented here is more accurate than Bergeron’s model. While in the short-line analysis (table 4.5) the results of both models are virtually identical in most cases. Like in the other test, this is because the approximations used in Bergeron’s model apply better to short lines than long lines. 4.1.3 Final Remarks of the Model This section presented the basics of a general transmission line and the development of the time-domain model for a single-phase line. Also, some analysis are presented using this time-domain transmission line model. This analysis increases the credibility of the presented model. This section also proved that this model is more accurate in describing the behavior of different transmission lines than Bergeron’s model. Since the most widely used models, like models with frequency-dependent parameters, use 4.1. TIME-DOMAIN DISTRIBUTED PARAMETERS TRANSMISSION LINE MODEL 93 -6 -4 -2 0 2 4 6 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Voltage (p.u.) (a) 0 0.2 0.4 0.6 0.8 1 1.2 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Record BM DM (b) Figure 4.5: Short DC line record compared with Bergeron’s model (BM) and with the developed model (DM). (a) Voltage (b) Current. an approach which retains the basic idea behind Bergeron’s model, this more detailed model could be used to improve other models. The added value of this model is the adoption of the distributed characteristics of all line parameters, which allows a more accurate description of the transmission line’s behavior in time-domain. These are some initial tests that were performed to validate the model. The objective of these tests is to deepen the understanding of the different models making comparisons between their performances, so as to observe their behavior before using the model into the fault location method. This section shows the deduction of a model for fundamental frequency parameters and single-phase, but the model can also be extended for cases with multi-conductor and frequency depended parameters. In this regard, the model has potential for improvements in areas such as electromagnetic transient simulation or any other analysis that requires a high accuracy in predicting the transmission lines behavior in time-domain. 100 BIBLIOGRAPHY CHAPTER 4 Bibliography Chapter 4 [1] S. Jiale, G. Shuping, S. Guobing, J. Zaibin, and K. Xiaoning, “A novel fault-location method for HVDC transmission lines,” IEEE Transactions on Power Delivery, vol. 25, no. 2, pp. 1203–1209, 2010. [2] W. G. on HVDC and FACTS, “HVDC projects listing,” IEEE Transmission and Distribution Committee, 2008. [3] J. R. Carson, “The rigorous and approximate theories of electrical transmission along wires,” Bell System Technical Journal, vol. 7, no. 1, pp. 11–25, 1928. [4] L. de Andrade, H. Leite, and T. Ponce de Le˜ao, “Time-domain distributed parameters transmission line model for transient analysis,” Progress In Electromagnetics Research B, vol. 53, pp. 25–46, 2013. [5] R. Chipman, Theory and Problems of Transmission Lines. Schaum’s outline series, McGraw-Hill, 1968. [6] P. Kundur, Power System Stability and Control. New York: McGraw Hill, 1993. [7] J. d’Alembert, “Recherches sur la courbe que forme une corde tendu¨e mise en vibration,” Histoire de l’acad´emie royale des sciences et belles lettres de Berlin, vol. 3, pp. 214–249, 1747. [8] F. J. Branin, “Transient analysis of lossless transmission lines,” Proceedings of the IEEE, vol. 55, no. 11, pp. 2012–2013, 1967. [9] H. W. Dommel, “Digital computer solution of electromagnetic transients in single-and multiphase networks,” IEEE Transactions on Power Apparatus and Systems, vol. PAS88, no. 4, pp. 388–399, 1969. [10] J. Marti, L. Marti, and H. W. Dommel, “Transmission line models for steady-state and transients analysis,” in Joint International Power Conference Athens Power Tech, vol. 2, pp. 744–750, 1993. [11] H. W. Dommel, EMTP Theory Book. Vancouver, Canada: Microtran Power System Analysis Corporation, 2th ed., 1992. [12] C. R. Paul, “A brief history of work in transmission lines for EMC applications,” IEEE Transactions on Electromagnetic Compatibility, vol. 49, no. 2, pp. 237–252, 2007. [13] D. Gilbert and I. Morrison, “A statistical method for detection of power system faults,” in Int. Conf. on Power System Transients, (Lisbon), pp. 288–293, 1995. [14] H. Zhengyou, F. Ling, L. Sheng, and B. Zhiqian, “Fault detection and classification in EHV transmission line based on wavelet singular entropy,” IEEE Transactions on Power Delivery, vol. 25, no. 4, pp. 2156–2163, 2010. [15] W. Kwon, G. Lee, Y. Park, M. Yoon, and M. Yoo, “High impedance fault detection utilizing incremental variance of normalized even order harmonic power,” IEEE Transactions on Power Delivery, vol. 6, no. 2, pp. 557–564, 1991. BIBLIOGRAPHY CHAPTER 4 101 [16] Q. jin Guo, H.-B. Yu, and A. dong Xu, “Modified morlet wavelet neural networks for fault detection,” in International Conference on Control and Automation, vol. 2, pp. 1209–1214, 2005. 102 BIBLIOGRAPHY CHAPTER 4 Chapter 5 Working Examples In this chapter, fault records of a HVDC line will be analyzed with the developed method in order to validate the method’s performance. The results will be compared with two commercially available methods: a single-end, and a two-ends method [1]. As said in Chapter 4, there is not commercially available HVDC impedance-based fault locator, but one work has been done to adapt this technology for use in HVDC [2] that uses the Bergeron’s model.The work developed here argues that the development of a specific line model for this method is advantageous because it increases the accuracy of the method, so the results of the method will also be compared to [2] to check the veracity of this argument. Tests with records of actual and simulated faults were carried out in order to prove the method with the highest number of possible variations. 5.1 Furnas HVDC Line The validation stage of the method developed in this work was carried out with assistance with the company Eletrobras Furnas. The company Eletrobras Furnas has a HVDC overhead line which was used as the basis for the tests shown in this chapter. 5.1.1 Furnas Transmission System Eletrobras Furnas (Furnas - Centrais El´etricas SA) is a Brazilian regional power utility and a major subsidiary of Eletrobras. The company has 15 hydroelectric and two thermoelectric plants with a total capacity of 10,050 MW which corresponds to 10% of Brazil’s electrical production. The company generates or transmits electricity to 51% of households in Brazil, and more than 40% of the nation’s electricity passes through their grid. The Eletrobras Furnas transmission system has 52 substations interconnected by 19.277,5 km of transmission lines with voltages of 138, 230, 345, 500, 750, and ±600 kV, which cross eight Brazilian states and the Federal District. Among the functions of 104 CHAPTER 5. WORKING EXAMPLES Eletrobras Furnas, stands out the operation and maintenance of Itaipu’s transmission system, composed of five transmission lines that cross 800 km from the state of Paran´a to S˜ao Paulo. This system consists of three 750 kV AC lines and two ±600 kV DC lines (see Figure 5.11). Figure 5.1: Eletrobras Furnas transmission system with focus in their HVDC lines. The HVDC lines that are part of Itaipu’s transmission system aim to solve the problem of differences in frequencies used by Brazil and Paraguay, to be able to connect the Brazilian transmission system with the Itaipu dam on the side that corresponds to Paraguay2. The HVDC system is composed of two dipole lines that go from the Foz do Igua¸cu rectifier station (in Paran´a State) to the Ibi´una inverter station (in S˜ao Paulo State) [3, 4]. The dipole 1 has a length of 792 km and the dipole 2 has a length of 816 km. The converters system are composed by thyristor bridge of 12-pulse. Each converter station comprises by two 300kV converters systems with 12 valves and 96 thyristors per valve. In Figure 5.2 is shown a top view of the Foz do Igua¸cu substation3, where its different components are emphasized. 5.1.2 The HVDC Fault Process When a fault is detected by the DC line’s fault protection, this protection orders the rectifier into inverter mode and this discharges the line effectively. This process is 1Photo source: Eletrobras Furnas’ website 2This HVDC line is also mentioned in Sec. 1.2.1 3Photo source: Google Maps 5.1. FURNAS HVDC LINE 105 Figure 5.2: Foz do Igua¸cu substation, 750 kV AC and ±600 kV DC. done by placing the thyristor’s trigger angle at values near to 180◦, so the converter temporarily reverses the polarity of the line’s voltage to extinguish the current and deionize the arc. The protection of the line is made at the converter level following two basic criteria: one by low level of DC voltage, and another by high-differential of DC voltage. The fault extinction is also achieved at the converters level, acting on the trips of the thyristors associated only to the faulted pole. In this way, is avoided the loss of the entire transmission capacity, and achieved only half of the loss. After some 80 - 100 ms, the line is charged again by the rectifier. If the fault was intermittent, then normally the line can support the voltage and the power transmission continues. Full power is then resorted in about 200 ms after the fault. But if the fault was permanent, there is a risk that re-charging of the line will result in a second fault. The HVDC line was designed in order to have 3 more restart attempts, the last two attempts are made with reduced voltage (80% and 40% respectively). It should be pointed out that the DC line fault clearing does not involve any mechanical action, and is faster than for an AC line. The DC fault current is also lower (the load current) than the AC fault current, and therefore the dead time before the restart is shorter than for an AC line. The reduced voltage restart is also unique for HVDC. For the fault location in the HVDC system, Furnas has a methodology based on traveling wave analysis that uses records taken directly from the fault. As previously mentioned (Sec. 2.3), these records can be decomposed into its waves with different frequencies to find the wave generated by the fault. This decomposition is made using 106 CHAPTER 5. WORKING EXAMPLES high-pass filters located in the converters at both ends, then the pulse is measured in the voltage signal of a capacitor located at the end of the filter. 5.1.3 The HVDC Fault Location Equipment The fault location equipment was supplied by ABB and is based on traveling wave techniques. The Furnas HVDC line has had two fault location equipment: the first was commissioned with the line in 1986. This first equipment had timers on each line-end that were activated when a wavefront was recognized, and each lineend simultaneously sent an indication to the opposite line-end via communication channel. When indication sent from each line-end was received by the opposite lineend’s equipment, the timer stopped. Figure 5.3 shows the operation of this equipment using a Lattice diagram. The fault distance can be calculated using equation 5.1. - z 9 9z S R t1 t2 d - - Fault traveling wave Pulse by communication channel d=1 2[l+ (t1−t2+tc)∗k∗c] (5.1) Figure 5.3: Lattice diagram. . Where dis the distance between the measurement point and the fault point, l is the total length, t1is the trig time at the line-end 1, t2is the trig time when the pulse signal is received on line-end 2 via communication channel, tcis the entire communication channel time, kis a correction factor for surge front delay, and cis the speed of traveling wave. Due to the expiration of its useful life, this equipment was removed in 2009 and replaced by one based on the same principles but with the support of modern technologies. The newer fault location equipment was also supplied by ABB [5]. In this equipment, satellite-synchronized clocks (GPS) are used in each line-end of the monitored line for absolute time marking of the arrival of the first incoming wavefront when a fault occurs (as shown in Figure 2.5). Then, the fault distance can be calculated using equation 5.2 d=1 2[l+ (t1−t2+offset)∗k∗c] (5.2) Where dis the distance between the measurement point and the fault point, lis the total length, t1is the trig time at line-end 1, t2is the trig time at line-end 2, offset is an offset constant for trig time difference, kis a correction factor for surge front delay and cis the speed of the traveling wave. The speed of the traveling wave 5.2. FAULT LOCATION TEST 107 is ideally the same as the speed of light (c), however a correction (k) is introduced to compensate for surge front delay, and an offset to compensate for trig time differences. The wavefront is measured trough two shunt capacitors, one at each line-end. The grounding conductor of the capacitors is equipped with a pulse transformer. The output of the pulse transformer is connected to a detector unit which will rectify the signal caused by the high derivative voltage drop. The detector generates a light pulse if a preset level of the line fault pulse is exceeded. The light pulse is received by a trigger unit in the control room. The pulse then triggers the GPS clock. Since the triggering circuit and the time registration of the wavefront arrival is common for both lines, information from the DC line protection is needed to identify the faulty line. The automatic calculated fault location is presented as an event on a list. The event includes date, time, line, and the distance to the fault. The presentation is made on a computer in the main cubicle, and calculations are performed in both stations. In this case, also post fault calculations can be manually performed using the individually stored fault time in each station. The formula as used in the automatic calculations can, in this case, be fed into Excel for the case where telecommunication channels are faulty. Figure 5.4 shows the HVDC fault location equipments. First the field equipments4 (a pulse transformer and a detector card), and then the control room equipment5 (a cabinet with GPS clock, computer for the analysis and data storage; and display unit). A set of these equipments is needed at each line-end. Is important to note that these equipment are to be used only with the fault location method and is estimated that manufacturing and installation costs is around 2.500.000 US$ for a dipole HVDC line6(four sets of equipment). Figure 5.57shows the dipole 1 output of the line at the rectifier end (Foz do Igua¸cu substation). In this photo can be seen the field equipment used in the measurement and fault analysis: shows the capacitor that collects the wavefront used for the traveling wave-based fault location equipment, the CT for current measurement and fault recording; and the PT for voltage measurement, protection and fault recording. The voltage and current signals recorded by these devices are used as input data in the fault location methodology developed in this work. 5.2 Fault Location Test The tests consist to estimate the fault location from the voltage and current fault’s records. The fault location is calculated using each method. Then, the results are compared with the actual fault distance in order to show which of the four methods can predict more accurately the fault point. 4Photo source: ABB 5Photo source: own work 6Estimated costs source: ABB 7Photo source: own work 108 CHAPTER 5. WORKING EXAMPLES (a) Field equipments. (b) Control room equipments. Figure 5.4: HVDC fault location equipments. Figure 5.5: Dipole 1 output of the line at the rectifier end. Actual fault records from the Itaipu HVDC line are used and also the Itaipu HVDC model was used in the fault simulations [6] in order to validate the method’s performance. All fault location distances are referenced to the rectifier station’s lineend. In order to make comparisons between results, they are not shown in distance values (km) but referred to percentage errors based on the total distances of the lines (%) as indicated in [7]. 5.2. FAULT LOCATION TEST 109 5.2.1 Method Performance to Actual Faults In this part was assessed the performance of the developed method under real conditions. For this test, two records of faults occurred in the Itaipu HVDC line were used. One fault was located correctly by the equipment installed in the line, while in the other fault, equipment was unable to make the detection. Both faults were analyzed using the developed method. The sample time intervals were 0.173 ms. which is higher than those of simulated fault records but is a typical sample time under real conditions. The first fault was near of the rectifier’s line-end. Field crews that carried out the inspection, found the cause of the fault at 91 km (see Figure 5.6). For this fault, the traveling wave was detected for the fault locator, and the analysis’ result was 92.0 km (0.1266 % of error). When the fault was analyzed by the developed method, the result was 91.26 km (0.0329 % of error). Then, the developed method was more accuracy than the traveling wave method for this fault. Figure 5.6: Fault origin located to 91 km from the rectifier line-end. In order to illustrate the fault analysis, Figure 5.7 shows the rectifier and inverter side records used by the developed method. The commercial equipment doesn’t use this type of records, instead it uses a high frequency sensor in order to detect only the traveling wave. The second fault was a high impedance fault occurred for unknown reasons. In this case, the equipment installed in the line was not able to calculate the location of the fault. The fault records were analyzed using the method developed and resulted in a distance of 513.28 km and a fault resistance of 384.02 Ω, which agrees with a high impedance fault. The location indicated by the analysis is an area of dense vegetation. In order to illustrate the fault analysis, Figure 5.8 shows the graphic result analysis made by the developed method. This represents the voltage profiles when the fault starts. The lowest voltage peak marks the fault point. 116 CHAPTER 5. WORKING EXAMPLES Fault location average errors test. (follow up) Distance Developed Bergeron’s 1-end 2-ends (km) method model traveling wave traveling wave 450 0,2480 0,248 0,7132 0,2122 460 0,0204 0,0237 0,4791 0,0220 470 0,2464 0,2465 0,2449 0,2561 480 0,1297 0,1294 0,0108 0,2597 490 0,0129 0,0127 0,2234 0,0256 500 0,1036 0,1039 0,2925 0,2086 510 0,2199 0,2199 0,6916 0,3073 520 0,2103 0,2099 0,1758 0,0731 530 0,2410 0,241 0,4100 0,1610 540 0,1764 0,1759 0,1059 0,3952 550 0,0592 0,0579 0,1283 0,6293 560 0,0573 0,0587 0,3876 0,1135 570 0,1739 0,1753 0,1534 0,3476 580 0,2427 0,2438 0,0807 0,5818 590 0,0623 0,0729 0,3149 0,0659 600 0,2230 0,2214 0,2010 0,3001 610 0,1055 0,103 0,0332 0,2158 620 0,0111 0,0138 0,2673 0,0184 630 0,1273 0,1298 0,2485 0,2525 640 0,2434 0,2451 0,0144 0,2633 650 0,0109 0,0029 0,2198 0,7208 660 0,2466 0,2448 0,2961 0,5450 670 0,1527 0,1501 0,0619 0,3109 680 0,0349 0,0317 0,1722 0,0767 690 0,0813 0,0838 0,3436 0,1574 700 0,1961 0,1977 0,1095 0,3916 710 0,2310 0,2317 0,1247 0,1243 720 0,1018 0,1183 0,3912 0,1099 730 0,2019 0,2007 0,1570 0,3440 740 0,0846 0,0827 0,0771 0,1718 750 0,0321 0,0343 0,4387 0,0623 760 0,1488 0,1505 0,2046 0,2965 770 0,2486 0,2488 0,0296 0,2194 780 0,0291 0,0448 0,2637 0,0148 Average: 0,1423 0,1430 0,2577 0,2379 Figure 5.15 shows a comparative graphic of the percentage of error of fault location results for faults at each 10 km of the HVDC line. 5.2.3 Sensitive Test to Fault Resistance As mentioned before, the developed method aims to bring improvements in high impedance fault locations. In order to evaluate the fault locator’s performance at different fault resistance (RF) levels, a comparative analysis is made using fault simulated data. For this test, faults were simulated in the HVDC system at every 50 km by varying RF, from 0 to 400 Ω in steps of 20 Ω increments. Then the faults were analyzed using each method and the results were compared. 5.2. FAULT LOCATION TEST 117 0 100 200 300 400 500 600 700 800 Developed Method Bergeron’s Model 1-end TW 2-ends TW Length (km) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Error (%) DDD DDDEEE Figure 5.15: Fault location errors test. In order to illustrate the test, Figure 5.16 shows a composition of several fault location results. For this case, the faults were located at 400 km. The graph shows how the onset of the fault changes, as RFincreases from 0 to 400 Ω. All records were analyzed 50 µs after the fault starts. 0 100 200 300 400 500 600 700 800 490 500 Length (km) Voltage (kv) 480 470 460 450 440 430 420 410 400 RF = 400 Ω RF = 0 Ω Figure 5.16: Line’s voltage profiles as RFchanges. 118 CHAPTER 5. WORKING EXAMPLES Figure 5.17 shows the test results for all fault location methods. Each graphic shows the error level along the line and as RFincreases. The blue areas denote less error, and red areas denote larger error as shown in the right-side bar. The results show that for the two-ends traveling wave method, the faults were detected in 67.8 % of the cases, and for the one-end traveling wave method, the faults were detected in 73.9 % of the cases. In both tests, the undetected faults were those of higher impedance. This makes impossible the location of the fault in those cases where it was not possible to detect. For the developed method, and for method of [2], the faults were detected in all cases. Error (%)RF (Ω) Fault distance (km) Figure 5.17: Sensitive test results for fault resistance. 5.2. FAULT LOCATION TEST 119 In order to illustrate the test, Table 5.4 shows the minimum and maximum error for each method, and the fault distance and RFwhere those errors were obtained. Table 5.4 also shows the total average error for all fault location results for the case where the methods work. Table 5.4: Fault location test errors. Method Minimum Error Maximum Error Average d(km) RF(Ω) Error (%) d(km) RF(Ω) Error (%) Error (%) Developed Method 10 280 0.0001 450 80 0.2440 0.0916 Bergeron’s Model 780 120 0.0004 350 400 0.2461 0.1052 2-end Trav. Wave 10 0 0.0148 780 340 6.7351 0.4566 1-end Trav. Wave 100 140 0.0915 550 280 8.8715 0.6724 For this test, the developed method had the most accurate results. The method proved to be more accurate than commercial methods and the method of [2]. The commercially available methods lose accuracy as RFincrease. The one-end traveling wave method identified high impedance faults in more occasions than the two-ends traveling wave method, but with the worse accuracy. 120 BIBLIOGRAPHY CHAPTER 5 Bibliography Chapter 5 [1] F. Magnago and A. Abur, “Fault location using wavelets,” IEEE Transactions on Power Delivery, vol. 13, no. 4, pp. 1475–1480, 1998. [2] S. Jiale, G. Shuping, S. Guobing, J. Zaibin, and K. Xiaoning, “A novel fault-location method for HVDC transmission lines,” IEEE Transactions on Power Delivery, vol. 25, no. 2, pp. 1203–1209, 2010. [3] C. Peixoto, “Itaipu 6300 MW HVDC transmission system feasibility and planning aspects,” Symposium on Incorporating HVDC Power Transmission Into System Planning, pp. 211–236, 1980. [4] A. Pra¸ca, H. Arakaki, S. Alves, K. Eriksson, J. Graham, and G. Biledt, “Itaipu HVDC transmission system 10 years operational experience,” in V Symposium of Specialists in Electric Operational and Expansion Planning, p. 12, 1996. [5] T. Montelius, “DC line fault locator,” tech. rep., ABB, Functional Description, 2011. [6] G. Sarcinelli Luz and N. da Silva, “First benchmack model for HVDC controls in ATP program,” in X Symposium of Specialists in Electric Operational and Expansion Planning, p. 10, 2006. [7] IEEE, “IEEE guide for determining fault location on AC transmission and distribution lines,” IEEE Std C37.114-2004, pp. 1–36, June 2005. BIBLIOGRAPHY CHAPTER 5 121 122 BIBLIOGRAPHY CHAPTER 5 Chapter 6 Conclusions & Future Research This chapter is devoted to evaluate the main contributions that result from this work. It includes a brief summary of the analysis, developments, and findings that constitute the core of this work. It also specifies the original contributions that have resulted while pursuing the general objective of this work. Finally, a number of future lines of research stemming from the developments presented are identified. This work has addressed the problem of Fault location in two-terminals HVDC lines. This issue is currently of relevance due to advances in the DC power transmission technology, and the increase of HVDC line projects around the world. This is also relevant and of great concern of the European countries, where HVDC projects seek to exploit the potential of renewable energy around the continent. The advantage of using DC technology in these type of projects is the ability to connect remote renewable power resources such as wind power in the North Sea, solar power in North Africa, by crossing large bodies of water. These projects are strongly encouraged as a sustainable way to face the global warming problem. DC technologies are necessary to deal with the environmental problems derived of traditional power systems. However, development of new power systems represent a challenge from the operational point of view, and for the search for new paradigms. This work proposes an impedance-based method to solve the problem of fault location. This approach permits to overcome the problems in the commercially available fault locators which are traveling wave-based. The Impedance-based method proposes the use of a time-domain distributed-parameters line model. The distributedparameters nature of this line model comes from the fact that approximations are not used to solve the line differential equations. The proposed method has been developed considering the following three innovative features: •Use of an operation principle different from that of commercially available methods, in order to avoid the weaknesses of those methods. •Use of a time-domain transmission line model specifically developed for the method, in order to achieve high levels of accuracy. 124 CHAPTER 6. CONCLUSIONS & FUTURE RESEARCH •Use of fault data currently available in all HVDC system, avoiding the use of special equipment dedicated for fault location analysis, in order to reduce costs and facilitate the method’s implementation in real HVDC lines. Whereas the impedance-based fault location methods constitute the class most commonly used in AC systems fault location, due to its simplicity and low cost, its application in HVDC has not been sufficiently studied because of difficulties in the implementation of the DC line models that are necessary for this methodology. Although designed for AC lines, these methods can also be applied to locate faults on DC lines since there is no essential difference in line primary parameters between AC and DC lines. But AC lines models used in these methods are a function of the system’s frequency, so they cannot be applied directly as models for HVDC lines since DC lines don’t have a fundamental frequency. The main problem in this formulation is to find a model that fulfills the functions of the traditional frequency-domain line models but in the time-domain in order to adapt it to an impedance-based fault locator. The telegraph equation needs to be solved in order to find a time-domain line model. But the telegraph equation is a second order linear partial differential equation with a coordinate of space and other of time, making it difficult to obtain a complete solution for them in terms of Vand Ias functions of xand t. To find an accurate solution to this equation is the main problem of transmission line modeling. The presented solution begins by dividing the partial differential equation into two equations: one in time-domain and the other in space-domain. Then, the general solutions of each one compensate each other, in order to describe the complete behavior of the line. Therefore, the general solution is given by the general solutions of its components in time and space. With the time-domain line model, the proposed impedance-based fault location method can be used for HVDC line analysis. The method has shown the better performance when compared with existing commercial methods, using both actual and simulated fault records. 6.1 Contributions and Findings Specific contributions and findings are summarized below: 1. This work develops an impedance-based fault location method for two-ended HVDC lines. The method was tested using both actual and simulated fault records, this records were analyzed using both the proposed method and commercial methods and the results were compared. For this test the proposed method proved to be more accurate than the currently available methods. The average of the results using the proposed method was about 40% more accurate than those of commercial methods. The novelty of this method is found in the use of a time-domain line model in order to obtain a high accuracy in the HVDC fault location. 6.1. CONTRIBUTIONS AND FINDINGS 125 2. This work develops a fault location method with more robustness against high impedance faults. Traveling wave-based methods have problems detecting high impedance faults since this kind of faults don’t generate large wavefronts. But impedance-based methods are less affected by this problem. This type of faults are more common in overhead lines. The method was tested using simulated fault records and varying RFfrom 0 to 400 Ω in steps of 20 Ω increments, these records were analyzed using both the proposed method and commercial methods and the results were compared. These tests showed that commercial methods can not detect high impedance faults, while the proposed method has a better performance in accuracy and detecting high impedance faults. 3. Another improvement that the proposed method could bring involves short HVDC lines. Short HVDC lines represent an important research area since almost 50% of the world’s HVDC cables have a length of 100 km or less. The use of traveling wave-based methods in short HVDC lines have an added difficulty because the wavefront’s velocity is very high, a high sampling frequency of measurement is required in order to record each wavefront’s arrival to each line-ends. The proposed method is based on another operation principle and does not need special measurement equipment. Since the line model can be applied to both overhead and cables, they could also be used in fault location for short HVDC cables. 4. With the advantages showed with the use of the proposed method, this method could replace the current traveling wave-based methods or, at least, complement them in cases when traditional methods don’t work. 5. The proposed method reduces process costs in HVDC line’s operation. Utilities are showing some reluctance to move from an established working technology to the promise of an unfamiliar technology as they deal with their limited resources. There are many new developments, however, that can help them become more effective, efficient, and creative, but it is human nature to resist change. Utilities have the responsibility for keeping the lights on, so moving out of that comfort zone is difficult. The challenge is being able to determine what technology is a suitable solution that best fulfills the mission of providing the customer with high-quality power and the proposed method proved to be a possible option with economical advantages. The method provides economical and technical advancements in the fault analysis field, by offering more accuracy and faster solutions to the problem and with less special and dedicated field measurement equipment requirements, leading to improvements in the repair and operational processes of HVDC systems. 6. In this work a time-domain transmission line model was developed based entirely on distributed parameters. This model was designed specifically to be used in the fault location method of this work. However, as seen in section 4.1, to deduct the model was not required the use of premises to limit the model to only fault analysis, making possible the use of the model in the simulation of