Single Phase to Ground Fault Detection and Location in Compensated Network

Transcription

1 Single Phase to Ground Fault Detection and Location in Compensated Network Matthieu Loos A thesis submitted for the degree of PhD in Engineering Sciences Academic year Thesis director: Professor Jean-Claude Maun

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3 Abstract This work takes place in the context of distribution power system protection and tries to improve the detection and location of earth faults. The protection problem is vast and many ideas emerge every year to enhance the reliability of the grid. The author has focused his energy into the compensated and isolated network protection in the specific case of single phase earth fault. This PhD thesis is divided in two main parts that might be considered as independent. The first part studies the detection of single phase earth fault and the second analyzes the fault location of such fault. Pragmatism was asked during these three years because a product development was necessary especially regarding the fault detection problem. The first part of the thesis took 18 months of research and development to obtain a prototype of transient protection able to detect single phase earth fault in compensated and isolated network. The sensitivity of the algorithm has been emphasized regarding the fault impedance and to detect earth fault up to 5 kohm depending on the network characteristic. The fault location problem has been much more theoretical although the problem links to the accuracy of the algorithm and its robustness regarding wrong fault location indication has been strongly considered. Compensated networks and in some conditions isolated networks are distribution from 12 kv up to 110 kv mostly used in East and North Europe but also in China. Others areas also work with such networks but they also have others systems and they do not use them on all the territory. These networks have the particularity to obtain very small fault current in case of single phase earth fault. Low current means the difference between a faulty and a sound feeder is not significant. Therefore classic overcurrent protection is completely useless to protect the network, forcing the development of more complex algorithm. A possibility to overcome the problem of the small fault current is to develop a transient protection. The transient occurring at the beginning of the fault has strong information to distinguish a faulty from a sound feeder. In this work I have chosen to use not only the transient but also the steady state to get the best sensitivity. Then the fault location has been investigated but the small information coming from the faulty feeder is not sufficient to have a precise enough position of the fault. Therefore, active system has been suggested to be implemented in the grid to increase the faulty current and have enough power for a precise location. Different existing algorithms based on the steady state at the nominal frequency are compared using a tool developed during this work. Recommendations are then made depending on the topology, the network parameters, the measurements precision, etc. Due to the complexities of the problem, a simulator has been coded in Matlab. The user of a possible fault location must then use this tool to understand and see the future fault location precision that he could obtain from different algorithm on his network. 3

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5 Acknowledgement This work has been made in three years. These years have been enjoyable for many reasons but one that is very important is people who contributed to the achievement of this work. Professor Jean-Claude Maun is certainly the first person to be acknowledged. Indeed, he is the person who gave me this very interesting job opportunity. I think this PhD thesis has sharpened my engineer skills and changed my way of thinking and solving problems. The people from Siemens AG especially Matthias Kereit and Stefan Werben have brought a strong support to the realization of this work. The conclusions and the contents would surely not have been so consistent without them. I also want to thank the people from Siemens Berlin where I have worked four months who have helped me to learn some German basic and discover the city. I also want to thank Professor Pierre Mathys for the remarks and comments that makes this document much better. Three years of research would not have been as fun if the colleagues were not there. A very special thanks to Pierre, Olivier and Gilles who have been my officemates and who have created a enjoyable environement with nice office decorations and very interesting talks. Of course, I want to thank the rest of the team Mélik, Quentin, Fabien, Michael, Momo, Yves, Martin and the youngers Benoit, Thomas for the working atmosphere and the friday nights. The Eco marathon project has been one of the most interesting project I had here aside of my thesis. This project has been a great success and it keeps improving each year thanks to Johan, Fabien, Gilles, Mélik and Bilal as assistants but also and of course the students. I hope the project will continue and I am sure the records will be beaten. I would aslo like to thank the secretary of our department Ariane who took care of the reimbursement and all the administrative stuffs link to this work. Working on a thesis is a special work where you always think about it days and nights, therefore I think to my friends who give more than one reason to relax. I will particularly remember all the chats with Johan, the drinks, games and party with the friends from Arlon. A personal thank goes also to Yas who has supported me during these three years more especially the two last years which had been heavy in work load due to my master at the Solvay Business School. Last but not least, I think this PhD could not be achieved without the support of my parents and family who gave me the opportunity to study at the University and always push me forward. 5

6 Contents I Introduction 17 1 Context 18 2 The fault detection 19 3 The fault location 21 4 Contributions 23 II Overview of Distribution Network Grounding Practices and Single Phase to Ground Fault Behavior in Compensated Network 24 1 Introduction 25 2 Distribution Network Grounding in Medium Voltage Solid Grounding Isolate Grounding Low Impedance Grounding High Resistance Grounding Resonant Grounding Examples of Industrial Grounding Single Phase to Ground Fault In Compensated Network Steady State Isolated network Compensated network Transients Symmetrical components to study the transients Discharging frequency Charging frequency The charging frequency model Charging transient magnitude considering the fault resistance Transient due to the fault resistance Neglecting the parallel resistance Considering the parallel resistance

7 CONTENTS Transient due to inception time Extinction of the fault Intermittent and restriking earth fault Shape of an intermittent earth fault Shape of restriking earth fault Confrontations of the Theory with the Field The topologies of the distribution The circulating current problem Asymmetric series impedance Network coupling Illustration with real recordings and simulations Summary 66 III Single Phase to Ground Fault Detection Algorithms 67 1 Introduction 68 2 Review of today fault detection devices The Wischer principle The QU-method The Wattmetric function The faulty feeder C0 method algorithm The capacitive behavior of the sound feeder The algorithm Disadvantages of the method The directional method algorithm The observation The algorithm Specific topology Discussion about the active power flow Possible direction of the 4 relays in a closed ring Tests and simulations of the methods Classic fault High impedance fault Coil effect Intermittent earth fault Summary 98 IV Fault Detection Prototype Development 99 1 Introduction 100

8 CONTENTS 8 2 The signal conditioning High pass FIR filter - Purpose and design Circulating current issue The detection The first suppression technique The second suppression technique Current condition The C0 method Integrating the current i Estimating C Error threshold computation Basis Feedback and updates from the tests Calculation of the error and its integration Device running criteria Blocking the algorithm Stopping the algorithm Characterization of the fault Faulty phase determination Directional method Implementation Feedback and updates from the tests Summary 120 V Fault Location in Compensated Network Introduction The needs of fault location in compensated network Today s fault location What fault location algorithm could bring State of the art of fault location and application Charging transient Fault passage indicators Traveling waves Steady state Challenges of steady-state fault location The compensated network problem Single-ended method Heterogeneous line Tree structure

9 CONTENTS Two-ended method Heterogeneous and tree structure Loop topology Loads and DGs impact on fault location Loads and DGs impact Loads and DGs model Summary 142 VI Fault Location Tool and Sensitivity Analysis in Compensated Network Introduction Fault location main problem Parameters and measurements accuracy Graphical User Interface Tool Purpose Structure Network description SimNet.m script RunSimNet and the GUI Sensitivity analysis Purpose of the sensitivity analysis The parallel resistance importance Size of distribution network The single-ended measurements precision Today s knowledge Improvement of Z0 knowledge Heterogeneous line The parallel resistance effect Two ended measurements precision The best symmetrical system The parallel resistance effect The loop advantage Heterogeneous line The load impact and bias error The impact The single-ended algorithm The two-ended algorithm A solution Summary 179

10 CONTENTS 10 VII Conclusions General conclusions Fault detection Fault location Future work and perspectives 186 VIII Appendices 195 A Network Information 196 B DSO Survey 198 B.1 The description B.2 Customer B.3 Customer B.4 Customer B.5 Customer B.6 Customer B.7 Customer C Fault location simulation network 220

11 List of Figures 2.1 Network representation of two feeders network with single phase earth fault Single phase earth fault representation with symmetrical components Representation of solidly grounded transformer Representation of a solidly grounded network with two feeders Single phase earth fault on phase A in a solidly grounded network The current is flowing through the shunt capacitance in case of single phase earth fault The voltage neutral is floating in isolated network The current flows are opposite for the sound and the faulty feeder Representation of a high resistive grounding in single phase to earth fault situation A phase angle of 90 is measured for a high resistive grounding system Representation of a compensated network in single phase to earth fault condition The isolated network has capacitive current circulating through the healthy phases in case of single phase earth fault Steady state amplitude on the faulty feeder depends on the healthy feeders Fortescue representation of the zero-sequence current flows in case of EF Fortescue representation of the zero-sequence current flows in case of EF No phase angle between the faulty and sound feeder with a perfect Peterson coil Phase angle appears between the faulty and sound feeder with a realistic Peterson coil Simplified zero sequence system Phase Angle of the faulty feeder depends on R NG Using the symmetrical components is equivalent to the distributed model for the transients consideration Representation of the discharge of the faulty phase Representation of the charge of the healthy phases Model of a network with three feeders to characterize the charging transients with symmetrical components Three charging frequencies are measured on a network with three feeders Charging transient with a 0 Ω earth fault Charging transient with a 100 Ω earth fault Charging transient with a 1.66 kω earth fault contains only 50 Hz signal Slow increasing of the 50 Hz voltage and current with R fault =1.66kΩ

12 LIST OF FIGURES Influence of the fault resistance Validation of the equation considering the parallel resistance Peterson coil effect on symmetrical components Transient current due to the Peterson coil is measured only on the faulty feeder Decreasing exponential occurs only on the faulty feeder Decreasing of V0 and I0 after fault extinction Hz resonating zero-sequence system Hz resonating zero-sequence system Typical intermittent earth fault Typical intermittent earth fault with coil effect Typical restriking earth fault Pfalzwerke distribution network Asymmetry in the series phase impedance creates circulating current Single conductors in parallel and trefoil position Zero-sequence voltage is measured during healthy operation due to mutual coupling Circulating current due to coupling with parallel asymmetric network Circulating current before the single phase earth fault on feeder J03 and J Simulation of the load power on the zero sequence circulating current The 7SN600 transient earth-fault relay from Siemens Detection of transients in the Wischer principle The EOR-D device of a-eberle Illustration of the QU method The Wattmetric function decision criteria A least square method is necessary to get a C0 value In case of low impedance fault, the error signal is very high High impedance fault with error signal Integration of the error signal to increase the sensitivity of the algorithm Transient has bigger error than the steady state Transient does not exactly matches the capacitive model No problem to know which feeder is faulty Detection of the faulty feeder is not possible with four devices in a loop Active power depends on the current and voltage behavior Main power flow in a compensated network during single phase earth fault Instantaneous zero-sequence active power power for small impedance fault Instantaneous zero-sequence active power power for high impedance fault Energy evolution of a low impedance fault Energy evolution of a high impedance fault Schematic active power flow in closed ring structure Simulation network to test the algorithm Zero-sequence current and voltage for a low impedance fault QU diagram of a classic single phase earth fault Integration of the error signal

13 LIST OF FIGURES Energy in case of classic single phase earth fault Zero sequence current and voltage for high impedance fault QU diagram in case of high impedance fault Integration of the error signal for a high impedance fault simulation Energy in case of high impedance fault Zero sequence current and voltage with a coil effect Coil effect disappears with the high pass filter QU diagram with a coil effect is easy to detect Integration of the squared error with a coil effect Energy for direction determination with coil effect Simulation of an intermittent and restriking earth fault The feeder 1 is not on a straight line in the QU diagram The integration of the squared error works well with intermittent earth fault The direction determination works correctly in case of intermittent earth fault Integration of the current i0(t) without (left) and with (right) high-pass filtering compared to voltage signal U High pass filter characteristic for signal conditioning Illustration of circulating current from real recording before a single phase earth fault happens Healthy feeder can be detected as faulty without dealing the circulating current Suppression of the 50 Hz component to delete the circulating current Deletion of the circulating component without filtering Illustration of the trapezoidal integration compared to a perfect integration Estimation of C0 in case of sound or faulty feeder Estimation of C 0 in case of faulty feeder with unrealistic C 0 value Threshold value depending on C0 value Minimum value of the threshold limited in case transient detection Evolution of the threshold depending on the current signal Relay picks up after the inception of the fault with Feeder 1 faulty and 3kOhm fault C0method values and threshold Updates make the relay picked up before the inception of the fault The threshold can be smaller in this case and detect the faulty feeder Voltage is decreasing when the fault has disappeared Flowchart of the direction determination The three zones of direction and determination in case of LIF The three zones of direction and determination in case of HIF Zero sequence active energy with circulating current in a four feeders sound loop Zero sequence active energy without circulating current in a four feeders sound loop Flowchart explaining the procedure to locate the faulty section in compensated network with ring possibilities Schematic describing the faulty section location in a ring structure

14 LIST OF FIGURES Model to determine the frequency of the charging transient Example of fault passage indicators for a radial feeder Effect of the fault used in the traveling wave fault location principle Connection of a parallel resistance to increase the fault current Example of signal increasing due to the connection of a parallel resistance Example of current increasing due to the connection of a parallel resistance Injection of a signal from the transformer neutral Schematic of a fault location model using a single ended method Computation of the current and voltage on the faulty section Topology of a tree feeder Schematic of a fault location model using a two ended method Identification of the faulty branch with a two ended algorithm Procedure to isolate the faulty branch in a tree feeder and locate the fault Closed ring structure made of more than two feeders Impact of the distributed loads if the fault current is not significant There is no impact on the fault distance if the loads are beyond the fault Method of load tap from [Altonen and Wahlroos, 2007] Standard error representation on a phasor measurement Bias error representation compared to the standard error Illustration of the PI model from the interface Positive sequence system node number Negative sequence system node number Zero sequence system node number Screenshot of the Graphically User Interface Algorithm selection - Popup button and list of fault locator Example of text box information Variance detailed example Checkbox display information Standard deviation edit box Algorithm option window The parallel resistance design button Additional questions are brought by the requirement of the fault locator The active system can make the fault location possible in compensated network Comparison of single phase earth fault between compensated and solidly grounded network Standard deviation for three different C0 total Fault location accuracy with single-ended method and actual knowledge of the network Fault location accuracy with improvement of the zero sequence impedance in single ended method The ratio X/R is not important compared to the absolute value of the impedance Variance contribution of the main parameter for single ended method versus the parallel resistance

15 LIST OF FIGURES Multiple measurements can help to improve the fault location Illustration of the zero sequence system two-ended method fault location Voltage value of the three symmetrical systems depending on the parallel resistance Zero sequence system variance with two ended solution Positive sequence system variance with two ended method Negative sequence system variance with two ended method Compensation effect with the loop structure Impact of the loads on the single ended algorithm The zero sequence system is not influenced by the loads The positive sequence system is strongly influenced by the loads The negative sequence system is almost not affected by the loads Load impact integration in the faulty area estimation A.1 Network length and topology A.2 Position of the phases B.1 Illustration of fault location problem B.2 Voltage difference between the faulty position and the measurement position 199 B.3 Illustration of the parallel resistance B.4 PI model used for fault location B.5 Grid representation with measurements devices B.6 Description by customer 5 of the fault location

16 List of Tables 4.1 Survey of the German Distribution Network topology Wischer direction logical table The different indication of the direction protection in closed ring Default value of the standard deviation of the parameters Example of the network initialization text file Example of line characteristic in the text file Measurements node in the text file Loads information in the text file Distributed generation information in the text file Accuracy of the single ended method and contribution of each parameter Single ended method accuracy if the knowledge on Z0 is improved Comparison of the symmetrical system for fault location Accuracy and contribution of each symmetrical system with two-ended method Accuracy of the each symmetrical system with two ended method in a loop. 172 A.1 Line parameters B.1 Example of information provided by the fault locator B.2 Network information of the customer B.3 Precision of the customer B.4 Network information of the customer B.5 Precision of the customer B.6 Network information of the customer B.7 Precision of the customer B.8 Network information of the customer B.9 Precision of the customer B.10 Network information of the customer B.11 Precision of the customer B.12 Network information of the customer B.13 Precision of the customer

17 Part I Introduction 17

18 1. Context This PhD thesis has been sponsored by Siemens with the goal of developing a new protection device for compensated network at the end of the first year followed by a study about the fault location in same network. Therefore the work has been very practical with regular feedback from the industrial party. Meetings and live meetings have been regularly held every 2 to 3 months to follow the work and get results. This way of working has been efficient to give new objectives or change the effort in the construction of the fault detection algorithm and a fault location strategy. A few months were necessary to get used to the subject and the problem related to single phase earth fault in compensated and isolated network. Five months later, several algorithms were presented with simulation results and sensitivity tests. Some real recordings were also available and have been tested to compare the different methods and to work on some fine tuning. Nine months after the beginning of the project, four months have been devoted to develop a first prototype using two of the different algorithms proposed. This work has been done in Berlin with a strong technical support of Siemens. Some weeks were still needed at the end of the internship to fine tune the methods and to test bench the device. Once the tests finished the algorithms have been transferred to the industrial partner who has started the phase of product development. Some feedback and live meetings have been necessary to fully transfer the knowledge developed on the fault detection method but while I was already working on the fault location problem. A review of the published methods has been made which has revealed different strategies to locate the fault. Based on the knowledge built during the first year and the prototype development, one strategy has been deeply investigated. However, the chosen way to locate the fault needs an active system to increase the faulty current. To understand the needs and the efforts the distribution system operators are ready to put to get a fault location system in their network, a survey has been written and distributed among the operators during a German meeting. The results were interesting and have oriented the study in a more practical way to meet some of the possible market needs. It has been noticed that the main problems for fault location in compensated network is not only technical due to the small fault current but also practical because the distribution system operators do not know all the symmetrical parameters required for an accurate fault location. The efforts have then been put to find the best technical way to locate the fault with a comparison of the different recent or existing algorithms which finally led to the development of a tool to indicate the precision of the methods with the actual knowledge the users have of his network. Results demonstrate that the fault location is indeed almost impossible with the actual way the compensated networks are used and therefore needs additional equipments. The goal of this tool is to provide the actions the operator has to handle to achieve the precision that he wants on the fault location. 18

19 2. The fault detection The three first chapters of this thesis concern the single phase to ground fault detection problem in compensated network. The algorithms have been developed for compensated network but they can be directly used for isolated network because they have similar behavior regarding single phase earth fault. The objective of the fault detection was to find and develop an algorithm able to beat the sensitivity of the Wischer relay from Siemens regarding the fault impedance. This problem has been tackled by a review of the compensated network characteristic in healthy and faulty conditions. Then some simulations and model improvements based on recordings have been developed and are part of the first chapter of this document. A comparison with the others grounding systems is presented at the beginning of this chapter to give an overview of the techniques and the arguments to choose a compensated network instead of a different grounding system. The single phase earth fault is then presented in compensated and isolated network using both symmetrical system and three phases power representations. The problem is divided in the steady state and the transients phenomena which are compared between the faulty feeder and the sound feeder. The differences between the faulty and healthy are emphasized to understand all the information available to have the best fault detection. Next to the important phenomena for the fault detection, an other phenomenon is presented which has been discovered during test of the algorithms with real recordings. It has occurred that the permanent loop topology (i.e. two feeders connected on the main substation and at their ends) in a compensated network can generate zero sequence current big enough to jeopardize the detection of the fault. This problem is caused by the creation of a mutual coupling between the symmetrical systems with the loop structure. A mathematical model of the coupling is then presented with simulations and real recordings to provide sufficient details of the issue. The second chapter presents two algorithms selected by Siemens to be implemented in a prototype. The description is more theoretical and the equations of both method are explained. The first method is named C0. It considers the sound feeder as a capacitance in the zero sequence system and assumes that the faulty feeder does not act as a capacitance. Therefore, an estimation of the zero sequence capacitance is made using a simple least square method. Then the quantification of the deviation from a perfect capacitive model is calculated and memorized. The second algorithm wanted to be a directional algorithm that can be placed not only in the main substation but also along the line. This method is able to indicate if the fault is forward or reverse. This indication is especially helpful in the case of a loop to identify which part is faulty. The solution has been to compute what it is called the zero sequence active energy using the information in the transients but also in the steady state to determine the fault direction. In conclusion of this chapter, some illustrations of the working 19

20 2. THE FAULT DETECTION 20 principle are presented with low impedance fault, high impedance but also circulating current problem. The third chapter of this document presents the practical implementation of the algorithms. The four months spent in Berlin to develop the prototype have revealed many points to be solved before obtaining a commercial product once the theoretical algorithms are set. Indeed the current and voltage signals coming from the measurements is not as pure as the one from the simulations. Therefore filtering is necessary to treat the signals before applying the algorithm but this filtering process should not filter the important information that might reduce the sensitivity. The computation power of a protection device is also different than then a personal computer which requires code optimization, etc. All these problems are described in this chapter. Also feedback from tests with real recordings have led to small changes in the algorithms.

21 3. The fault location The hardest part of the work was probably the fault location. The small fault current in compensated network makes it a real challenge to have reliable fault location. A lot of papers claim great solutions and great algorithms for fault location but the precision of these methods in real conditions have always been a question. However, even if the author does not claim to have brought new methods that could improve fault location, the approach taken in this work looks very interesting to identify the effort to be made to have a useful fault location. The industrial partner, Siemens, has also asked for a further development of this approach, so that the work will continue after this PhD thesis. The fourth chapter of this report is the first regarding the fault location. This one is an introduction to the fault location problem. Firstly it is very important to understand what is the need of fault location from the industry and especially for distribution system operators. In compensated network, two steps are necessary before repairing a fault in a power line. The first step is to identify which section on a feeder is faulty. A section is an homogeneous electrical part of the feeder ranging between 100 meters to several kilometers. Once this section is identified, the second step consists in a very accurate fault location made by using high sampling rates devices to dig the ground along only few meters to do the repairs. This work has been focused on the first step because it looked to be the one that requires a lot of time that could be shorten by a powerful and well used algorithm which could be able to identify one or two likely faulty section. Details about the procedures are then described. Next, a short state of the art of the fault location methods is explained. Four different strategies to locate the fault, for the most part, inspired from the transmission grid problem are briefly presented. The charging transient has a relation of the distance with the frequency. This transient is caused by a sudden connection of one phase to the ground. Some equations are presented from bibliographical resources with some models to locate the fault with this mean. Then a simple method based on several direction indicators is explained followed by the traveling waves solution. The last one concerns the steady-state at 50 Hz and is the solution chosen for this work. Several explanations are provided to justify the choice of the steady state method for fault location in compensated network. Some of the arguments raised are the heterogeneousity of distribution feeder, actual sampling frequency, etc. Then the following part of the chapter concerns a deep description of the steady-state 50 Hz fault location algorithm using an active system to increase the faulty current. Single ended and two ended measurement methods are detailed with equations using symmetrical components. The problems met in distribution system such as heterogeneousity are solved and improvement of the actual method is made for the loop structure. Finally the impact of the loads and distributed generations is investigated and solutions are proposed. The fifth and last chapter of this document concerns the real contributions brought by this work on the fault location problem. The goal of the fault location in this work is to 21

22 3. THE FAULT LOCATION 22 provide an area to investigate in which the fault has strong chance to be. No distance is given by the algorithm because there will always be errors on the result. The estimated faulty area must be the smallest possible but the size depends on the accuracy the user has on his network parameters and measurements. It also depends on the topology and the structure of this network where different equations can be used if possible. Therefore a graphical user interface has been built in Matlab. The purpose is to estimate which algorithm is the best to get the best accuracy for a specific fault position. Many variables are implied in a fault location process and often the result from the fault locator will not be as accurate as expected. An estimation of the variable contribution in the total faulty area is also provided to indicate the user that it has to improve his knowledge on specific variable to significantly improve the precision. Once the explanation and the details about this tool are described, an extensive sensitivity analysis is considered. The goal of this sensitivity analysis is to bring general information regarding specific topology to the user interested in a fault location system. The information provided in this report should be interesting enough to explain where the efforts have to be made to get the precision required to significantly improve the first step of the fault location process. Indeed, additional measurements can be placed or measurement campaign can be performed to improve the knowledge on the zero sequence impedance and parallel resistances must be placed to increase the fault current. All these questions are supposed to be answered at the end of the reading. Finally the last part of the chapter explains that the impact of the load is to create a bias error instead of contributing to the size of the faulty area. Indeed only the statistical errors are considered for the faulty area but the model error (coming from a line model or neglected infeed current as the loads or distributed generations) shifts this faulty area. If the area is small compared to this bias error, the fault location could be completely wrong. Therefore estimation of the loads impact has to be taken into account. This mostly influences the positive sequence system and very slightly the negative sequence system. Solutions are then suggested to avoid wrong fault location to the profit of a bigger faulty area. It has been considered a larger area including the default is better than an smaller area which is not at the right place.

23 4. Contributions This PhD thesis has taken three years to be set including the four months spent in Berlin to develop the prototype. During this research time the contributions have been various both in the academic and the industrial sector. Several meetings with Siemens have been held in Brussels and in Berlin to follow up the work which have led to many technical reports every 2-3 months. A list of the reports sent to the industrial partner can be found in the Bibliographical contribution section. The development of the fault detection methods have conducted to a Patent application that has been finalized in a Patent publication in May This patent fully describes the two algorithms presented in this work. A prototype has been built with Siemens AG that has been transformed into a SIPROTEC product at the beginning of 2013 and is now tested in the Scandinavian countries. The fault location is for the moment a more theoretical approach and an industrial product is more complex to set. Nevertheless, Siemens has shown strong interest in the simulator tool presented in the last chapter of this document. A version useful for Siemens internal use at the beginning and perhaps for commercial purpose in the future will be developed starting in November Regarding the academic part, five conference papers have been written and presented in Europe and North America. The papers concern both the fault location and fault detection issues in compensated network. Such papers have made new connections in the academic power system sectors in an international level and have also brought constructive feedback from an international audience. 23

24 Part II Overview of Distribution Network Grounding Practices and Single Phase to Ground Fault Behavior in Compensated Network 24

25 1. Introduction This first chapter of the thesis reviews the different techniques used to ground the distribution network and the single phase to ground fault behavior in compensated and isolated network. It explains the choice of compensated network and the problem that occurs. The first section describes every strategy with their advantages and disadvantages using isolated, low resistance, high resistance, solid or resonant grounding. The goal is to give the reader a clear understanding of why the compensated network is used and the difficulties it implies compared to other groundings. The second section considers the compensated and isolated network behavior during single phase to ground fault. The aim of this section is to provide all the required knowledge to understand the single phase fault detection and location problem and to understand the way the algorithms have been developed. The steady-state signal is discussed and the difference with the isolated network is explained. The transients occurring with a single phase ground fault are detailed such as a short, high frequencies, discharging transient or a longer, medium frequencies, charging transient is analyzed and transient due to the Peterson coil is explained. The difference between high impedance and small impedance fault is highlighted. Then intermittent and restriking earth fault are explained because they occur quite often in compensated network. The increasing share of distributed generations (DGs) in the distribution network drives the operators to use their network more and more in closed loop structure. This specific topology is also studied and the impact on the symmetrical components in case of fault is explained. Model validation is illustrated with the utilization of the Alternative Transients Program (ATP). The third section is an illustration of the explanation made along this chapter. Real recordings coming from compensated networks in Germany are shown and comparison with the theory is made. 25

26 2. Distribution Network Grounding in Medium Voltage There are many different strategies regarding the distribution network grounding and it can be stated that there is no universal solution. Every technique has its own advantages and disadvantages which are described in this section. This choice depends more on a historical, legislation reasons and the will for rapid fault fixing rather than on being a solution a technical problem. The purpose of the grounding is the choice of specific network behavior in case of single phase earth fault which is the most frequent earth fault in a power system [Gerstner et al., 2013, Gomez-Exposito et al., 2008]. Indeed, the grounding has no impact in a healthy balanced system. The decision in the grounding will affect the protection strategy used by the system operator. The fault current behavior will differ and the protection algorithms used in one kind of grounding are useless in others. The following figure 2.1 illustrates a classic three phases network with a single phase earth fault. The connection of the transformer neutral will depend on the grounding and is part of the discussion. The phase to phase capacitances have been neglected as well as the series impedances for the sake of clarity. Figure 2.1: Network representation of two feeders network with single phase earth fault In case of single phase to ground fault, the three symmetrical systems are connected in series as illustrated in the figure 2.2 where lines are modeled with PI line model. This representation with the symmetrical components simplifies any unbalanced three phase power systems into three balanced system [Fortescue, 1918]. The fault current will then depend 26

27 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 27 on the capacitance of the positive and the negative system respectively in parallel with the source and transformer impedance or only with the transformer impedance. The positive and negative sequence capacitances are generally high impedance compared to the transformer, therefore the biggest part of this current will go through the negative and positive transformer impedance. Regarding the zero-sequence system, the connection of the transformer neutral is in parallel with the zero sequence capacitances, therefore it will depend on the transformer connection to know the current flowing through the zero-sequence system. The faulty current characteristic in single phase to ground fault is then mainly defined by the transformer connection, the others symmetrical systems having an insignificant influence. Figure 2.2: Single phase earth fault representation with symmetrical components This section reviews the existing system grounding in the different country with the solidly grounded, ungrounded, low impedance, high resistance and resonant grounded network. The aim is to provide the necessary knowledge to the reader to understand the general context of the compensated network and why they are used in some countries.

28 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE Solid Grounding Behavior One strategy to operate the medium voltage distribution network is to solidly connect the neutral of the transformer. This means there is no impedance between the system neutral and the ground. However, the meaning of a solidly grounded network can depend in some country. For example, The National Electrical Safety Code (NESC) [ANSI/IEEE, 2002] in the US defines an effectively grounded system as: An effectively grounded system is intentionally connected to earth through a ground connection or connections of sufficiently low impedance and having sufficient current carrying capacity to limit the buildup of voltages to levels below that which may result in undue hazard to persons or to connected equipment. This technique leads to a strong faulty current which could damage the network but it can be quickly detectable and the protection can run effectively. The figure 2.3 represents a solidly grounded transformer with its connections to the three phases of the bus bar. Figure 2.3: Representation of solidly grounded transformer Once the transformer is connected to the bus bar, it will feed several lines where the loads are connected. The figure 2.4 represents a solidly grounded distribution network with two feeders during single phase earth fault. The arrows shows the current loop of the fault. If one phase is touching the ground, the source voltage is applied on a small impedance which is the sum of the series impedance of the line Z l, the earth impedance Z E and a fault impedance if there is one Z f. I f = V LG Z l + Z E + Z f (2.1) The series impedance can be considered in the symmetrical system as: Z l = Z 1 + Z 2 + Z 0 = 2Z 1 + Z 0 (2.2) 3 3 If there is no rotating electrical system in the grid, the positive and negative impedances are the same. The identification of the zero sequence impedance and the earth impedance is very difficult but some authors make the assumption that it is simply proportional to the positive impedance [Gonen, 1987]. This strategy might be correct for fault detection but it is not accurate enough for fault location purpose as it is studied in the concerned chapter.

29 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 29 Figure 2.4: Representation of a solidly grounded network with two feeders Z 0 = K 0 Z 1 (2.3) Another solidly grounded strategy consists in connecting the network to the ground in multiple position (called Multi-grounding). This happens in case of single phase loads. In this condition, a fourth wire is connected to the neutral of the transformer to provide low impedant way of return for the loads [Roberts et al., 2001].This fourth wire must be grounded every 400 meters or less. The following benefits compared to the single point grounded neutral system [Nelson, 2002] are: 1. Safety is enhanced for the utility personnel because it reduces the voltage difference in the ground also known as stray voltage. 2. The cost of equipment is lower. 3. Reduction of the zero sequence impedance which improve the ground fault return. 4. The surge arrestor can be optimized. The grounding is more efficient, therefore less voltage increasing must be considered to effectively stop the current. The main disadvantage of this method is a more complicated installation and maintenance over the long term. Detection methods The grounding as described above shows strong faulty current in the faulty feeder. The detection is then very easy for low impedance fault and the simple used of overcurrent protection is enough. For example, the figure 2.5 shows a simulation with the ATP/EMTP simulation software the current in a solidly grounded distribution network on a feeder with a load of 14 MW. The load is balanced and the over current can easily detect the low impedance fault. In this simulation the impedance is 1kΩ. However, high impedance fault with unbalanced loads in

30 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE I a 400 I b I c Current [Amp] Fault inception time [ms] Figure 2.5: Single phase earth fault on phase A in a solidly grounded network Multi-grounding network as developed in America creates strong zero sequence current (i.e. unbalanced current) in healthy network and high impedance fault creates current magnitude not higher that the unbalancing. Very complex algorithm must then be applied in such case and are considered in [Masa, 2012]. 2.2 Isolate Grounding Behavior Ungrounded the neutral of the transformer makes the network isolated from the ground. Such networks are used in medium voltage or in weak network to maintain power when single phase to ground fault occurs and no automatic tripping occurs [Detjen and Shah, 1992]. However, the reality is that the power lines and the earth are both electrical conductor separates by an insulator which makes the whole system a natural capacitance. If one phase is touching the ground, this capacitance creates an electrical way for the fault to circulate, the fault current magnitude is then proportional to the overall zero sequence capacitance of the network in case of single phase to ground fault. The next figure 2.6 illustrates the isolated network with its natural capacitance and the connection with the fault current in case of single phase to ground fault. In this case, the fault current on the faulty phase c can be estimated as: I 1 = I 2 = I 0 = V 0 X 0C (2.4) I c = 3I 0 = 3V 0 X 0C (2.5) Regarding the equation 2.4, this is correct for the fault current but not for the current in the feeder because the symmetrical systems have their own capacitances X 1C,X 2C [Lewis Blackburn and J. Domin, 2006].

31 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 31 Figure 2.6: The current is flowing through the shunt capacitance in case of single phase earth fault A three phases system has a floating neutral meaning the neutral is equal to the ground voltage in a sound network if it is correctly balanced. The capacitances create a balanced system setting the neutral around the earth voltage. However, if a single phase to ground fault occurs, the floating neutral will be set by the phase touching the ground and its impedance. The phase-to-ground voltage is then increasing on the healthy phases as it is illustrated by the figure 2.7 where the faulty phase as a voltage near zero and the healthy phase has a voltage increased by 3. This voltage increasing requires additional electrical insulation of the cables and the overhead lines to handle this higher electric tension between the conductor and the ground. Otherwise, multiple phases fault to ground could occur and severely damage the network. Figure 2.7: The voltage neutral is floating in isolated network In addition to the increased voltage on the healthy phases, a high voltage transient occurs caused by the oscillation of the capacitances and the series inductance of the lines. The phase touching a low resistive ground can be considered as a voltage step on an system with several zeros and poles. It leads to a step response oscillation with a ringing phenomenon. Such transients occur also in compensated network and will be deeply studied in the chapter 3. A problem that can occur in ungrounded system is over voltage due to load imbalance or ferroresonance effect [Walling et al., 1995]. The ferroresonance effect comes from the line capacitance (or even the transformers capacitance which creates a self-ferroresonance effect) in case of open line which creates a resonance with a non-linear inductance. This nonlinear inductance comes from a saturation of the iron-core of the transformer. Such fer-

32 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 32 roresonance has unsteady operation point which can be dangerous in ungrounded system [Valverde et al., 2007]. Detection methods To detect such fault, the current amplitude does not help because it is the same order of magnitude as the sound current if the total zero sequence capacitances of the network is not excessive. However, the zero sequence voltage V 0 will increase due to the unbalanced voltage created by the fault. If this value exceeds a defined threshold, the user can be sure there is a single phase to ground fault in his network but he does not know which is the faulty feeder because the voltage applied is the same on the whole distribution power grid. The current and voltage signal gives the opportunity to select the faulty feeder with simple algorithm. Some protection devices use the transient as detailed in the Wischer Protection [AG, 2010] and similar one [A-Eberle, 2004]. Such devices are fast but might not be very sensitive to high impedance fault because the transient does not appear in such fault. This problem is deeply investigated in the further sections and chapter to solve this sensitivity difficulty. Another solution is to use the zero sequence steady state of the current in faulty and healthy feeder. The healthy feeder acts as a capacitance and the faulty feeder acts as an inductance. This behavior can be understood by the figure 2.6 because the current flows are reversed for the sound and faulty feeder. The figure 2.8 shows a ATP/EMTP simulation of an ungrounded network with the zero sequence voltage at the bus bar and the zero sequence current flowing through thestandar and sound feeder. The magnitude of the signal has been changed to ease the comparison between the phase angles. Faulty I o Sound I o V o time [ms] Figure 2.8: The current flows are opposite for the sound and the faulty feeder 2.3 Low Impedance Grounding This system connects a low resistance in the transformer neutral to limit the fault current between 50 to 600 primary amperes. This current limitation allows simple over current protection because the magnitude difference is still significant and the insulation does not have to be enhanced because the healthy phases voltage are not increasing too much in case of single phase-to-earth fault.

33 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 33 The low impedance grounding can be done by a reactance or a resistance in delta/wye transformer. Another strategy consists in the connection of a zig-zag transformer, the impedance of the transformer is usually enough for a low impedance grounding but sometimes, additional reactance is necessary. This grounding is then a compromise to maximize the benefits of the solidly grounded such as easy protection and the aim of limiting the faulty current to avoid damage on the grid. 2.4 High Resistance Grounding Behavior The resistance connected to the transformer neutral is equal or slightly less than the total capacitance to ground of the system. This condition limits the potential transient over voltages and minimizes the fault current with a magnitude around 1 to 25 primary amperes. Such grounding is mainly used for industrial application because it avoids strong fault current that might damage the materials and it reduces the over voltages created by ungrounded systems [Baldwin Bridger, 1983]. It allows also continuity of service which can be a strong cost decision in industry with continuous process. Figure 2.9: Representation of a high resistive grounding in single phase to earth fault situation In case of single phase to earth fault, the voltage on the sound phases will rise and a line-to-line insulation is required especially if the tripping of the system is slow. However, it seems the voltage increasing will be smaller than in the ungrounded method and therefore less insulation could be required. Fault detection The current in the high resistive grounded network is not strong enough to be detected with a classic overcurrent protection. The figure 2.10 above shows the zero-sequence signal in a simulation of a high resistance grounding. The difference between the faulty and the sound feeder can be seen by the phase

34 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 34 V 0 I 0 Faulty I 0 Sound time [ms] Figure 2.10: A phase angle of 90 is measured for a high resistive grounding system angle in relation to the voltage. It is also important to notice the absence of charging transient like in the isolated network. The current on the sound feeder is not very capacitive because the voltage is not rising and therefore the zero-sequence voltage does not rise as in the isolated network. The current flowing through the fault is coming from the transformer neutral which is connected to a resistance. The faulty current measurement in the zero-sequence system is then active. 2.5 Resonant Grounding Behavior The resonant grounding is widely used in Eastern, Northern Europe and China but is is spreading in Italy and south of Europe distribution networks. Figure 2.11: Representation of a compensated network in single phase to earth fault condition

35 2. DISTRIBUTION NETWORK GROUNDING IN MEDIUM VOLTAGE 35 The connection of the transformer neutral is made to the ground with a reactance called Peterson coil which impedance is close to the total zero sequence capacitance. This network is also known as Compensated Network because the Peterson coil compensates the current created by the zero sequence capacitance in case of single phase to earth fault. This solution creates a zero-sequence impedance theoretically infinite at the 50 Hz frequency. Hereby, the faulty current is reduced to a minimum value which is in an ideal steady state case zero. The capacitance and the coil in parallel creates an infinite impedance of the zero sequence system at 50 Hz which theoretically extinguishes the fault arc. Fault detection The fault detection in compensated network is much more difficult than in the others groundings because the fault current is almost zero. Therefore, many protection devices use the transients behavior at the fault inception to detect the faulty feeder. These transients come from the charging of the healthy phases due to the voltage increasing and the discharging transient due to the faulty phase de-energization. Such transients occur also in isolated networks because the voltage increasing and decreasing is almost the same. In consequence the transient protection devices working on the compensated network can also be applied in isolated networks. However, if the network is not perfectly compensated, a steady state current remains and circulates through the fault. Such current can be exploited to detect the fault; it has been done in this work and it will be explained in the next chapter. 2.6 Examples of Industrial Grounding Mining A medium-high-resistance grounding has been developed for underground mining systems [Lewis Blackburn and J. Domin, 2006]. This grounding is more and more used for hazardoustype applications because it emphasizes the personnel safety. This system limits the fault current to primary amperes with a four wire system which is enough to provide safe, reliable and fast relay to trip off the faulty feeder. Oil Extraction The Marathon Oil Company wanted to improve the life and reliability of their electrical system. They have submersible pumps and motors and they wanted to protect them from the voltage transients and over voltage conditions. The installed solution is a specific High Resistance Grounding. The major advantage is that it allows the user to continue the operation if the fault is not situate in a dangerous area. Marathon Oil Company has run during several hours their pumps during single phase earth fault condition without damaging the electrical system [Revolt and Shipp, 1999].

36 3. Single Phase to Ground Fault In Compensated Network In this chapter, the performance of an earth fault in compensated and isolated networks will be detailed in three steps. Firstly, the steady state of the fault is presented. This steady state occurs in case of continuous earth fault. It means that the contact between the faulty conductor and the earth is permanent - e.g. an overhead line falling on the ground. The difference between isolated and compensated network is explained and a model of the faulty current and the sound current is done. Secondly, the transients are analyzed. They contain the largest amount of information to detect the faulty feeder. Every kind of transients is studied like the influence of the inception time, the influence of the fault resistance, the fault extinction and the transient due to the charge of the healthy phases and the discharge of the faulty phase. Their relation with the electrical quantities of the network are described and a model is suggested for every kind of transients with the help of the symmetrical components. Thirdly, a short description of the intermittent and restriking earth fault is presented. These are faults where the connection between the faulty conductor and the earth is not permanent for several reasons such as insulation recovery, tree branch, burning object, etc. This description uses real recordings to link the theory presented with the reality of the field. A distinction between intermittent and restriking earth fault is made and the difficulty to detect them is explained. 3.1 Steady State The steady state is very different between the isolated network and the compensated network. The steady state is the 50 Hz constant component of the signal, therefore the transients are not studied in this subsection. The compensated network has an inductance which reduces the fault current and has a capacitive behavior if well compensated. On the contrary the isolated network has a circulation of capacitive current coming from all healthy feeder. The fault current depends then on the total network zero-sequence capacitance Isolated network In isolated network, when an earth fault occurs, all the capacitive current from the healthy phases flows to the fault as the diagram 3.1 below shows it. The measurement of the zerosequence current 3I0 is completely different on the faulty and the healthy feeder. The series impedances of the feeders have been neglected for the sake of the clarity. However, the 36

37 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 37 current circulating through this series impedance is small compared to a solidly grounded system. Therefore the voltage drop along the line is very small and the contribution of the series impedance is then insignificant. The main contribution in a sound feeder is the shunt capacitances that link the feeder to the ground and create a loop with the earth fault. Practical and theoretical results have both shown that the influence of the series impedance can be neglected and that the current is measured as capacitive in absence of loads. The voltage on the faulty phase is very small because it is connected to the ground, then capacitive current is circulating almost in the two healthy phases and this creates a zero-sequence current due to this unbalance. Figure 3.1: The isolated network has capacitive current circulating through the healthy phases in case of single phase earth fault The equations below show mathematically why the zero-sequence current on the faulty feeder measured is inductive if the phase current flowing in the healthy phases is capacitive. The loads have no impact on the zero-sequence current because they are supposed to be balanced in the European distribution power system. 3I0 sound =I A1 + I B1 (3.1) 3I faulty 0 =I A2 + I B2 + I fault (3.2) I f = I A2 I B2 I A1 I B1 (3.3) 3I0 faulty 0 = I A1 I B1 = 3I sound 0 (3.4) Due to this diagram 3.1 and the equations 3.4, it is easily understandable that the measurement of the zero-sequence current of the faulty feeder is the sum of the zero-sequence current coming from every healthy feeder. The calculation can be done for a network with more than two feeders and this will result in a sum of every current in the two healthy phases of each feeder. The zero-sequence current of the faulty feeder will be seen as an inductive current instead of a capacitive current due to the direction of it. The capacitive current from the faulty feeder is not visible in the zero-sequence system because this current comes back through the fault and the sum on the three phase makes zero. The next figure 3.2 shows a simulation on ATP/EMTP of the zero-sequence current I0 of each feeder and the zero-sequence voltage U0 in an isolated network with two feeders. The two feeders network

38 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 38 shows that the steady state amplitude is the same for the faulty and sound feeder because the capacitive current of the feeder in default is not visible. This might be a future problem if the network has small capacitive feeder and one highly capacitive. If this feeder with significant capacitance is faulty, the faulty current measured could be very small. If the feeder is a short overhead line, for example, no zero-sequence current could be measured in healthy condition. All these problems are dealt in the chapter on the fault detection algorithm. Faulty I o Sound I o Steady State V o time [ms] Figure 3.2: Steady state amplitude on the faulty feeder depends on the healthy feeders The figure 3.3 shows the same network diagram but with the symmetrical model of the zero-sequence system. It is simple to understand why I faulty 0 = I0 sound. Figure 3.3: Fortescue representation of the zero-sequence current flows in case of EF Due to the insulation of the transformer - visible on the left, no connection after Z T o, the current that circulate through the F2 measurement transformers will circulate through the F1 measurements transformer in the opposite direction. In this case, the detection of an earth fault in isolated network regarding the steady state is very easy using specific algorithms because the faulty feeder will measure the sum of every capacitive current from the sound feeders and the current measured will be seen as inductive instead of capacitive. The difficulty might come in case of intermittent earth fault as detailed further because no 50 Hz steady state is measured. In this case, transient system must be used for the reason explained further in this report.

39 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK Compensated network In case of single phase earth fault in compensated network, looking at the zero-sequence steady state current on the faulty feeder, the current has also the capacitive characteristic like the sound feeder. If a perfect Peterson coil - i.e. no consideration of the parallel resistance simulating the coil losses - compensates all the capacitive current - i.e. 100% tuned meaning the zero-sequence impedance is infinite - then there is no current in the fault and the faulty feeder is seen as perfectly healthy. The measured zero-sequence current on the faulty feeder will be the current circulating through the sound capacitances of this feeder. Figure 3.4: Fortescue representation of the zero-sequence current flows in case of EF To perfectly compensates the zero-sequence capacitance of the whole distribution network, the admittance of the total zero-sequence system must be zero. This admittance consists in the neutral of the transformer in parallel with the zero-sequence capacitance: 0 = 1 ωc 0 ωl NG (3.5) L NG = 1 ω 2 C 0 (3.6) If the Peterson coil does not perfectly compensate the zero-sequence capacitances then the measured current will be the capacitive current of the faulty feeder minus the uncompensated current. Therefore, if the network is slightly overcompensated, the faulty current will be capacitive with higher magnitude than the current measured in perfectly compensated network. On the opposite, if the network is slightly under compensated, the faulty current will be capacitive with a smaller magnitude. I f =I NG + I C0 (3.7) 1 I f =V 0 ( ωc ) ωl NG R NG (3.8) I f is the fault current, I NG is the current circulating in the transformer neutral, I C0 is the current due to the zero-sequence capacitance and R NG is the resistance emulating the losses in the coil. If the current in the transformer neutral has no active component then the faulty current will be purely capacitive or inductive depending on the tuning factor. The figure 3.5 shows the zero-sequence current I 0 on a sound and a faulty feeder with the voltage U0 in case of a perfectly inductive Peterson coil. The phase angle depends only the Peterson

40 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 40 coil imperfection and not on the inductance value. The current looks more or less capacitive depending on the compensation tuning. Extreme case can occur if the faulty feeder has a small capacitance and the Peterson coil is highly under tuned. This could create a measured zero-sequence current on the faulty feeder that looks inductive instead of capacitive because the faulty current is bigger than the capacitive current of the feeder. The scale is fit for the sake of visibility but does not represent any real amplitudes comparing the voltage and current value. Faulty I o Sound I o Max Sound & Fault feeders V o time [ms] Figure 3.5: No phase angle between the faulty and sound feeder with a perfect Peterson coil In reality, the Peterson coil is not a perfect inductance and can be modeled with a parallel resistance approximately 20 times the value of the reactance. This resistance models the imperfection in the insulation of the windings and the iron losses [Leitloff, 1994][Welfonder, 1998]. Applying a voltage in the transformer neutral creates a small active current in addition to the compensation current because the insulation of the windings is not perfect. The figure 3.6 shows the steady-state current for a sound and a faulty feeder, the faulty feeder has an active component differentiating its steady state from the healthy one. Faulty I o Max Faulty feeder Sound I o V o Max Sound feeder time [ms] Figure 3.6: Phase angle appears between the faulty and sound feeder with a realistic Peterson coil

41 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 41 In some countries such as France [Coemans, 1994], real parallel resistance can be connected in parallel to the coil for fault location/detection purpose by increasing the faulty current. The active current is seen as a phase angle between I 0 on the faulty feeder and I 0 on the sound feeder. The parallel resistance of the Peterson coil creates a way for the circulation of an active current through F2. If the Peterson coil is not perfectly tuned, it does not impact the phase angle of the faulty feeder current but it impacts its magnitude. The magnitude of the voltage has no importance then its magnitude has been scaled to the current magnitude to ease the comparison between the phase angle. Modeling the Peterson coil imperfection: This work has modeled the Peterson coil imperfection and has established a relation between the resistance value and the phase angle of the steady state zero-sequence current with the zero-sequence voltage. Comparing to the significant value of inductance L NG with the small impedance of the transformer and the line, the network can be simplified by neglecting the smallest one. The simplified zero-sequence symmetrical system is shown on figure 3.7. The network modeled has only two feeders but the lines are in parallel therefore the problem can be extended to multiple feeders by considering C0 sound = soundfeeder C 0. The positive and the negative symmetrical systems have also been neglected in the figure for the sake of the illustration and because they have no impact in this problem due to the small value of the transformer impedance compared to the capacitances in these systems. Most of the current is flowing through the transformer. Figure 3.7: Simplified zero sequence system Concerning the sound feeder 1, the current and voltage measurements are directly applied on the capacitance. If a voltage V 0 is applied, F1 will measure a current I 0 = V 0 that has jωc0 sound a phase angle of 90. With these assumptions, the current measured by F2 can be calculated and the phase angle can be determined. The current circulating through F2 is the sum of the current circulating through C sound 0 and the Peterson coil. The variable x is equal to x = R NG ωl NG.

42 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 42 V 0 I F 2 0 =Z(jω) (3.9) Z(jω) =(jωc sound R NG + 1 3jωL NG ) 1 (3.10) 3jωR NG L NG Z(jω) = ω 2 3C0 sound (3.11) L NG R NG + jωl NG + R NG 3ωR NG L NG then Z(jω) = (3.12) ( ω 2 3C0 sound L NG R NG + R NG ) 2 + (ωl NG ) 2 ωl NG and Arg(Z(jω)) = π 2 + atan( R NG (1 ω 2 3C0 sound L NG ) ) (3.13) if R NG =xωl NG (3.14) then Z(jω) = 3xωL NG (3.15) ( ω 2 3C0 sound x) and Arg(Z(jω)) = π 2 + atan( 1 x(1 ω 2 3C sound 0 L NG ) ) (3.16) The next figure shows a graphical representation of the impact of the parallel resistance R NG on the phase angle between I 0 on the faulty feeder and V 0. This result comes from an EMTP/ATP simulation using line distributed model and the theoretical faulty feeder comes from the equation X NG is the reactance of the Peterson coil. The angle is the phase angle between the zero-sequence voltage V 0 and the zero sequence current I 0 on the concerning feeder. Phase Angle comparing to V0 [ ] Faulty Feeder Sound Feeder Eq x=r NG /X NG Figure 3.8: Phase Angle of the faulty feeder depends on R NG A remark regarding this graphic concerns the slight difference between the equation 3.16 and the simulation of the faulty feeder if the x ratio is small. The explanation comes from the fact that we have neglected of the series impedance which might be improper in this condition because the faulty current is higher and the compensation is very bad which creates significant neglected terms in the equation 3.16.

43 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK Transients Every electrical power system consists in a bunch of inductances, resistances and capacitances. All these assembled components will create a resonant system in case of sudden change in the circuit conditions. The sudden change studied in this work is the single phase earth fault in isolated and compensated network. The transients with a higher frequency than the fundamental are the same for both compensated or isolated network because the Peterson coil has a very big impedance compared to the capacitance. Hereby all studied transients are for both network except if it is precised in the report Symmetrical components to study the transients As explained in the first chapter, a phase to earth fault is represented as the connection in series of the three symmetrical components. The symmetrical components have been developed for steady state calculations but according to [Lehtonen, 1992, Greenwood, 1991] they can also be used for transient studies. This conclusion gives us the opportunity to use this model to understand transients phenomena in a simpler way because we assume that there is no mutual coupling between the symmetrical systems. However very high frequencies as the discharging transient discussed in [Welfonder, 1998] may not be described because the assumption to create the three symmetrical systems are not so accurate with such frequencies. In practice, such frequencies are filtered by the anti-aliasing filter of the protection, hereby they will be briefly discussed. The next figure 3.9 shows the zero-sequence current on each feeder using the symmetrical components and using the distributed 1 model using ATP. Figure 3.9: Using the symmetrical components is equivalent to the distributed model for the transients consideration Usually the positive and negative sequence impedances are very small compared to the zero-sequence impedances in such networks because of the transformer impedances. These 1 Distributed model means a network using distributed overhead line and underground cable as provided by EMTP/ATP software. This model has been used to plot the blue curve of this chart.

44 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 44 two systems will be neglect in this section to make the calculation easier. Also the zero sequence system is independent of the loads in Europe due to the delta-wye connection Discharging frequency The discharging transient appears in both isolated and compensated network. This is caused by the sudden drop of the voltage on the faulty phase. The energy contained in the line to earth capacitances of the faulty phase is evacuated through the fault but the line inductance between the capacitance and the fault creates an oscillating system. This frequency is very high - more than 1 khz - because it involves only the capacitance of the line and its inductance. Usually a traveling wave model is used to consider them [Lehtonen, 1992, Pundt, 1963, Welfonder, 1998]. Welfonder has determined an equation of this discharging frequency based of this traveling wave model and concluded this discharging process is depending on the distance of the fault (d [km]) and the linear parameter of the faulty feeder (l d [H/km] and c g [F/km]). f discharge = 1 4d l d c g (3.17) The assumptions for this equation are such as the inductance of the transformer coil is large compared to the inductance of the lines, it can be then considered as opened. The fault is considered as a closed extremity because such discharging frequency occurs only during metallic fault. The voltage on the bus bar is the maximum value and the fault voltage is zero. The wave propagation speed is v= 1 with L and C the inductance and capacitance of the ld d g line per kilometer. The frequency can be found with the fault distance f discharge = v 4d. These assumptions show that only the faulty part of the network has to be considered in the model of the discharging frequency. Figure 3.10: Representation of the discharge of the faulty phase The amplitude of this discharge transient depends on the value of the voltage when the fault happens. Also it varies linearly with the frequency. If the frequency is high, the initial amplitudes can be relatively high. However, in real network, the skin effect and the line

45 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 45 resistance quickly reduces this transient. The figure 3.10 below represents the propagation of the discharging frequency using a three phases diagram Charging frequency When an single phase earth fault occurs, the voltage on the faulty phase is suddenly falling to zero but at the same time it moves the neutral voltage of the transformer and increases the phase to ground voltage on the healthy phases. This voltage variation was explained by the figure 2.7 in the isolated network section. The healthy phase to earth capacitances on the sound phases will be charged by the voltage increasing and it will produce a transient also known as the charging transient caused by the resonance of the inductance and capacitance of the system. It has relatively high frequency - generally higher than 100 Hz and lower than 2 khz. Figure 3.11: Representation of the charge of the healthy phases The Peterson coil is designed to stop the steady-state fault current (at nominal frequency) in the fault but not the transient. This coil is not playing a role because its impedance is too high at the transient frequency. Therefore the contribution of the Peterson coil on this transient can be neglected and the charging transient study is exactly the same as for the isolated or the compensated networks. For example, if the frequency is 100 Hz, it means that the coil impedance will be 4 times larger than the impedance from the capacitances, therefore 80% of the transient will circulate through the capacitances. Figure 3.11 shows how this transient flows in the network. I ta2 labels the transient current in the phase A on feeder 2. The cable-type current transformer only measures the transient from the healthy feeder because:

46 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 46 Sound F eeder 3I0 tsound =I ta1 + I tb1 (3.18) F aulty F eeder 3I tfaulty 0 =I ta2 + I tb2 + I f (3.19) I f = I ta1 I tb1 I ta2 I tb2 (3.20) 3I tfaulty 0 = I ta1 I tb1 (3.21) The t index stands for transient. This equation 3.21 means that even if the protected feeder is very short which means its zero-sequence capacitance is very low, transient will be very high if this feeder is faulty because it does not depend on the own C 0 of the faulty feeder but on the total C 0 from the sound feeders. If this feeder is sound, no transient will be measured because its capacitive current is too small to be measured The charging frequency model The two equations below 3.22 [Welfonder, 1998] and 3.23 [Druml et al., 2003] are describing the charging frequency with the network parameters. Different assumptions are made in the two case. Welfonder is considering the distance of the fault, the phase to phase capacitance C p and the faulty line impedance l d where these parameters are neglected in the equation developed by Druml. Both are considering the transformer impedance and the phase to earth and phase to phase capacitances. f charge 1 2π (1.5L T + dl d )2(C g,tot + C p,tot ) (3.22) f charge 1 1 (3.23) 2π 3L T C 2E According to both equations, not only the faulty feeder parameters is necessary but also the whole network capacitance. This work has made a deeper investigation regarding this charging frequency with the use of the electromagnetic transients program ATP. Both models make the assumption that only one charging frequency occurs in the network because they simply model the sound feeders as a global capacitance. With such model there is only one capacitance which resonates with the transformer and faulty line impedance. However, if the network model keeps every feeder separated and using the symmetrical components as stated in the section 3.2.1, the network model is shown in the figure 3.12 considering three feeders. A zero-sequence voltage step can be considered occurring in the bus bar, therefore every 1 feeder will resonate depending on its own parameter f cf x = LF. If the Peterson coil x C F x is large enough to be neglected, then the transients will circulate through the fault and be measured on the faulty feeder. The figure below 3.13 shows the result of a simulation using very different line characteristics (i.e. underground cable for F3 and overhead line for F1). The measurement on one feeder shows several frequencies and the faulty feeder contains every frequency because of the connection of the fault which is a return path for the sound current as illustrated on figure For example, on the figure 3.13 the feeder 2 is the faulty one, every frequency of the others feeder is contained in this feeder but they do not contain every frequency from the others. Also the magnitude of the FFT is the same which proved that the transient is circulating through the fault.

47 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 47 Figure 3.12: Model of a network with three feeders to characterize the charging transients with symmetrical components Figure 3.13: Three charging frequencies are measured on a network with three feeders Charging transient magnitude considering the fault resistance This small section illustrates the impact of the fault resistance on the transient magnitude and damping. The illustration in this section shows a simulation of the transient with different fault resistance value. The current and voltage signals have been filtered by a band pass filter to suppress the 50Hz component. Therefore the transient is more visible 2. A fault resistance of 0Ω is illustrated on figure The zero-sequence current 3I0 and voltage V0 are illustrated and the phase angle between the voltage and the current in a faulty and healthy feeder can be compared. The faulty feeder shows an inductive transient current and the sound feeder shows a capacitive transient current. This conclusion fits with the schematic on figure 3.11 which shows the transient flow as the steady state flow in an isolated network. Regarding the transient duration, the fault starts at 35 ms and the transient is completely gone at 90ms of simulation which makes almost three nominal periods of useful information to 2 The filter is the same as used in the 7SN600 Wischer developed by Siemens

48 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 48 detect the faulty feeder. The old transient protections are working very well in such condition because they are usually based on the comparison of polarity between the voltage and current transient. It is easy to identify the faulty feeder at the fault inception using this criteria with such clear fault. The transient frequency is around 200 Hz, the simulated network has one underground cable reducing this frequency as stated by the charging frequency equation. The higher frequency seen at the very beginning of the fault corresponds to the discharging frequency, it is usually not visible in the classic protection because they run at 2 khz or maximum 8 khz, which is too small. Transient V o Transient Sound I o Transient Faulty I o time [ms] Figure 3.14: Charging transient with a 0 Ω earth fault The figure 3.15 represents the transient with a 100Ω fault resistance. The transient is still visible but the damping factor is very high which makes the duration very short. The transient exists for only half a second and its frequency does not change with the fault resistance (f charge 1 LC ). The transient on the faulty feeder is still inductive and the sound feeder is still capacitive then the detection is still possible. Transient V o Transient Sound I o Transient Faulty I o time [ms] Figure 3.15: Charging transient with a 100 Ω earth fault Very high resistive fault makes things totally different. The charging transient is no more visible because its energy is too small and the damping very high as shown by the figure 3.16 with a fault resistance of 1.66 kω. It is not possible to measure the charging transient, the discharging is measured but a classic protection device does not see it. This discharging cannot be use to determine if it is capacitive or inductive and detect the faulty feeder the

49 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 49 same way as the charging transient. The other oscillation is the 50 Hz which is not well filtered because it increases slowly as it is considered in the next section of this work. Transient V o Transient Sound I o Transient Faulty I o time [ms] Figure 3.16: Charging transient with a 1.66 kω earth fault contains only 50 Hz signal Transient due to the fault resistance The fault resistance does not have an impact on the phase angle between the zero-sequence current and the zero-sequence voltage. This resistance reduces the charging transient process as considered in the section above and makes the 50 Hz voltage V 0 and the current I 0 growing up slowly. Faulty I o Sound I o V o time [ms] Figure 3.17: Slow increasing of the 50 Hz voltage and current with R fault =1.66kΩ Figure 3.17 shows the increase of voltage V 0 and the sound current I 0 for a fault resistance of 1.66 kω. The faulty I 0 is not growing because it is an overhead line with low capacitances. The time constant of the growing voltage and current depends on the Peterson coil tuning with the zero sequence capacitance and the fault resistance. If the Peterson coil is well tuned and the fault resistance is high, the time constant is the highest. If it is not well tuned, a low frequency oscillation will appear. Based on the symmetrical components, the network in case of single earth fault can be simplified with high resistance fault. The impedances of the line and transformer are neglected because the fault current is very small and their impact does not create significant voltage

50 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 50 drop. The positive and negative sequence circuits have also been neglected because most of the current is flowing through the transformer and not into the symmetrical capacitances. Figure 3.18: Influence of the fault resistance L NG is the inductance of the Peterson coil, C 0 is the total capacitance of the network, R NG is the parallel resistance of the Peterson coil and R f is the fault resistance. This work has developed the equation to model the voltage increasing, firstly by considering a perfectly inductive Peterson coil and secondly by considering a parallel resistance to model the leaks in the coil Neglecting the parallel resistance Firstly the value of V 0 is determined with an infinite parallel resistance R NG. I f is the current through the fault resistance R and s is the Laplace variable: V 0 =E 3R f I f (3.24) I f =I NG + I C0 (3.25) I f =V 0 ( 1 + s2 C 0 3L NG s3l NG ) (3.26) E =V 0 + 3R f V 0 ( 1 + s2 C 0 3L NG ) (3.27) 3sL NG V 0 sl NG Considering the parallel resistance E = s 2 (3.28) 3C 0 L NG R f + sl NG + R f The parallel resistance on the Peterson coil R NG is considered. The same development as the previous section can be used but the faulty current has I RNG. V 0 =E 3R f I f (3.29) I f =I LNG + I RNG + I C0 (3.30) 1 I f =V 0 ( sc 0 ) s3l NG 3R NG (3.31) V 0 =E 3R F V 0 ( R NG + sl NG + s 2 3R NG L NG C 0 ) s3r NG L NG (3.32) V 0 E = s3r NG L NG s 2 9R f R NG L NG C 0 + s(3r NG L NG + 3R f L NG ) + 3R f R NG (3.33)

51 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 51 A simulation on ATP has been done with and without the parallel resistance R NG =20X NG. A Matlab/Simulink model has been created to test equation below and compare it with the simulation. The fault resistance R f =1666 Ω. The next figure shows that the equation fits the simulation but the presence of R NG gives some differences which cannot be neglected. Using Matlab/Simulink, the figure 3.19 shows that the previous equation is correct when we consider the parallel resistance R NG in ATP V o w/out R NG Theoretical V o w/out R NG V o with R NG Theoretical V o with R NG 2 V o [kv] time [ms] Figure 3.19: Validation of the equation considering the parallel resistance Transient due to inception time When an earth fault appears a sudden voltage V 0 is present on the Peterson coil. The connection of an inductance to a sinusoidal system could also create a transient depending on the inception time because the magnetic flux cannot be discontinuous. By solving the equation of the RL circuit as figure 3.21, the equation 3.34 is obtained. The inductance of the transformer has been neglected because it is very small compared to L NG and no R NG. The parameter φ i is the phase angle with the voltage at the fault inception. ˆv 1 i NG (t) = Rf 2 + (ωl NG) [cos(ωt + φ i) cos(φ i e R F t L NG )] (3.34) 2 Figure 3.20: Peterson coil effect on symmetrical components The term φ i is -90 if the fault occurs at the maximum voltage on the faulty phase and is 0 if the fault occurs at the zero-crossing voltage on the faulty phase. If the fault does not

52 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 52 appear at the maximum voltage (i.e. cos(φ i ) 0), a decreasing exponential appears on the zero sequence current. However, the figure 3.21 explains that this current appears only on the faulty feeder because it is the only way for a non periodic signal to circulate. It does not flow through the capacitance. The figure 3.20 shows the same effect but with the symmetrical components representation. The capacitances block the current and the parallel resistance is very large which limits the circulation of current in it. Figure 3.21: Transient current due to the Peterson coil is measured only on the faulty feeder Figure 3.22 illustrates the case if the fault does not occur at the maximum voltage on the faulty phase. The exponential decrease is visible and it confirms that it is only observable on the faulty feeder. The worst case is when a fault occurs near zero volt. This case does not seem very realistic because an insulation breakdown would occur before the voltage is reaching zero. The time constant of this decreasing current is several periods if the fault is nearly metallic. Sound feeder Faulty feeder time [ms] time [ms] Figure 3.22: Decreasing exponential occurs only on the faulty feeder

53 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK Extinction of the fault In compensated network, the fault extinction creates a resonating zero-sequence voltage and current. The figure 3.23 shows the fault the zero-sequence current and voltage oscillating after the fault extinction. The symmetrical components are disconnected and the zero-sequence system is an RLC which oscillates. V o I o Fault Extinction time [ms] Figure 3.23: Decreasing of V0 and I0 after fault extinction The frequency of this system depends on the tuning of the Peterson coil and how much it compensates the network capacitances. If it is 100% tuned, the frequency will be 50 Hz but if it is 90% tuned, it will be 52.7 Hz as the next equation details it: f res = 1 2π L NG C 0,tot (3.35) The zero-sequence voltage and current are slowly decreasing depending on the parallel resistance of the Peterson coil R NG. If the parallel resistance of the coil R NG is small, the decrease of the voltage and the current will be strong but if R NG is high, the time constant of this decrease will be very long. If there is no R NG, there is no decreasing of the voltage because there are no losses. 1.5 x V o V A Fault Inception Fault Extinction time [ms] Figure 3.24: 50 Hz resonating zero-sequence system

54 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 54 The figures 3.24 and 3.25 illustrate this frequency with a parallel resistance of approximately 20 times the reactance of the coil X NG. The first figure is a 100% tuned Peterson coil and the second one is a 90% tuned Peterson coil. The zero-sequence voltage is in blue and the phase to ground voltage of the faulty phase is plotted in red to illustrate the difference of frequency. On the first figure, the voltage V 0 is 50Hz because it is exactly the same frequency as V A. The voltage on the faulty phase is increasing slowly until it has reached the steady state then V 0 will be zero. Here V 0 is 53 Hz because the tuning of the Peterson coil is around 90 %. When V A has reached its steady state amplitude, V 0 will not be exactly zero because the healthy phases are still not stable, V A is oscillating. Some time is necessary until the decrease of V 0 is completed to recover the pre-fault steady state. V o V A Fault Inception Fault Extinction time [ms] Figure 3.25: 52 Hz resonating zero-sequence system In not perfectly compensated network, slow oscillation appears before the voltage is stabilized. This oscillation can be calculated by resolving the RLC circuit. The phase angle between V 0 and V A just after the fault extinction is depending on the tuning of the Peterson coil. Then a 100 % compensated network will have a 180 phase angle but a 90 % will have a 90. The decreasing of V 0 shows that the healthy phases are slowly discharging. 3.3 Intermittent and restriking earth fault In the literature the difference between intermittent and restriking earth fault is not clear. Lorenc is characterizing these faults by a duration time and a pause time [Lorenc et al., 2003]: Duration time is the time during which a fault is present in the network. Pause time is the time between the extinction of the fault and the inception of the next one. The healthy phases are slowly discharging by the resonance of the zero-sequence system. The duration time of the intermittent and restriking earth faults are almost the same. It ranges from a few ms to some periods. Concerning the pause time, it seems that intermittent earth faults have a regular and shorter pause time than the restriking earth faults. Usually intermittent single phase earth

55 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 55 fault has a duration time less than 100 ms. Schinerl describes the intermittent earth fault as a series of insulation breakdown in underground cables because of reduced voltage withstand [Schinerl, 2005]. This also creates a periodic ignition of the fault which can be characterized by regular and short pause time also. This is not a general definition accepted by the whole scientific community but this report uses this definition Shape of an intermittent earth fault The shape of the fault can be understood with the theory presented in the above sections. The fault is generally one peak followed by a few cycles before the fault extinguishes itself. This peak consists in the sum of the charging process, discharging process and Peterson coil effect [Altonen et al., 2003]. In most of the intermittent earth fault, the recordings can be explained as: First fault, a high peak is present because the healthy phases are not charged. This high current is mostly a charging transient or the Peterson coil effect. Once the fault is gone, the zero-sequence current I 0 is capacitive; this is the resonance of the zero-sequence system. I 0 amplitude depends on the capacitances of the feeder. The healthy phases are slowly discharging. This is the pause time. The second fault appears. It has a smaller charging current, lower than the first peak because the healthy phases are almost charged, a small discharging current because the faulty phase is almost discharged and perhaps a small Peterson coil effect depending on the inception time and on the voltage amplitude. The sampling frequency of these recordings is 800 Hz which is too slow to see the discharging frequency if a discharging process was visible. First fault High current to charge the healthy phases V o No fault Slow Discharge of the healthy phases End of the second fault Faulty I o End of the first fault Second fault Less amplitude because healthy phases are almost charged time [ms] Figure 3.26: Typical intermittent earth fault When the fault ignited again, the zero-sequence voltage V 0 is sometimes close to zero or sometimes close to the maximum. It depends on the tuning of the Peterson coil as explained in the previous section. Regarding the coil current and voltage, the voltage is V 0 and the current is a 50 Hz or lower signal which is globally equal to the sum of the zero-sequence current. The peaks are

56 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 56 very short so the Peterson coil has no effect on them because the inductance of the Peterson coil is high for transient above 50 Hz. The peak current circulates through the fault because its impedance is much lower. The only effect of the Peterson coil is a decreasing exponential current as described above. This effect could be visible on the first fault but it will be very weak in case of intermittent earth fault because the voltage ˆv f at the ignition of the fault is small. The next figure 3.27 shows this effect on the first fault. First fault Transient due to the Petersen coil effect V o Faulty I o End of the first fault Slow discharge of the healthy phases New fault time [ms] Figure 3.27: Typical intermittent earth fault with coil effect The detection of the faulty feeder could be difficult with these faults because the fault is short and has small energy. It is impossible to identify the faulty feeder during the pause time because the fault has gone Shape of restriking earth fault The fault on restriking earth fault is the same as intermittent earth fault; it is short and it consists in the sum of the discharging, charging and Peterson coil effect. However, the restriking earth fault has a longer pause time as the next figure illustrates it. Discharge of the healthy phases Resonance of the zero sequence system V o Faulty I o Second fault Filtered fault time [ms] Figure 3.28: Typical restriking earth fault The discharge of the healthy phases is longer meaning that the voltage on the faulty phase recovers a higher amplitude before the second fault occurs. Then the amplitude of the second

57 3. SINGLE PHASE TO GROUND FAULT IN COMPENSATED NETWORK 57 fault can be much higher than the intermittent fault because the healthy phases are more discharged. On this recording, the problem is the extremely short duration of the fault. The fault lasts a few milliseconds. Therefore, the fault is strongly filtered by the measurement system and sometimes only one sample in a low sampling frequency device represents the fault. In reality, the zero-sequence current and voltage must be the highest during the fault duration as explained previously and then decreased. The detection of these faults is also difficult for the same reason as the intermittent earth fault; the fault has a really short duration time. But the restriking fault has more energy due to the longer discharge of the healthy phases. As for intermittent earth fault, it is not possible to detect the faulty feeder during the pause time because every feeders act as a capacitance.

58 4. Confrontations of the Theory with the Field 4.1 The topologies of the distribution Distribution network have many different topologies which leads to different fault detection strategies. The simplest network structure is the radial structure where the feeders are connected to the main substation and they feed their loads where secondary substations are connected. Usually the feeder has branches where lines are connected to substation to feed a different area of several hundreds meters next to the main power line. The feeder is known as a tree structure. Another common topology is the loop structure. Two feeders or more are connected to the main substations and their ends is connected in the same secondary substation. The feeders create an electrical loop. Some operators disconnect the ends between the two feeders so that no current can circulate. If the ends are disconnected, the topology is called open ring and if they are connected, the topology is called closed ring. Even if the network is run in open ring, operators have the possibility to run it in closed ring, usually for fault location purpose as explained in the related chapter. Of course, many of these loops have branches as the radial topology. In distribution network, the loads are connected along the feeders. This is a huge difference with the transmission grid where lines are powering loads at the end which is called a node in a meshed network. The loads are distributed and several substations are connected to the main feeder. The rise of ecological awareness and the liberalization of the electrical market have significantly increased the distributed generation (DG) such as photovoltaic panels, wind turbine, co-generation, etc. They are also placed along the feeder and might change after a single phase earth fault. A survey with six German Distribution System Operators (DSO) has indicated that they use mainly loop structure operating in open ring condition. Almost every DSO has distributed generation in its network. The results are shown on table 4.1. The distributed compensation is an additional Peterson coil placed in the network. It can happen in case of very strong capacitive feeder. The smaller Peterson coil is connected in a secondary substation. The figure 4.1 below shows an example of real distribution network in Germany. Distributed compensation coil is on the feeder J02, the feeders are radial with branches and operated in closed ring. Many tests case have been provided by this DSO which has permitted the test of the algorithm developed during this work on difficult and complicated cases. 58

59 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 59 DSO 1 DSO 2 DSO 3 DSO 4 DSO 5 DSO 6 Radial x 50 % 40 % x 20 % x Open Ring 100 % 50 % 60 % 90 % 80 % 80 % Closed Ring x x x 10 % x 20 % DG 30 % Yes Yes Yes x Few Distributed Compensation 30 % x 0 % x x x Table 4.1: Survey of the German Distribution Network topology 4.2 The circulating current problem Asymmetric series impedance The problem found with the recordings was a strong zero-sequence current without zerosequence voltage or a very small zero-sequence voltage during healthy operation. This observation was made only in loop topology and not in radial network, the comparison between the current level in each feeders from the same loop has revealed that the current is actually circulating in the loop. This current generation comes from a zero-sequence voltage difference between the two feeders that make the loop. The cable has a small series impedance and therefore a small voltage difference creates a strong zero-sequence current. This voltage difference comes from an asymmetry of the series phase impedance [Druml et al., 2009, Druml et al., 2001, Kalyuzhny and Kushnir, 2007]. This creates a mutual coupling between the positive sequence and the zero sequence system, therefore when there is strong load in the network, the zero sequence current will increase. The figure 4.2 shows the problem that occurs when the phase impedances are not symmetric in the feeder 1 and the feeder 2. The load is symmetric and a loop structure is feeding it which is often the situation in the distribution network in Germany. If each phase of a feeder has the same impedance then the current will be uniformly distributed between the two feeder depending on the impedance differences. However if the phase impedances are not equal within one of the feeder, the current distribution will not be balanced. The example in this section shows an impedance which is two times smaller than it should be. The consequence is that a current of 66 Amps is flowing through this impedance instead of 50 Amps, the sum of the phase current gives a zero-sequence current different of zero even for the balanced feeder. The zero-sequence current looks like it circulates in the loop; because the whole system is balanced this is the only electrical way it has. This is a real problem for protection using the 50Hz component and the zero-sequence current. The example is a simple problem because it does not consider the mutual coupling between the phases. If it has been considered then this circulating current could occur even if the series impedance is the same and therefore the cables buried in the ground are exactly the same. The circulating current can be mathematically described as a coupling between the symmetrical system. The impedance of a three phase feeder can be expressed by the following equation with the matrix Z abc : Z abc = Z a Z ab Z ac Z ba Z b Z bc Z ca Z cb Z c (4.1)

60 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 60 Figure 4.1: Pfalzwerke distribution network This matrix represents the series impedance and mutual coupling of a three phase conductor. For example, Z ab is the impedance between the phase a and the phase b. Z a represents the impedance of the phase a. The Fortescue matrix transformation A can transform this impedance in symmetrical components: A = a 2 a 1 a a 2 where the symbol a is the phase angle of 120 : (4.2) a = e j 2π 3 (4.3) The matrix impedance of the symmetrical components is computed with the equation below: Z 012 = A 1 Z abc A (4.4)

61 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 61 Figure 4.2: Asymmetry in the series phase impedance creates circulating current The result of this equation leads to the following matrix: Z a + Z b + Z c +Z ab + Z bc + Z ca +Z ba + Z ac + Z cb Z a + az b + a 2 Z c +(Z ab + az bc + a 2 Z ca ) +a(z ba + a 2 Z ac + az cb ) Z a + a 2 Z b + az c +(Z ab + a 2 Z bc + az ca ) +a 2 (Z ba + az ac + a 2 Z cb ) Z a + a 2 Z b + az c +a 2 (Z ab + a 2 Z bc + az ca ) +(Z bc + az ac + a 2 Z cb ) Z a + Z b + Z c +a 2 (Z ab + Z bc + Z ca ) +a(z ba + Z ac + Z cb ) Z a + az b + a 2 Z c +a 2 (Z ab + az bc + a 2 Z ca ) +a 2 (Z ba + a 2 Z ac + az cb ) Z 012 = Z a + az b + a 2 Z c +a(z ab + az bc + a 2 Z ca ) +(Z ba + a 2 Z ac + az cb ) Z a + a 2 Z b + az c +a(z ab + a 2 Z bc + az ca ) (4.5) +(Z ba + az ac + a 2 Z cb ) Z a + Z b + Z c +a(z ab + Z bc + Z ca ) +a 2 (Z ba + Z ac + Z cb ) Usually the mutual coupling between the phase impedance is considered as the same for every phase. This assumption makes the matrix Z 012 diagonal and no coupling between the symmetrical systems exist. Z 012 = Z Z Z 2 (4.6) Z 0, Z 1 and Z 2 are respectively the zero-sequence series impedance, the positive-sequence series impedance and the negative-sequence series impedance. The position of the cables influences the series impedance of the feeder. The mutual coupling between the phases is the same if the cables are laid in a trefoil position as shown in the figure 4.3 because this impedance depends on the distance between the two electrical conductors. In the trefoil position this distance is equals but not in the parallel position. The unbalanced series impedances create a mutual coupling in the impedance matrix. Therefore, the equation 4.6 becomes a non diagonal matrix.

62 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 62 Z ab/ba Z bc/cb Z ab/ba Z bc/cb Z ac/ca Z ac/ca Figure 4.3: Single conductors in parallel and trefoil position Z 012 = Z 0 M 01 M 02 M 10 Z 1 M 12 M 20 M 21 Z 2 (4.7) In this case the series impedances are equals and the symmetrical system coupling comes from the difference in the impedance mutual coupling. In the case described by the figure 4.2, the mutual coupling also comes from a difference in the series impedance. Therefore if the mutual coupling is not neglected, the following equation clearly shows that the generation of a positive sequence current can generate a zero sequence voltage: V 0 V 1 V 2 = Z 012 I 0 I 1 I 2 (4.8) The figure 4.4 represents the coupling between the zero-sequence system and the positivesequence system - the negative-sequence system is neglected. During healthy operation, the zero-sequence voltage and current are usually very small in European distribution networks because the loads are balanced. Many protection devices as described in the next chapter 2 use the zero-sequence components to detect a single phase earth fault. The presence of the zero-sequence voltage can be a criterion for the detection of such an earth fault. In a radial network, the small V 0 generated produces only capacitive current because it is the only way out for the current and this does not disrupt the algorithm because this current is very small and healthy. However, in loop the voltage difference creates random zero-sequence current which will disrupt some algorithms. More complex system can be found with multiple loops in the network where there is coupling between the positive and zero-sequence system but also between the loops themselves Network coupling Circulating current can also happen if is the network is perfectly symmetric. If a network with zero-sequence current is close to a network with loop structure, a magnetic coupling can occur between the two networks and therefore zero-sequence current will circulate in the loop due to an induced voltage. This problem is usually encountered in railways network where loads are not symmetric. The figure 4.5 illustrates this problem. The circulating current can also be temporary if the parallel network has a single phase earth fault which leads to strong zero-sequence current. A low zero-sequence voltage will be measured but a strong zero-sequence current [Druml et al., 2009].

63 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 63 Figure 4.4: Zero-sequence voltage is measured during healthy operation due to mutual coupling Illustration with real recordings and simulations The Pfalzwerke network illustrated in 4.1 operates two closed ring structure with zerosequence circulating current measured. The recordings have been done by a digital fault recorder SIMEAS-R at 16 khz. The recordings of the zero sequence voltage show no voltage before the fault because the threshold of the SIMEAS-R is too high and therefore the triggering occurs only during single phase earth fault. According to the simulation of the network, the voltage is around 20 V primary before the fault inception which is below the trigger of the SIMEAS-R. The figure 4.6 shows circulating currents in the German distribution network. Circulating currents are measured in both loops. The proof that they are circulating is that the sum of the four currents is zero. The remaining current is mainly the capacitive current created by the small zero sequence voltage. In the loop of two feeders, the circulating current is around 1 Amp primary. In the loop of four feeders, circulating currents are between 2 Amp and 3 Amp primary. The voltage shows the presence of a fault in the network because the voltage produced by the unbalanced impedance seems to be too small. For a fault, the amplitude is varying at each period and the signal is not as stable as the circulating current. Around 20 earth faults have been recorded from this network, most of them were temporary. The circulating current has always been measured on the loop of four feeders with different but very stable amplitude. These measurements seem to consolidate the idea of a coupling between the load or positive sequence system and the zero sequence system. On the loop of two feeders, the circulating current was not always measured and the amplitude was always smaller than on the multi loop. Due to this circulating current, the earth fault signal is corrupted by a current that does not have specific behavior - i.e. capacitive or inductive. In compensated or isolated networks, several protection devices are using the capacitive behavior of the sound feeder as reference. Anything that has a non capacitive behavior will be considered as a faulty feeder. For example, an algorithm evaluating the active current as a fault indicator will measure an active current on every healthy loop. This can lead to wrong fault detection but this problem will be handled in the next chapter.

64 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 64 Figure 4.5: Circulating current due to coupling with parallel asymmetric network A network with a loop of two feeders and a loop of four feeders has been simulated trying to reproduce the real network from the field measurement with the data available. Underground cables have been studied; the feeders are in parallel for 2 kilometers and are separates by approximately 40 cm. The length of the lines has been adapted to match the zero sequence capacitance of each feeder of the real network and its serial impedances. The position of the cables has been set in the way to obtain a difference in the phase impedance and consider the mutual coupling between the loops. However, the flat position has not been implemented because the distribution system operator had indicated that the cables were laid in a trefoil position. A trefoil position has been implemented without symmetrical position to obtain a mutual coupling between the systems. There are two different bus bars connected to their own transformer but these transformers have the same neutral and the Peterson coil is compensating both networks with an overcompensation of 10%. Each transformer has a nominal power of 10 MVA. The four feeders loop consists only of cables and the two feeders loop consists of a mix of overhead lines and cables. The simulations have been performed, for different value of the perfectly balanced load from 0 to 50% of the nominal power of the transformer. The zero sequence voltage remains very small and does not disturb the protection devices. Its maximum amplitude has been measured to 0.5% of the nominal voltage. This voltage is measured on the both bus bar and the radial feeder will produce a zero sequence current which is not circulating. However, this zero sequence current measured on the radial feeder is caused by the voltage on the zero sequence capacitances of the line. This current is a sound one for the protection devices that protect the network. The circulating current amplitude is proportional to the load because the positive sequence current is directly influencing the zero sequence system. The zero sequence current can represent 6% of the nominal current of the network. Simulations have proved the link between the positive sequence system and the zero sequence system due to unbalanced serial impedances in the loop. This current can have a big impact on protection because this current does not have the expected behavior for a proper detection of the faulty feeder. In case of high impedance fault it can be observed that the zero sequence current caused by the fault is smaller than the zero sequence circulating

65 4. CONFRONTATIONS OF THE THEORY WITH THE FIELD 65 U 0 [V prim ] I 0 [A prim ] I 0 [A prim ] I 0 [A prim ] J03 J07 Circulating current J14 J15 Circulating current J16 J17 Fault Inception 0 Circulating current time [ms] Figure 4.6: Circulating current before the single phase earth fault on feeder J03 and J Loop of two feeders Loop of four feeders Zero seuqnece current [A] Load (% nominal power transformer) Figure 4.7: Simulation of the load power on the zero sequence circulating current current. However, this circulating current is probably steady during the whole fault because the load is not disturbed by a single phase earth fault in such network. The phase to phase voltage does not vary in case of single phase to earth fault. This current is then stable if the consideration that the load is constant during the time window for the earth fault detection. Estimating the phase angle and the amplitude of this current during the pre fault state could allow filtering this component without filtering the 50 Hz component produced by the fault at least for the first 100 millisecond after the fault inception. Active filter and non linear filter could be a solution [Druml et al., 2009]. This problem has been presented during the IEEE PES GM Conference [Loos et al., 2012].

66 5. Summary This chapter has introduced the neutral problem of the transformer and the connection of the distribution network to the earth. The neutral connection choice depends on the will for a rapid tripping time, safety, material protection and faulty operation of the network in case of single phase earth fault. The solidly grounded networks have a strong faulty current leading to an easy fault detection in case of low impedance fault. Isolated networks have faulty current magnitude depending on the total zero sequence capacitance and need extra insulation to handle the voltage increasing on the healthy phases. The compromise between these two networks consist in the installation of a resistance to limit the faulty currents and the voltage increase on the healthy phases. This strategy is used for some industrial process where a continuous operation even during a phase fault event could save a significant amount of money. Then the compensated network is another solution used in some areas for distribution network to reduce the fault near 0. An inductance is placed in the transformer neutral and its value is the same as the total zero sequence capacitance of the network. It results in a therotical infinite impedance of the zero sequence system. The impact of a single phase earth fault in compensated and isolated network has been presented. The steady state current is completely different between these two stragies. The isolated network has an inductive faulty current seen from the zero sequence system and the compensated one has capacitive faulty current with a slightly active part due to the coil imperfection. The transients are studied, the one with the highest frequency is the discharging transient caused by the sudden voltage drop on the faulty phase, its value is determined using the distributed line model. Then the most visible and useful transient is the charging transient caused by the voltage increasing on the healthy phases. This transient has a capacitive behavior on the sound feeder but an inductive value on the faulty feeder in the isolated and compensated network. Others transients have been considered such as the coil transient due to a magnetic flux discontinuity at the fault inception. This decaying current is measured only on the faulty feeder. Then the transients occuring in case of high impedance is presented and modeled with some equations developed during this work. At last, the decaying voltage after a recovery is described. The network can recover its initial healthy value several tenth of periods after the fault is gone. The reality has shown the impact of the Peterson coil which creates intermittent earth fault by stopping the current of the steady state. The transients discussed in this chapter are visible during such fault but the power decreases during restriking because the network has not recovered completely when the fault reappears. A confrontation of the developed theory with recordings have shown that circulating current happens in loop structure. Therefore modeling of this event has been made and has shown that unbalanced impedance creates mutual coupling between the symmetrical system causing zero sequence current during healthy operation. 66

67 Part III Single Phase to Ground Fault Detection Algorithms 67

68 1. Introduction This second chapter presents two algorithms developed to detect single phase-to-earth fault in compensated and isolated network. Both methods are based on the statement that the sound feeder can be considered as pure capacitance in the zero-sequence system while the faulty feeder is not. The first developed method is the C0 method which detects the deviation from a pure capacitive model and indicates if the feeder is faulty. The second method is a directional method measuring the active energy flow in each feeder to determine the forward or reverse direction of the fault. The first section presents a review of the existing methods to detect the fault in compensated network. This work focuses mainly on the sensitivity regarding the fault impedance and the tripping delay. Depending on the algorithm, some methods are intrinsically more sensitive to the fault impedance (e.g. they are not using only the beginning of the fault) but they are not faster for tripping. We present every steps of the algorithms with figures describing the phenomena. The technical specifications with a scientific explanation of each decisions is detailed such as the filter used, the numerical integration of the signal, the length, etc. This is made for both the C0method and the directional method. The technical questions linked to the prototype development is detailed in the chapter IV. Some basic simulations and recordings are presented to illustrate the performance of the developed method. Complicated tests made during the development of the prototype are also referred for the interested readers. This second chapter presents the core of this work made during the first and an half year of this PhD thesis. This part has been completed by the delivery of a functional prototype to Siemens AG which has led to a new product released in mid

69 2. Review of today fault detection devices 2.1 The Wischer principle Several decades ago, Siemens AG has developed a method to detect earth-fault in compensated and isolated network. The protection is an analog electronics device considering the fault inception. The protection is called Transient earth-fault relay SIPROTEC 7SN600 and the principle is based on the Wischer principle [AG, 2010]. A picture of the device is illustrated by the figure 2.1. Figure 2.1: The 7SN600 transient earth-fault relay from Siemens The Wischer principle is built around the transient flowing assumption developed in and considers that the transient is the same for both the compensated network and the isolated network. The aim of this method is to identify the direction of the charging transient flow in the zero sequence system. The figure 2.2 shows a diagram of the principle. To do that, the 50 Hz component of the current and voltage signals must be filtered. In practice, a oscillating circuit is set playing the role of a band-pass filter centered at 50 Hz. The output of this filter is then subtracted from the original signal. This operation results in the transient signal whose frequency is usually higher than 100 Hz. The frequencies smaller than 100 Hz are filtered due to the band-width. Once the transient is isolated, the polarity of the fault inception is computed. This polarity is computed by comparing the instantaneous value with a threshold. If the transient reaches this threshold then it will be considered as positive or negative. The transient is always decreasing therefore the polarity is determined for the first increase of the signal. If this first inception maximum is missed then the logic will be wrong because the current and voltage 69

70 2. REVIEW OF TODAY FAULT DETECTION DEVICES 70 I0 Oscillating circuit 50 Hz - I0 Transient + V0 Oscillating circuit 50 Hz - V0 Transient Comparator Direction + Figure 2.2: Detection of transients in the Wischer principle have a phase angle of 90 and not then the polarity after a zero crossing is changing. The consequence of this principle is that the Wischer logic uses only a very small part of the energy available in the transient because it uses only the magnitude at the first maximum which reduces its sensitivity regarding fault impedance. If the polarity of the transient has been determined, the logic table 2.1 is used. If the voltage and current polarity are the same then the fault is in reverse direction, otherwise it is in the forward direction. It could happen that the voltage or the current is too small and cannot be measured, in such case no indication is provided to the user. I V Result Pos Neg Forward Pos Pos Reverse Neg Neg Reverse Neg Pos Forward Pos/Neg - none Table 2.1: Wischer direction logical table Additional analog logic has been implemented in the relay such as detection of continuous earth fault based on the presence of a zero-sequence voltage. The Wischer principle is very simple and therefore very reliable. However, several tests have been made during this work regarding the sensitivity of this protection and the conclusions were that it was not very sensitive for fault impedances higher than 1 kohm [Masa, ]. This can easily be explained with the theory developed in the high impedance fault section where the charging transient cannot be measured In general, the charging transient does not exist anymore once the fault is higher than 1 kohm therefore all the signal is at 50Hz which is filtered by the device. The consequence is that the protection does not see any transient from which it can determine the fault direction. However, the theory developed in this work has shown that the fault inception still indicates a fault direction and will be considered in the proposed algorithms. Another problem with this principle is the case of strongly capacitive network. More and more distribution networks are fully underground in cities which makes them very capacitive. As stated in the charging transient frequency, the more the network is capacitive the lower is the frequency. Some practical cases have shown that the transient frequency could be lower

71 2. REVIEW OF TODAY FAULT DETECTION DEVICES 71 than 100 Hz which is strongly filtered by the relay. Again, this case shows that the filtering of the 50 Hz component destroys some useful information about the fault and hence reduces the relay performance. On the contrary, this principle seems to be unaffected by the circulating current because they are only a 50 Hz part of the signal which is filtered by the device. However, the continuous fault indication might be impacted by the circulating current because it uses the zero-sequence voltage presence to indicate if the fault is still present. This case is very specific because zerosequence voltage is usually very small with circulating current for the reason explained in the last chapter. Many devices are operating with similar principle with the comparison of the polarity such as [Trench,, Vamp, ]. 2.2 The QU-method The a-eberle company has developed a digital device ago based on the QU-method. The protection is called Earth fault-detection-relay EOR-D and it is able to work in isolated and compensated network [A-Eberle, 2004]. The figure 2.3 presents a picture of the device. Figure 2.3: The EOR-D device of a-eberle The QU method has been presented in 2003 by [Druml et al., 2003, Druml et al., 2009] and it is based on the charging transient and its capacitive behavior in sound feeder. The statement that summarizes the principle is that if the sound feeder can be considered as a simple capacitance in the zero-sequence system, the detection can be made if the feeder does not act like a capacitance. By measuring the zero-sequence voltage and zero-sequence current, the algorithm will integrate the current to obtain the zero-sequence charge. Then the following equation will have to be satisfied: v 0 (t) = v 0 (t 0 ) + 1 ˆ t i 0 (τ)dτ (2.1) C 0 An illustration of the principle is made on figure 2.4. A QU diagram with the voltage on the X-axis and the integration of the current on the Y-axis clearly identifies the sound feeder because it is a straight line. The faulty feeder does not have this behavior but it does not have to be modeled because the capacitive model of the sound feeder is very simple and a deviation from this model can indicate if the feeder is faulty. The determination of the fault direction can be made by looking at the slope at the fault inception. If the slope is negative, it means the fault is forward and if it is positive it means the fault is reverse. The analogy with the table used by the Wischer can be made, if the t0

72 2. REVIEW OF TODAY FAULT DETECTION DEVICES x 104 Fault I 0 Sound I 0 V q 0 Faulty q 0 Sound 1 q 0 (As) Time [ ms ] V 0 [p.u] Figure 2.4: Illustration of the QU method current and voltage and the same polarity then the slope will be positive. The slope can be computed as the derivative of the dq 0(v 0 ) v 0 at the fault inception. Several tests have been made using an Omicron CMC256 to send current and voltage signal simulation to the device. The EOR-D is very sensitive for high impedance fault and detect fault up to 5 kohm depending on the network topology and characteristics. The device provides also a direction indication and therefore needs the inception of the fault to make a correct detection. If the beginning of the fault is missed for any reason then the algorithm is blocked and no indication is given. The device is affected by the circulating currents because it does not filter the 50 Hz component unlike the Wischer principle. However a second version of the device, the EOR- 3D, can handle this problem by using an active filter method which filters only the circulating and not the faulty part of the signal. 2.3 The Wattmetric function Another classic way to detect single-phase earth fault in compensated networks the Wattmetric function. The statement of this protection is that the faulty feeder generates a negative active power and the sound feeder produces positive active current. According to the considered theory, this is clear because the current and voltage transient had the same polarity during a single phase earth fault on a sound feeder but had 180 of phase angle for the faulty feeder. The Wattmetric function does not filter the 50 Hz component and this component does not have a 180 phase angle for the faulty feeder. Therefore, the measurement of the phase angle will depend on the compensation factor of the Peterson coil. The figure 2.5 below illustrates the computation of the power of the same signal as the QU-method. Depending on the zone of the results, the Wattmetric function shows which feeder is faulty. This function works well if the voltage and current do not have phase angle error measurement. In case of high impedance faults, the difference between the faulty and the sound feeders is very small and the power phasor could be in the unknown area where no decision can be made with sufficient confidence.

73 2. REVIEW OF TODAY FAULT DETECTION DEVICES 73 3 x Unknown Q0 0 Forward Fault Reverse Fault P0 x 10 5 Figure 2.5: The Wattmetric function decision criteria

74 3. The faulty feeder C0 method algorithm 3.1 The capacitive behavior of the sound feeder A model of a sound feeder has been detailed in the previous chapter and we assume that a sound feeder behaves as a capacitance. The steady state is clearly a capacitance and the charging transient does act as a capacitance also. Moreover the non capacitive effects occur only on the faulty feeder such as the coil effect due to a fault inception not at the voltage maximum or the coil imperfection creating an active current flow. The protection device has an anti-aliasing filter which limits the frequency to 2 khz for the SIPROTEC v4 and 16 khz for the SIPROTEC v5. The impact of the discharging frequency is neglected and its energy is usually much smaller than the others phenomenon. The equation of the sound feeder for the whole signals is: ˆ C 0 v 0 (t) = i 0 (τ)dτ (3.1) The zero-sequence system is only considered because its impedance is much larger than those of the positive and negative sequence. The measurement of the zero-sequence current and zero-sequence voltage are provided by neutral current and voltage transformer or three phases measurement transformer. In this last case, the zero-sequence signals are computed by the protection device using the next two equations: v 0 (t) = 1 3 (v A(t) + v B (t) + v C (t)) (3.2) i 0 (t) = 1 3 (i A(t) + i B (t) + i C (t)) (3.3) Also the zero-sequence current and voltage can be obtained from a sensitive input in the digital relays which improved the accuracy. Regarding the faulty feeder, the capacitive behavior is not verified. Firstly, the steady state has an active part depending on the leakage of the Peterson coil. Secondly, the charging transient is inductive. And thirdly, if the fault appears not in the maximum voltage, a slowly decaying transient will be measured. All these phenomena could be modeled independently and identified to detect the faulty feeder but a general assumption could be: ˆ C 0 v 0 (t) i 0 (τ)dτ (3.4) The strongest advantage of this consideration is that every phenomena is considered whatever the frequency is. Compared to the Wischer principle, more information will be used 74

75 3. THE FAULTY FEEDER C0 METHOD ALGORITHM 75 because no filter is needed and because the signal after the fault inception can also be used to enhance the faulty feeder detection. The Wattmetric function does use every information but only at the fault inception because it computes a power which is the largest at the fault inception that moment. The QU-method it is much more sensitive at the fault inception because it considers every phenomena which are not capacitive. Therefore it is a better model of the wattmetric function but it does not run if the fault inception is missed and then cannot detect the faulty feeder. 3.2 The algorithm The idea of our new algorithm is to determine iwhich feeders acts as a capacitance. For this purpose, only the measurement of the zero-sequence current 3I0 and the zero-sequence voltage U0 are required. The following method has been presented during the CIRED conference in 2013 [Loos et al., 2013a]. This method has also been patented by Siemens AG. Based on the capacitance equation 3.1, the algorithm detects if the feeder is faulty or not. Firstly the zero-sequence current and the zero-sequence voltage of each feeder must be measured. Secondly, the zero-sequence charge is computed by integrating the zero-sequence current: q 0 (t) = ˆt t0 i 0 (τ)dτ (3.5) From this result and if the zero-sequence capacitance of the feeder is known, an error signal can be computed: ɛ(t) = v 0 (t) 1 C 0 q 0 (t) (3.6) However, the zero sequence capacitance is usually unknown. It has to be estimated from the measurements. A least squares method can be applied to estimate the zero-sequence capacitance if there are enough samples. The least square method will tend to reduce the value of ɛ because it reduces the distance between the straight line and the samples as mathematically detailed in 3.2. Physical criteria can be set such as C0 must be only positive and belong to a range bounded by known minimum and maximum values. Such criteria are very powerful especially for low impedance faults where the straight line from a least square method has a negative slope as the figure 3.1 illustrates it. The computation of the error signal can be graphically understood as the distance between the measured voltage and the slope. The distance is always vertical because the Volt unit is much more important than the Coulomb unit in this problem. The figures 3.2 below shows the two terms of the equation 3.6, the blue curve is the faulty part of the signal which does not match at all the voltage curve instead of the red dashed curve fitting perfectly the voltage curve. The second figure on the right illustrates the error signal; a strong error signal still exists during the steady state, the explanation is because the faulty feeder has very low capacitance (overhead line) and the current measured is inductive instead of capacitive. This figure proves why most of the compensated network protections for single phase to ground fault are transient protection, once the steady state is reached, the difference between the faulty and the sound feeder is very hard to measure. The capacitive model is also verified

76 3. THE FAULTY FEEDER C0 METHOD ALGORITHM Samples LS line LS Line Samples V 0 [V] 20 V 0 [V] 0 0 Line slope = 1/C0 ε(t) Slope but feeder faulty q 0 [C] x q 0 [C] x 10 3 Figure 3.1: A least square method is necessary to get a C0 value in this case because the transient of the sound feeder matches very well the transient of the voltage which is not the case for the faulty feeder. However once the steady state reached, the difference is very small. ε(t) [V] V 0 q0f aulty C0 q0sound C time [ms] error ε(t) [V] x 105 ε(t) Faulty ε(t) Sound time [ms] Figure 3.2: In case of low impedance fault, the error signal is very high The next figures 3.3 show a more difficult case with a high impedance fault. The difference between the sound and the faulty feeder is extremely tight and there is a strong need to catch the fault inception to get most of the faulty information required to make a decision. However, due to the increasing of the voltage, the information about the faulty feeder lasts longer as seen in the plot of the error signal. Some discontinuities can be seen on the faulty part, this is caused by the re-estimation of the zero-sequence capacitance each period. Thirdly the integral of the squared error is computed to accentuate the extreme variation. The integral starts from the fault inception t0 until the present t and stops once the fault has disappeared. int ɛ (t) = ˆt t0 ɛ 2 (τ)dτ (3.7) The integration has a memory impact on the detection, this is very important for high impedance fault where the difference between a faulty feeder and a sound feeder is very small.

77 3. THE FAULTY FEEDER C0 METHOD ALGORITHM V 0 q0f aulty C ε(t) Faulty ε(t) Sound q0sound 50 C0 20 Voltage [V] 0 ε(t) [V] time [ms] time [ms] Figure 3.3: High impedance fault with error signal The small differences will be accumulated and after several periods, the difference between the sound and faulty feeder will be much easier to detect. The figure 3.4 shows the integration of the signal represented at the figure 3.3, the y-axis is in logarithmic value which makes the difference between the sound and the faulty feeder significant Faulty Sound ε 2 [V 2 s] time [ms] Figure 3.4: Integration of the error signal to increase the sensitivity of the algorithm The value drops at 120 ms because the algorithm computes five periods and reset the value to avoid drifting of the value. The detection is easiest during the fault inception, however, the next part of the figure shows that the difference between the sound and faulty feeder is visible - there is a factor 40,000 between both signals - and a detection can be made even if the algorithm misses the fault beginning. This functionality is not possible on the device presented in the first section because they are all focus on the transient and does not make use of the steady state component. The reset of the integral value put it to zero but it increases linearly which is not well represented on the figure because of the logarithmic scale. The distinction between the faulty feeder and the sound feeder is made by a threshold. The design of this threshold is quite complex because the value of the integral depends mostly on the fault impedance and the zero-sequence capacitance. This observation has made a threshold inversely proportional to C 0 and a coefficient k which depends on the current level, to take into account the fault resistance, of the monitored feeder. The equation below mathematically describes the threshold design:

78 3. THE FAULTY FEEDER C0 METHOD ALGORITHM 78 T hreshold = k A C 0 (3.8) The term A is a general constant which has to be designed by a rule of thumb and by the experience for fine tuning. The value of C 0 is limited to a maximal and minimal value which are realistic for a distribution network and k can take two value; if the current is smaller than 20% of the rated current the value of k is 1 otherwise it takes the value 5. The charging transient on the sound feeder increases the error value. The threshold is also dynamic and is increasing at every period by a factor 5% to take into account the drifting of the error. All these actions make the algorithm very sensitive with a threshold as close as possible as to the limit of the sound feeder. More details about the rule of thumb and the experience taken from the tests are described in the chapter 3.3 concerning the prototype development. 3.3 Disadvantages of the method The developed method considers the zero sequence capacitance independent of the frequency which is not exactly true because of the presence of the series impedance, noise and modeling error. Then in case of low impedance fault, transients with high charging frequencies (above 500 Hz) do not fit exactly the capacitive model on sound feeders. This is creating a higher error signal than the normal noisy error signal on the sound feeder which could lead to a wrong detection if the C 0 method is adjusted with too sensitive settings. This problem is illustrated on figure 3.5 where the zero-sequence charge signal has been computed and superposed to the voltage signal, the frequency of the transient is correct but not its magnitude which is correct for the steady state. q 0 (t)/c 0 [Volt] Voltage V 0 F 1 Faulty F 2 Sound F 3 Sound time [ms] Figure 3.5: Transient has bigger error than the steady state This also depends on the sound line capacitance as it is shown, feeders with relatively strong capacitance have less problem because the ratio steady state to transient magnitude is relatively important compare to low capacitive feeder where the transient magnitude is much more important than the steady state magnitude. The QU diagram 3.6 below shows that the transient does not exactly fit the capacitive model. The result could be an error detected on the sound feeder. The problem is that these errors are integrated and can be as high as the result of a high impedance fault. The solution is to increase the threshold to a reasonable value to take into account these deviations if a transient is detected.

79 3. THE FAULTY FEEDER C0 METHOD ALGORITHM F 1 Faulty F 2 Sound F 3 Sound q 0 (t)/c 0 [Volt] V 0 [Volt] Figure 3.6: Transient does not exactly matches the capacitive model To prevent any wrong detection, the threshold of the C 0 method must be high enough to consider the errors created by the transient. A dynamic threshold is then necessary to keep a high sensitivity regarding high impedance fault. This dynamic threshold is detailed in the development chapter 3.3. The algorithm must be able to detect transient or sudden high peak of current which will lead to a bigger error. If the algorithm is detecting such current, it will automatically increase its threshold and when no transient is measured and the error signal reset, the full sensitivity is recovered. Another problem of this method is regarding the closed ring topology and specific position of protection device in this closed ring. The problem with the new algorithm is that it uses the relation between the zero-sequence voltage and zero-sequence current to determine if the feeder is faulty or not. In radial structure network, there is no problem with this information as seen on figure 3.7. Busbar : Sound : Faulty : Faulty flow Secondary substation Figure 3.7: No problem to know which feeder is faulty However, on closed ring structure, the faulty current can circulated in several feeders and the information faulty or sound is not enough to determine which feeder is faulty. This

80 3. THE FAULTY FEEDER C0 METHOD ALGORITHM 80 problem is shown on the next figure 3.8. Some DSOs are using devices at the end of the feeder on the secondary substation. The goal is to isolate the faulty feeder in a loop structure. If they are only protection devices in the main substation, the C 0 method will detect both feeder as faulty because the faulty current is spreading in both direction and non capacitive behavior is measured by every device. Therefore no selection between the two feeders of the loop can be isolated as faulty. The solution made by some DSOs is to place devices at the secondary substation. This system works very well with transient protections because they measure the faulty flow and they do not model the behavior of the sound feeder. Busbar : Sound : Faulty : Not working : Faulty flow Secondary substation Figure 3.8: Detection of the faulty feeder is not possible with four devices in a loop The C 0 method cannot select the faulty feeder from the loop but it considers the whole loop as faulty. The faulty information is flowing in the whole loop which does not make any piece of the loop as a zero sequence capacitance. On the contrary, the transient protection measures only the flow of the faulty current which allow them to make direction decision. This is a problem for the C 0 method because it means it will not operate properly in specific topology where four measurement devices are put in a ring structure, that is a reason why Siemens has asked the ULB the research in a directional method.

81 4. The directional method algorithm 4.1 The observation One disadvantage of the C 0 method presented is that it is a faulty/sound detection and not a forward/reverse principle. This difference causes problem for loop structure with two ended fault detection where some DSOs are selecting the faulty feeder inside the loop. Another method has been developed to solve this direction problem. This method has been presented during the Eurocon 2013 conference [Loos et al., 2013b] and has also been patented by Siemens AG. The principle is based on the same assumption as the C 0 method supposing the sound feeder is capacitive. The integration method which accumulates the deviation from a perfect capacitive model wanted to be preserve also to increase the sensitivity of the protection. Every phenomena described in the first chapter has to be considered also to make use of all information available for forward detection. However, the use of these phenomena is completely different and is more equivalent to the Wattmetric function. The statement is that the sound feeder consumes active power and faulty feeder supplies active power. This can be understood as the charging of the capacitance, during a steady state a capacitance does consume only reactive power but when it has to charge, it needs active power. This can be explained mathematically with the equation of the active power. First we define the zero-sequence instantaneous power: p 0 (t) = v 0 (t)i 0 (t) (4.1) Then, the definition of the active power is the integration of the instantaneous power over one period T divided by the length of this period: P a 0 = 1 T ˆT 0 p 0 (t)dt (4.2) If the voltage and current sinusoidal signal is periodic and constant, then the integration of perfect sinus over one period is clearly zero because the exchange of over one period in a capacitance is zero. However, if the voltage is increasing or decreasing, so is the current, the instantaneous power over one period will not be constant, therefore the integration - i.e. the active power - is not equal to zero. The next figure 4.1 represents different situation where the voltage and current is increasing with an inductive or capacitive behavior. The instantaneous power is showed on the right, its frequency is two times the signal frequency due to the phase angle. The active power for this period is also displayed as a title of each instantaneous power plot. The graphic representation clearly shows that the 81

82 4. THE DIRECTIONAL METHOD ALGORITHM 82 1 Constant Voltage Current 0.5 P a = 0 p(t) Inductive up Inductive down Capacitive up Capacitive down time [ms] P a = P a = P a = P a = time [ms] Figure 4.1: Active power depends on the current and voltage behavior integration of the power will lead to a positive or negative active power because the swept surface is bigger in the positive part than in the negative part in case of charging. The following schematic 4.2 reminds the three main power flows of active power in a compensated network, i.e. the steady state, the charging transient and the coil effect. The power flows have the same direction in the faulty feeder. The charging transient flows from the fault to the sound feeder capacitance as indicates by the blue arrows. The active steady state is due to the imperfection of the Peterson coil and is represented by a parallel resistance. This resistance creates a way where steady state active current circulates and is indicated by the red arrows. The coil effect is less important but could happen if the fault does not occur at the maximum voltage value on the faulty phase. This creates a phenomena described in where a decaying current during several periods occurs caused by the inductance of the Peterson coil and is represented by the black arrows. These phenomena are used to make a direction criteria which is not the case of all the existing transient protections. For example, the old Wischer device filters the 50 Hz component, this suppresses the steady state and also the transient in highly capacitive network where the charging frequency is low. 4.2 The algorithm Based on the concept that capacitance are consuming or producing active power during not steady event, this work has defined an instantaneous active power to observe the variation of the active power during the fault. The zero-sequence is only used for the fault detection

83 4. THE DIRECTIONAL METHOD ALGORITHM 83 Figure 4.2: Main power flow in a compensated network during single phase earth fault therefore, the zero-sequence instantaneous active power is defined by the equation 4.3 below: p a 0(t) = 1 T ˆt t-t p 0 (τ)dτ (4.3) Two simulations have been made for a small impedance fault with a strong charging transient and a high impedance fault with a small increasing of the voltage. The first figure 4.3 shows the instantaneous active power for a faulty and a sound feeder for a small impedance fault. The charging transient is clear and most of the active power is produced during this transient. The sound active power is positive at the fault during the beginning of the fault and the faulty feeder is negative. During the steady state, the active power is zero for the sound feeder because it is a capacitance but this is not true for the faulty feeder because the imperfection of the Peterson coil creates a circulation of active power during the steady state, that is the reason why the faulty instantaneous active power is not zero. The shape of the instantaneous power can be understood by a combination of the 50 Hz component and a transient around 200 Hz frequency. The first spike of the transient is big in absolute value because both current and voltage is high near the fault inception. However, several oscillations are very small after the first one because the voltage are around zero, then the transient disappears. The polarity changes 20 ms after the fault inception comes from the sliding window used to compute the instantaneous active power, the first half of the oscillation is not within the window anymore and this changes the polarity because the overall surface of the instantaneous power p0 changes. However this spike is not important because the tendency clearly shows a distinction between the faulty and the sound feeder. This can be seen on the figure 4.1 is the first half period of a transient signal is avoid, the result polarity is changing. The effect of the steady state active current circulation through the faulty feeder is visible with a negative power during the steady state. The next figure 4.4 is the result of a high impedance fault simulation. A small high frequency transient can be seen and is the discharging frequency but is usually filtered by the protection device. The voltage and current is increasing slowly which creates a positive instantaneous zero-sequence active power for the sound feeder and a negative one for the faulty feeder. The discharging frequency has nearly no impact because the frequency is too high and decreases to quickly. The fault inception is important because it determines the polarity

84 4. THE DIRECTIONAL METHOD ALGORITHM Faulty p 0 a Sound p 0 a Faulty i 0 Sound i 0 Voltage v time [ms] Figure 4.3: Instantaneous zero-sequence active power power for small impedance fault of the active power. The imperfection of the Peterson coil is more important in relative value in case of high impedance fault. The interpretation of the instantaneous zero-sequence active power is not easy because for the small impedance fault, the transient was decreasing but for the high impedance fault a transient is increasing and in both cases the result is positive for the sound feeder and negative for the faulty feeder. The physical explanation is that the capacitance does need active power to reach the voltage level where they will oscillate. The faulty feeder is one of the return path of this active energy, then its flowing is in the opposite direction. The signal interpretation is easy for the fault inception because the voltage and current has the same polarity the first half period for the sound feeder. This is the opposite for the faulty feeder. However, active power remains after this first half period. According to these observations, a simple criteria is to measure the zero-sequence active power and make a decision on the polarity. However, high impedance fault produces several periods of active power, an integration of this signal should ease the direction determination. The following equation has been set for this purpose: e a 0(t) = ˆt t 0 p a 0(τ)dτ (4.4) This energy is a good criteria for the fault direction determination because the energy is going in one direction. The integration of the power on the figure 4.3 is represented in the figure 4.5, the tendency is clear and the detection of the direction is easy. Both signals increase in their respective direction. The interesting part is the steady state signal which continues to increase for the faulty feeder. This is a strong advantage compare to the classic

85 4. THE DIRECTIONAL METHOD ALGORITHM Faulty p 0 a Sound p 0 a Faulty i 0 Sound i 0 Voltage v time [ms] Figure 4.4: Instantaneous zero-sequence active power power for high impedance fault transient methods that stop after the measuring the transient signal. However, regarding the whole energy delivered during the transient, the energy produced by the steady state is very small in case of low impedance fault. This is not the case for high impedance fault. 1 x 10 3 Energy [J sec ] Sound e a 0 Faulty e a time [ms] Figure 4.5: Energy evolution of a low impedance fault The following figure 4.6 illustrates the integration of the high impedance fault simulation represented with the instantaneous active power in figure 4.4. The direction determination could be made only on a positive or negative value criteria but a more complex value has been calculated for the threshold settings which is explained in the next chapter.

86 4. THE DIRECTIONAL METHOD ALGORITHM 86 2 x 10 4 Energy [J sec ] Sound e a 0 Faulty e a time [ms] Figure 4.6: Energy evolution of a high impedance fault 4.3 Specific topology Some DSOs are using the transient protection in specific topology where the C0 method could not be used, therefore the direction method is better if the sensitivity between both method is comparable. As it is explained in the next section of this chapter, the C0method, it is not possible to place four devices in the ring structure. This is not a problem for the directional method because it measures the polarity of the zero-sequence active energy which makes the direction decision possible. However, the results will depend on the fault energy, position and the network characteristics - actually, this is the same problem as for the others transients protections Discussion about the active power flow In case of closed ring, the active power flow has two ways to circulate; the aim is to charge the healthy capacitance of the network. Here is a schematic of the active current circulation, red arrows illustrate the steady state and blue arrows illustrate the transient. The transient can have different direction depending on the fault position and the feeder impedance the steady state too but because the transient is more important, only the transient will be considered. Busbar F1 F2a F2ae : Transient flow to F1 : Transient flow to F2a : Transient flow to F3 F3 F2b F2be Secondary substation Figure 4.7: Schematic active power flow in closed ring structure

87 4. THE DIRECTIONAL METHOD ALGORITHM 87 The direction that the transient will take is explained in This schematic indicates the way the active flow can circulate. Regarding the steady state, the current is circulating from the fault towards the Petersen coil. This current will be split in two parts because there are two ways towards the coil because of the loop. The distribution of the current going into one way and the other depends on the impedance of each ways. Then it depends on the feeder s impedance and fault position. For example, if the fault is at the beginning of the feeder and the feeders of the loop are the same then most of the current will flow left according to figure. If the fault is at the end of the feeder, then the current will be approximately 50% in each direction. Concerning the transient part of the active current, the direction is not determined by the Petersen coil but the healthy capacitance that are charged by the increasing voltage. On the radial part of the network, the flow of the current is always going from the bus bar to the capacitance. In a loop, there are two ways for the current to circulate. From the fault, part of the current will charge the capacitance inside the loop, and part will charge the capacitance of the others feeders. Depending on the network structure, a relative amount of current will flow outside the closed ring, towards the sound feeders. This current will help to detect the fault forward because is negative. The current charging the loop will flow depending on the fault position and the feeders impedance. This current can give a positive or a negative polarity to the active power flow measured by the relays in the loop. This will lead to a forward or reverse direction Possible direction of the 4 relays in a closed ring If the fault occurs on the feeder 1, here are every possibilities of direction indication. The forward and reverse is based on the convention that forward is in the direction of the feeder the relay protects. Fault position F2b F2be F2a F2ae 1 middle F2b Forward Forward Reverse Forward 2 middle F2b Forward Forward Reverse Reverse 3 end F2b Forward Forward Forward Reverse (4) near F2b Forward Reverse Reverse Forward (5) near F2be Reverse Forward Forward Reverse (6) F1 Reverse Forward Reverse Forward (7) F3 Forward Reverse Forward Reverse Table 4.1: The different indication of the direction protection in closed ring Case 1: The fault is in the middle of the feeder 2b and the capacitance of the feeder 2a are charged by both sides active energy is coming from F2a and F2ae. The forward direction of F2be can come if F3 is highly capacitive and active energy from the fault is charging the capacitance of F3 by F2be and F2ae. There is no problem to identify the faulty feeder in this case. Case 2: The fault is in the middle or at the beginning of the feeder 2b. The reverse direction of F2ae can come if F3 is lowly capacitive and active energy from the fault is charging the

88 4. THE DIRECTIONAL METHOD ALGORITHM 88 capacitance of F3 only by F1e. There is no problem to identify the faulty feeder in this case. Case 3: The fault is at the end of the feeder 2b. The impedance from the fault to the bus bar is almost the same for F2a and F2b, the active energy needed to charge F3 will flow through F2a and F2b. There is no problem to identify the faulty feeder in this case. Case 4: If for any reason, the impedance of the feeder 2a is much smaller than the impedance of the feeder 2b and if the fault occurs at the beginning of F2b, then the active energy will flow through feeder 2a to charge the capacitance at the end of the feeder 2b because the shortest ohmic way is through feeder 2b. Another condition is that F3 does not have high capacitance. In this case, there is a problem to identify the faulty feeder but it might be only a theoretical case. Case 5: If for any reason, the impedance of the feeder 2a is much smaller than the impedance of the feeder 2 and if the fault occurs at the end of F2b, then the active energy will flow through feeder 2a to charge the capacitance at the beginning of the feeder 2a because the shortest ohmic way is through feeder 2b. In this case, there is a problem to identify the faulty feeder but it is perhaps only a theoretical case. Particularly, if the threshold of the direction method is well evaluated, the F2a will indicate unknown because only a very low active energy is going through it. Case 4 and 5 depends on a very specific network topology but this is not sure that this case is often met. Case 6: This is the result for the fault outside the ring. The protections on the main bus bar see the fault behind them and the protections on the secondary see the fault ahead. Case 7: This is the result for the fault beyond the ring on the feeder 3.

89 5. Tests and simulations of the methods This section tests the two algorithms with simulations and some real recordings. The goal is to validate the theory with the different phenomena presented in the theory. The classic earth fault with a nice charging transient is illustrated, the high impedance fault without charging transient is shown, the coil effect and also intermittent faults are illustrated. The technical problems link to the development of the algorithm and the first prototype are considered in the next chapter. The simulation with the software EMTP/ATP and the network has been created with the ATPDraw tool. the figure below shows the network using the distributed line model. Figure 5.1: Simulation network to test the algorithm 5.1 Classic fault The classic fault is a 1 Ohmic fault resistance in a medium capacitive network. The network information can be found in the appendix A. All tests will be done with this network for the sake of illustration. Deeper tests can be found in the appendix and are described in the technical chapter. In this example, the fault occurs at the end of the feeder F1. The transient between the feeder F1 and F3 can be seen and the difference between the faulty feeder and the sound is easy. F3 does not have strong capacitance which makes the steady state very low and its transient also. The signals are measured in the secondary measurement with a ratio 200:1 for the voltage and 100:1 for the current. The charging transient is also visible on the voltage but less because of the high value of the voltage near its nominal value. The current is only capacitive and very small compare to the nominal current value. 89

90 5. TESTS AND SIMULATIONS OF THE METHODS 90 Voltage V 0 [V sec ] F1 1 F2 F3 Current I 0 [A sec ] time [ms] Figure 5.2: Zero-sequence current and voltage for a low impedance fault If the C 0 method is first considered, the estimation of the zero-sequence capacitance is well done. The figure 5.3 illustrates this estimation. The straight lines are the least squared line with a slope equals to C 0. The feeder 1 which is the faulty feeder has a strong dispersion of its samples which makes the capacitance estimation not true. The feeder 2 has a good estimation but the transient puts the samples not on the straight line which will create error. The feeder 3 which has a very small capacitance but the estimation looks quite good because all the samples are on the straight line. 1.5 x Feeder 1 Feeder 2 Feeder 3 q 0 (t) [C] V [Volt] 0 Figure 5.3: QU diagram of a classic single phase earth fault The integration of the error signal shows the same conclusion. The faulty feeder is easily detected but the second feeder has also a strong error because of its transient. This transient creates a bigger error signal than the feeder 2, even if the capacitance is smaller, the threshold on feeder 3 has been increased to take care of the error caused by the transient. The error on the feeder 3 is more than 30 times the error on the feeder 2. The slow increasing between 20 ms and 40 ms is due to an increasing of the voltage which activates the algorithm before the fault occurs. However, according to the polarity problem of the current and voltage, the faulty feeder can already be detected. The filter design is discussed in the next chapter. Regarding the direction method, the following figure 5.5 shows the sensitivity of the method. A zoom is made on the figure on the right to see the threshold value. Even if the third feeder as a very small capacitance, the method is still able to determine the fault

91 5. TESTS AND SIMULATIONS OF THE METHODS Feeder 1 Feeder 2 Feeder 3 ε time [ms] Figure 5.4: Integration of the error signal direction. 2 x x 10 4 Feeder 1 Feeder 2 Feeder 3 Energy 2 4 Feeder 1 Feeder 2 Feeder 3 Energy time [ms] time [ms] Figure 5.5: Energy in case of classic single phase earth fault 5.2 High impedance fault The same network has been used with a fault impedance of 3000 Ohm. The figure 5.6 shows the zero-sequence current and voltage, they are rising slowly because of the high impedance fault. The difference between the faulty and the sound feeder is extremely difficult, only the fault inception has different polarity and the rising of the current has a small phase angle. The current and voltage values is also much smaller than the classic fault with transient. The voltage does not reach the 100 V on the secondary side and the current is ten times smaller. The capacitive behavior of the feeders is visible on this simulation and the faulty feeder has only a very small part of resistive current which is circulating through the imperfection of the Peterson coil. The QU diagram shows also this problem in the figure 5.7. The feeder 1 is the faulty feeder and the feeder 3 is a small capacitive overhead line. The difference between the estimated slope of feeder 1 and 3 shows how the faulty feeder will be detected. Also the estimated slope is computed during the first period of the fault and the figure 5.7 shows all the samples for the next 7 periods. Therefore, the algorithm will compute a slope which will tend to the blue area. That is one reason why the beginning of the fault is very important. The integration of the error signal clearly identifies the faulty feeder but it takes more than one period to make the difference between the faulty and the sound feeder. Indeed, in the figure 5.8, the blue threshold is reached during the second period. The sound feeders are

92 5. TESTS AND SIMULATIONS OF THE METHODS 92 Voltage V 0 [V sec ] Current I 0 [A sec ] F1 0.1 F2 F time [ms] Figure 5.6: Zero sequence current and voltage for high impedance fault 5 x 10 4 Feeder 1 Feeder 2 Feeder 3 q 0 (t) [C] V 0 [Volt] Figure 5.7: QU diagram in case of high impedance fault very distant from their threshold but the faulty feeder is 5 times bigger than its threshold. After five periods of computation, the threshold and the integral of the squared error is reset to avoid drifting of the signal. This might be a problem because the faulty information is extremely small and the inception of the fault is not considered after this. Therefore, once the feeder has been detected faulty, it remains faulty until the zero-sequence voltage decreases. The algorithm is still running for the sound feeder in case they become faulty. Indeed, during the research, it has been stated that if it is possible, the algorithm should continue running in case of another earth fault on the same phase in another feeder. The probability is extremely small, especially on the same phase. If the fault occurs on a different phase, the fault will become a two phase fault which will strongly increase the faulty current. The current algorithm is then unnecessary in this case. The feeder 2 has a higher error than the feeder 3 because of its very small capacitance, small error on the small capacitance creates big error and therefore the threshold must be increased. This is the case because the threshold of the feeder 2 is much higher than the threshold on the feeder 3. Regarding the direction method, the increasing of the energy is making the decision possible for every feeder. This method is very sensitive and the forward or reverse indication can be provided. After 5 cycles, the direction detection stops until the voltage is decreasing which means the fault has gone. Once the voltage is increasing again, the algorithm restarts and the direction can be done. A zoom indicates the limits have been reach to detect the reverse fault on the low capacitive feeder 2. The reverse threshold is set at 1.6e-6 J and the computed energy on the feeder 2 reaches 6e-6 which is slightly more than 3 times the threshold value

93 5. TESTS AND SIMULATIONS OF THE METHODS Feeder 1 Feeder 2 Feeder ε time [ms] Figure 5.8: Integration of the error signal for a high impedance fault simulation compared to a factor 100 for the feeder 3. However, the important thing in this detection is the indication forward which is easily made with the feeder 1 even if the fault impedance is extremely high. Difficulty has occurred in case of circulating current as it is mentioned in the development part. The figure 5.9 shows the result of the high impedance fault simulation. A zoom is made on the right figure to illustrate the threshold value relatively to the computed active energy value. A discussion about the tuning of the forward and reverse threshold is made in the development chapter. Energy 2 x Feeder 1 Feeder 2 Feeder 3 Energy 1 x Feeder 1 Feeder 2 Feeder time [ms] time [ms] Figure 5.9: Energy in case of high impedance fault 5.3 Coil effect The fault inception has been edited in the simulation so the fault does not occur when the voltage is maximum with a small fault resistance of 1 Ohm. The following figure 5.10 shows the zero-sequence voltage and the three zero sequence currents of the three feeders. The difference between the faulty feeder and the sound is easily visible. The charging transient is weaker than the classic fault and this is explained in the theory developed on the previous chapter. Also the voltage transient is not visible in this case and it was visible if the fault occurs at the maximum voltage on the faulty phase. This is because the charging of the sound capacitance is not a step which makes the system oscillating slowly. The polarity difference shows the faulty feeder. The coil effect is actually not very visible due to a filter. Indeed, during the development, the necessity of a high pass filter has been proved as it is explained in the next chapter. The non filtered signal shows clearly the coil effect on the figure This effect occurs only during low impedance then it is not necessary to have this information to detect the fault,

94 5. TESTS AND SIMULATIONS OF THE METHODS 94 Voltage V 0 [V s ec] Current I 0 [A s ec] F1 F2 F time [ms] Figure 5.10: Zero sequence current and voltage with a coil effect the transient is enough. This effect occurs if the fault on the faulty phase occurs when the voltage is not maximum. In reality, most of the faults occur at the maximum of the voltage because the breakdown is more likely to happen. However, some recordings show this coil effect indicating the fault could occur when the phase to ground voltage is near zero. One reason could be due to activities forcing the breakdown such as road work, materials touching the phase, etc Non Filetered Signal Filtered Signal Current I 0 [A sec ] time [ms] Figure 5.11: Coil effect disappears with the high pass filter The charging transient has a smaller with the coil effect than without. This is due to non step voltage on the sound capacitance leading to a reduced oscillation of the system. The QU diagram on figure 5.12 shows a strong deviation of the faulty blue plus samples. This leads to an easy detection. The charging transient still does not make a perfect straight line for the sound feeder 3 which has to be considered in the threshold. Regarding the faulty feeder 1, a non capacitive behavior is clearly identify even if the coil effect is mostly not considered because filtered. The low capacitive feeder does not show strong deviation from the estimated straight line but small error will be increased because the error is computed by dividing with C0 which is also very small. The integration of the squared error makes the detection easy of the faulty feeder during the beginning of the fault. The error on the sound feeders is almost the same for both feeder. The feeder 2 has the algorithm starting one period later because the current is too small at the fault beginning. Indeed, for the others feeders, the filter used creates a small increasing of the current before the real fault inception which triggers the algorithm, this is the reason why the integral does not increase directly after the run of the algorithm. This small increasing

95 5. TESTS AND SIMULATIONS OF THE METHODS x Feeder 1 Feeder 2 Feeder 3 q 0 (t) [C] V 0 [Volt] Figure 5.12: QU diagram with a coil effect is easy to detect can be seen on the figure 5.10 before 40 ms. This increasing is more important on the feeder 1 because it has not completely filtered the coil effect. This is not the case for the feeder 2 due to its very small zero sequence capacitance. This result can be seen on the following figure The threshold is higher for the feeder 2 because its capacitance is smaller, the threshold for the feeder 3 is higher than it would be if no transient was measured. Indeed, the transient creates errors requiring a decreasing of the sensitivity at the beginning to still consider this feeder sound Feeder 1 Feeder 2 Feeder 3 ε time [ms] Figure 5.13: Integration of the squared error with a coil effect The energy makes the direction decision also very easy. The direction is correct for every feeder. The feeder 2 has the smallest energy which makes it more difficult to detect but the faulty feeder is quickly considered as forward. The determination is made in the first period, the fault occurs at 40 ms and the thresholds are reached before 50 ms. However, the computation of the energy is made every 20 ms than the protection will indicate the direction in the worst case 20 ms after the fault inception. The fault could occur in anywhere in the considered 20 ms window which could reduce the tripping time but this is a random parameter. 5.4 Intermittent earth fault The last presented test is the simulation of an restriking earth fault. Three single phase to ground faults are simulated on the same network as the tests made in the previous sections. The first fault occurs at 47 ms and lasts 5 ms, then a restrike occurs around 75 ms and lasts

96 5. TESTS AND SIMULATIONS OF THE METHODS 96 2 x Feeder 1 Feeder 2 Feeder 3 1 x 10 4 Feeder 1 Feeder 2 Feeder Energy Energy time [ms] time [ms] Figure 5.14: Energy for direction determination with coil effect also 5 ms, a pause is then made to let the capacitance recharges and a last restrike happens at 165 ms. The fault resistance is set at 1 Ohm and occurs at the maximum of the phase voltage to avoid any coil effect. The signal is illustrated on the figure 5.15 with the zero sequence voltage and zero sequence current. The charging transient amplitude depends clearly on the state of charge of the sound capacitance. If a fault has occurred one period before the restrike, the charging transient is very weak as the second fault indicates. Voltage V 0 [V sec ] F1 1 F2 F3 Current I 0 [A sec ] time [ms] Figure 5.15: Simulation of an intermittent and restriking earth fault The QU diagram of the simulation is illustrated on the figure The feeder 1 does not followed a straight line with the samples. The feeder 3 is impacted by the charging transient but the tendency is clearly on a straight line. At each fault inception, the samples form have a negative slope tenancy and the addition of the 50 Hz component and the transient does not have especially this tendency but indicates clearly a non capacitive behavior. The integration of the squared error illustrated on the figure 5.17 shows the detection of the faulty feeder works properly. The faulty feeder is quickly detected faulty at the first fault. The thresholds are automatically increased because the charging transient. This is an automatic way to reduce the sensitivity of the method. After five cycles, the integration of the error is set to zero and the algorithm restarts to check if a new fault has not occur in other part of the network and to avoid drifting of the integral. The thresholds are low because they do not measured transients. They are increased at the fault restrikes. The feeder 3 which is sound has its error increasing due to the charging. The faulty feeder 1 has a much bigger error as illustrated by the figure 5.17 in logarithmic scale. However, the threshold is a bit too high in this case because the restriking does not bring as much energy as the first fault inception. The fault disappears a few ms after its inception, therefore no steady state information can

97 5. TESTS AND SIMULATIONS OF THE METHODS x Feeder 1 Feeder 2 Feeder 3 q 0 (t) [C] V 0 [Volt] Figure 5.16: The feeder 1 is not on a straight line in the QU diagram be used to increase this error. The detection of the last restrike is a problem of fine tuning the threshold which is discussed in the next chapter Feeder 1 Feeder 2 Feeder 3 ε time [ms] Figure 5.17: The integration of the squared error works well with intermittent earth fault Regarding the direction determination method, it is easily and quickly detected as forward or reverse. The restriking does not impact the decision and increases the value in the right direction. This is illustrated on the figure A problem might come if a fault occurs on another position in the network. The energy should have to be reset if another feeder is detected as faulty. However, if the restriking of the fault occurs periodically, the energy calculated at the beginning will decrease and become negative after a few periods. Energy x 10 3 Feeder 1 Feeder 2 Feeder 3 Energy 1 x Feeder 1 Feeder 2 Feeder time [ms] time [ms] Figure 5.18: The direction determination works correctly in case of intermittent earth fault

98 6. Summary This chapter describes the actual transient protection devices to detect single phase earth fault in compensated network. As their name indicates it, most of them use only the transient because most of the fault information is contained in this part of the signal. The QU method considers a model of the sound feeder and detects any deviation from this model. Such methods are more accurate because they use more information. Then the methods developed during this work is presented. The first algorithm is a detection strategy based on the assumption the sound feeder is capacitive in the zero sequence system. Using the zero sequence voltage and current, an estimation of the zero sequence capacitance of the monitored feeder is made. Deviation of the samples from this estimated value creates an error signal which is integrated and compared to a threshold. If this threshold is reached, it means the model is not capacitive and is considered as faulty. Otherwise, the feeder is healthy. This method is sensitive but is impacted by the non perfectly capacitive behavior of the charging transient and cannot work at the end of closed ring topology to distinct the faulty feeder inside a loop. This is due to the fact that the faulty information is circulating in the whole loop and therefore no part of the loop has a capacitive behavior and everything is detected as faulty. This last problem has been solved by the design of a direction method. The direction method calculated the zero sequence active energy flowing through a feeder. This energy can be positive or negative depending if the feeder is faulty or not. The charge of the capacitance creates a positive active energy and the fault produces this active energy which is flowing outside the faulty feeder and is seen as negative. The other phenomena such has the steady state with the generation of active current is also negative and adds in the faulty feeder detection. This solution determines a direction of the fault flow which allows the determination of the faulty feeder in a closed ring structure. 98

99 Part IV Fault Detection Prototype Development 99

100 1. Introduction This chapter focuses on the development of the fault detection prototype. The technical problems specific to the development are presented such has filtering, circulating current, recordings difference with simulations, threshold design, etc. The author has spent four months in the Siemens AG department in Berlin to develop a prototype of the C 0 method and directional algorithms. The implementation has been made in C code on a 7SN64 SIPROTEC V4 device based upon a micro-controller. This brings many constraints compared to a Matlab script using a computer processor in term of computing time and performance. Several adaptations have been done. Also lot of the methods used during the research part are Matlab functions. These functions have been recoded with some differences accuracy or processing speed. This problem is presented in this chapter. Several methods have sometimes been tested during the development before choosing one, the different strategies are shown and a discussion is made about the choice made during this period. Lot of recordings have been tested to develop the most accurate prototype, therefore lot of phenomena which did not occur in the simulations have been discovered and additional processes have been implemented to deal with these problems. The recordings are mostly coming from the Pfalzwerke network where two rings structure are operated; one with two feeders and one with four feeders. The circulating current can be strong in these loops and a method to run the algorithms with such problem has been implemented. The parameters accessible to the users are presented. The indications provided by the device are also shown and explanations about the delays and tripping times are detailed. Once the prototype has been developed, many tests have been made to compare the performance with the old Wischer Relay and also the A-Eberle EOR-D Transient protection. This has been reported to Siemens which has decided to build the first product end of 2012 and has started to deal it in the European Nordic Country. The conclusions of these tests are presented in this chapter and the test results are provided in appendix. 100

101 2. The signal conditioning 2.1 High pass FIR filter - Purpose and design The current signal i0(t) and the voltage signal u0(t) must be filtered by a high pass filter. This high pass filter blocks the small oscillations and the DC offset of the current and voltage which disrupts the algorithm. During the design of the algorithm, tests on recordings have shown very small oscillations (around 5 Hz) of the current I0. This is probably caused by measurement errors coming from the measurement transformers. This has a big impact when this current is integrated, the algorithm can handle most part of this oscillation by changing the estimated capacitance value but the accuracy is better with filtering. The two next figures illustrated this problem (signals are from real recordings). Normally, the signal q0(t) in red should fit the signal u0(t) when they are decreasing. They must have the same phase angle and quite the same amplitude. Picture without high-pass filtering shows the necessity of this filter. Without filtering the relation between q0 and u0 is not linear and the estimation of C 0 is bad. With the high-pass filter, the small oscillations of the current are deleted and the signal q0(t) has a much better relation with the voltage which increases the sensitivity of the algorithm regarding faulty feeder. The relation between the voltage and the charge is linear and the estimation of C0 can be well done as the figure 2.1 shows it. u0 q0 u0 q time [ms] time [ms] Figure 2.1: Integration of the current i0(t) without (left) and with (right) high-pass filtering compared to voltage signal U0 The filter used is non recursive and has 40 samples. The processor used in 7SN64 is not fast enough to support floating point arithmetic for the filtering so the coefficients have to be transposed to integer values. The 32-bit integer range is sufficient for the summation; the resolution on the coefficients must be fine enough to realize nearly the same frequency response as with floating point coefficients. After the summation, the result is converted to IEEE floating point format. With this process the time consuming floating point operations are reduced to a minimum 101

102 2. THE SIGNAL CONDITIONING 102 with fixed-point data. To use the whole 32-bit range, the integer coefficients are calculated with the following equations (postulate: the input values are 16-bit integer values). INT 32_MAX q = n 1 k=0 ( a (2.1) n,k MAX_SAMP LE) With INT32_MAX = maximum 32-bit integer value and MAX_SAMPLE = maximum sample value = a i,k = floor(a n,k q + 0.5) (2.2) A FIR filter has been designed. The FIR is a choice for stability imposed by Siemens. The coefficient has been designed in Matlab with the function fdatool. To design again or a new filter based on this one, here are the parameters to enter in the fdatool window of Matlab: Response type: High-Pass filter Design method: FIR Constrained equiripple Filter order: 40. Number of samples per period at a sampling frequency of 2kHz. Frequency Specifications: Units Hz, Fs=2000, Specify stop band edge, Fstop=1. Magnitude specifications: Units db, Astop=80, Apass=1. The figure below shows the Bode representation of the filter. Figure 2.2: High pass filter characteristic for signal conditioning 2.2 Circulating current issue The recordings have shown strong circulating currents which disrupt the algorithm because these currents do not have a capacitive behavior in the sound feeder. As explained in the theory chapter, the circulating currents come from a physically unbalanced system which creates symmetrical system coupling.

103 2. THE SIGNAL CONDITIONING 103 The C 0 method is using the capacitive performance of the sound feeder to make the distinction between a faulty and a sound feeder. However, in some networks topology, some zero sequence current can be not capacitive even in a sound feeder. In closed ring structure, undesirable 50 Hz zero sequence current I 0 can be measured even without earth fault. The measurement of this current I 0 appears as a circulating current in the loop structure. This current is depending on the load and on the unbalance of the series impedance for example caused by cable lying. This phenomenon creates a coupling between the symmetrical system and the load consumption of positive current produces a small zero sequence voltage. This voltage creates zero sequence current especially if the feeders are in a ring structure because it creates an electrical circuit where the impedance is very small. Usually, these circulating currents produce high a zero sequence current but no - or a very small - zero sequence voltage. An example of circulating current is shown on the next figure 2.3. The circulating current can be seen before the fault occurs. Current I 0 [Amp prim ] Voltage V 0 [V prim ] 5 x time [ms] Figure 2.3: Illustration of circulating current from real recording before a single phase earth fault happens The results of the C 0 method and the directional algorithm can be seen on the figure 2.4. The monitored feeders on this figure are both healthy but the results show that they are detected as faulty with the C 0 method. It delivers a completely wrong result. This is not the case for the directional method because the transient is very strong which reduces the impact of the circulating current. However, this will have an impact in case of very high impedance fault because the signal is much smaller The detection To deal with the circulating currents, they have to be removed from the signal going into the algorithms. The first problem is the detection of the current. The theory shows that a small zero sequence voltage is able to produce strong current. This is validated by the recordings because none of them have measured only sound behavior because the zero sequence voltage was too high and starts to record. All recordings show earth fault with only the beginning being healthy. This can be seen on the figure 2.3 where the voltage is near zero. Therefore, the detection of the circulating current will occur if the zero sequence voltage is smaller than the threshold voltage to trigger the fault detection methods and if the current is higher than a set value. This set value is defined as a value that will not impact the algorithms for fault detection.

104 2. THE SIGNAL CONDITIONING ε x 10 3 Feeder 1 Feeder 2 Energy time [ms] Figure 2.4: Healthy feeder can be detected as faulty without dealing the circulating current Because not every closed ring has these circulating currents, it is not necessary to filter the 50 Hz component every time. A detection method of the high circulating current has been implemented. The algorithm will not filter the 50 Hz at each fault which will improve the global sensitivity of the algorithm. To detect this current, the algorithm computes the root mean square value of the current if the zero sequence voltage is not reached. If the RMS current reaches a threshold (high circulating current detection threshold) during 1 s and no V 0 pickup has been detected, then circulating current is detected on this feeder and the 50 Hz component will be filtered. Remark regarding threshold and 1 s detection time: It appears that the fundamental would be the best quantity to detect the circulating current. However this quantity is not available so the RMS value is used. To avoid any wrong detection a delay of 1 s is used. This seems to be practical since bigger load changes are rare The first suppression technique The first technique developed is the filtering of the circulating current which means the suppression of the entire 50 Hz component. 0.5 Current [A sec ] Current [A sec ] 1 0 Faulty Feeder Sound Feeder time [ms] Figure 2.5: Suppression of the 50 Hz component to delete the circulating current The biggest problem with this method is the lack of sensitivity. Filtering the 50 Hz component severely reduces the sensitivity regarding the fault impedance. Indeed, high impedance

105 2. THE SIGNAL CONDITIONING 105 fault has only a 50 Hz component which makes the detection of the faulty feeder impossible because all the important information is filtered. This solution has been aborted after several tests during the prototype development The second suppression technique The second developed technique is the suppression of only the circulating currents considering they are exactly at 50 Hz and are remaining constant during the detection process. The solution of the pre fault evaluation is used to suppress this circulating current without suppressing the valuable information at 50 Hz. This current is assumed to depend on the load and the load is not affected by a single phase earth fault because it is fed by the phaseto-phase voltage of the network. The circulating current will not vary during the beginning of the fault. If no zero sequence voltage is detected - i.e. the voltage does not reach the threshold starting the algorithm - the zero sequence current is measured and stored in memory for the last 3 periods. At the next periods, the current memorized three periods before is subtracted from the actual measured current. This new current is used in the algorithm if there is relay pick up. Three periods are used because in case of high impedance fault, a part of the beginning of the fault could be missed and this is not a circulating current. Three periods ensure that the algorithm is not measuring any information from the fault. This deletion technique is shown on the figure Current [A sec ] Current [A sec ] time [ms] Figure 2.6: Deletion of the circulating component without filtering 2.3 Current condition One last condition needs to be fulfilled before running the C0 algorithm and and the directional algorithms. The RMS value of the current for the 20ms samples must be high enough (>2.5 ma secondary current). If the value is too low, the least-square method to estimate the capacitance of the network could not work properly. This means that for extremely short lines, the algorithm will never run when a single phase earth fault occurs outside this feeder. It will only run when an earth fault is on this line because the current is not the capacitive current from the zero sequence capacitance of the feeder, but the current from the total capacitance of the network. The indication available will only be: Faulty/Forward or Current I0 too low which is not a real problem.

106 3. The C0 method 3.1 Integrating the current i0 The integration of the zero sequence current is done with the use of the trapezoidal rule. This rule uses the two closest points of the data received and calculates the area formed by the trapezoid from 0 to these points. This is the red surface on the figure below. The error on the integral is shown in blue on the following figure 3.1. Figure 3.1: Illustration of the trapezoidal integration compared to a perfect integration However, a 2 khz sampling frequency is high enough to reduce this error to a value very small compared to others errors in the signals. ˆb a f(b) + f(a) f(x)dx (b a) 2 (b-a) corresponds to the time between two samples; at 2 khz (b-a) = sec. general equation for the value of q 0 (k): (3.1) The 3.2 Estimating C0 q 0 (k) = ([i 0 (j + 1) + i0(j)] )k j=1 (3.2) Once the fault inception is found, 20 ms of the signals are recorded to estimate the capacitance of the feeder. This way, 40 samples are recorded for this first period. We suppose that these points form a straight line corresponding to the equation u 0k = 1 C0 q 0k + err where 106

107 3. THE C0 METHOD 107 err is a possible offset in the measurement. The method used to determine the slope 1/C0 and the offset err is the least square method. It is described below: The purpose is to minimize the equation 3.3; this is the minimization of the distance between the samples of coordinates (q0k,u0k) and a straight line where the slope and the y-intercept are unknown: N E(C0 1, err) = (u 0k C0 1 q 0k err) 2 (3.3) k=1 u 0 k and q 0 k are the k th sampled value of the signals u 0 and q 0. As the value C 1 0 and err that minimize E has to be calculated, the following equation is defined: Some manipulations results in: E C 1 0 = 0 (3.4) E err = 0 (3.5) E C 1 0 N = (u 0k C0 1 q 0k err)q 0k = 0 (3.6) k=1 E N err = (u 0k C0 1 q 0k err) = 0 (3.7) k=1 The two equations can be rewritten as: N ( k=1 N ( k=1 q 2 0k)C ( q 0k )C ( In matrix representation, the result is: N N q 0k )err = u 0k q 0k (3.8) k=1 N k=1 1)err = k=1 N k=1 u 0k (3.9) [ Nk=1 w A = k q0k 2 ] Nk=1 w k q 0k Nk=1 w k q Nk=1 0k w k b = [ Nk=1 ] w k u 0k q 0k Nk=1 w k u 0k (3.10) (3.11) wk is the weight of each sample k. In this algorithm, the weight of each sample is the same (i.e. wk=1). Then we obtain an estimation of C0 1 and err given by the equation: [ ] C 1 0 = A 1 b (3.12) err

108 3. THE C0 METHOD 108 The algorithm has measured and computed the samples u0k and q0k. Every cell of the matrix A and b must be computed. Then the determinant of A must be computed (here wk=1): deta = A(0, 0)A(1, 1) A(0, 1)A(1, 0) = N Then the inverse of the matrix A must be calculated: C 0 and err can be found as: N N q0k 2 ( q 0k ) 2 (3.13) k=1 A 1 = 1 [ A(1, 1) A(0, 1) deta A(1, 0) A(0, 0) ] k=1 (3.14) C0 1 = 1 deta (N N N u 0k q 0k q 0k u 0k ) k=1 k=1 k=1 (3.15) err = 1 deta ( N N q 0k u 0k q 0k + q0k 2 u 0k ) k=1 k=1 k=1 k=1 (3.16) The result is then illustrated on the following figure Slope not limited but feeder faulty 40 U Line slope = 1/C0 U q0 x q0 x 10 3 Figure 3.2: Estimation of C0 in case of sound or faulty feeder The next step for C 0 is to compare the value with a minimum C 0min and a maximum value C 0max. The minimum value C 0min can be considered as 10 % of the capacitance seen from the device toward the underlying network (direction bus bar to loads ). In case of a ring structure the whole ring needs to be considered plus eventually the underlying network parts. C 0max is defined as 10 times the maximum capacitance of the considered network part. This could avoid the algorithm to not detect any fault because of a false value of C 0 for example negative C 0 which is not possible if the feeder is faulty. Once C 0 has been estimated for the first 20 milliseconds, a new estimation of C 0 is done for the next 20 milliseconds of data received. The previous data are not used for the estimation which make available the possibility to find the real value of C 0 when the fault is gone.

109 3. THE C0 METHOD x Slope limited in case if C0 is too low U q0 x 10 4 Figure 3.3: Estimation of C 0 in case of faulty feeder with unrealistic C 0 value 3.3 Error threshold computation Basis With the first estimated value of C 0, it is possible to compute a threshold value for the integration of the error. When C0 is small, the current is also small because of the du equation: i 0 (k) = C 0 (k) 0 dt. Then the signal to noise ratio is smaller with small current which leads to a bigger error ɛ(t). To be insensitive to this problem - i.e. a sensitivity proportional to the line length - a threshold for ɛ 2 depending on C 0 is used. The threshold is proportional to 1/C 0 ; this is shown on the next figure 3.4. In the device, the threshold is equal to 1/(Th.Red.Fact.*C 0 ) on the secondary value. This threshold is then compared to a minimum and a maximum value. For an extremely long line, the threshold for a healthy feeder is very low and this could lead to an error due to a too strong sensitivity. The threshold is then limited to a reasonable value (default max threshold = 1/(Th.Red.Fact.*C 0min ) and default min threshold = 1/(Th.Red.Fact.*C 0max )). The problem in case of very short line is the contrary, the function could be not sensitive enough to detect a fault and this high threshold must be limited Threshold 0.25 C0min C0 C0max Figure 3.4: Threshold value depending on C0 value The threshold is dynamic. This means that this threshold is evolving during the fault to be the most sensitive without getting wrong tripping. When the integral is reset, the threshold is evaluated again. In case of low impedance fault, transients occur and they are not fitting properly the capacitive model of the algorithm. The error computed is then high even for sound feeders and could lead to a fault detection on a sound feeder. The solution is to temporarily increase the threshold (if it is too low) to a minimum value to take into account

110 3. THE C0 METHOD 110 this error. If new transient occurs, the threshold is increased by 5%. Once the integral is reset, the transient is gone and a new, more sensitive, threshold may be set. This configuration is graphically explained by the figure Threshold 0.25 Threshold is limited C0min C0 C0max Figure 3.5: Minimum value of the threshold limited in case transient detection If the threshold is high enough, it is only increased by 5% when a transient is detected. If the threshold is lower than 25, it will be set to 25 at the first transient detection and increased by 5% at each new transient. 30 Threshold Integral is reset Threshold is low Current Fault Inception Transient detected Threshold increased time [ms] Another transient detected Threshold increased of 5% Algorithm is blocked Voltage is decreasing Algorithm is resumed Transient detected Threshold increased Integral is reset No transient detected Sensitivity is high Figure 3.6: Evolution of the threshold depending on the current signal The way to detect the transient is done by computating the rms value of the current. A transient will generally create a high step in the root mean square value, detecting these steps will be considered as a transient. The step must be at least higher than 0.2 Amp secondary to be considered as a transient. An example of the threshold evolution is illustrated by the figure 3.6. When a circulating current is detected, the 50 Hz component is filtered; only remain frequencies higher than 50 Hz. The estimation of the zero-sequence capacitance is not so accurate hence the threshold must be high by default. If the threshold is lower than 100, it will directly be put to 100 and will be increased by 5% if current rms jumps are detected.

111 3. THE C0 METHOD Feedback and updates from the tests Several tests have been made and the sensitivity during high impedance fault was not as high as expected. One reason is the difficulty to set the threshold so that false alarms are avoided while keeping a high sensitivity. The other reason is that the inception of the fault is not used in case of high impedance fault. As it is shown in the next figure 3.7, the voltage is detected more than one period after the inception of the fault. The signal comes from a simulation from ATP but similar events often occur on real distribution network. Figure 3.7: Relay picks up after the inception of the fault with Feeder 1 faulty and 3kOhm fault Looking at the error signal and the active energy on the next figure 3.8 to determine if the feeder is faulty or not, the value of ɛ 2 for the feeder 1 is higher but does not reach the threshold and therefore it is considered as healthy instead of faulty. Figure 3.8: C0method values and threshold By looking at the value of ɛ 2, the first idea could be to reduce the threshold to detect the faulty feeder. This idea is not working because others recordings and simulations with lowest impedance faults create an ɛ 2 for the sound feeder which is higher than the ɛ 2 of the faulty feeder in this recording. To increase the sensitivity, the following solution is suggested: use the information before the relay picks up to take into account the inception of the fault. The way to do it is to run the algorithm even without voltage pick up and if the next period has a voltage pick up, the last ɛ 2 with its threshold and zero sequence active energy must count in the result computation. In this case, if the current is high enough to make an estimation of C 0, this

112 3. THE C0 METHOD 112 means that the fault impedance is very high. If the fault impedance was very low, there would be no current before the algorithm picks up because the inception of the fault would be catched. The threshold can then be decreased by a factor ten to increase the sensitivity. Due to this decreasing of the threshold and because the ɛ 2 is increasing continuously on every feeder, it is better to increase the threshold at each cycle of the algorithm to take into account this drift. However, if there is a jump of the rms current ies, this is the indicator to increase the threshold because of a low impedance fault - LIF - rising. This LIF could create a transient that will increase ɛ 2 on every feeder. The next figure 3.9 shows that the improvement is able to catch the inception of the fault. Figure 3.9: Updates make the relay picked up before the inception of the fault This increases the error computed signal ɛ 2 of the faulty feeder and also identifies the event as a high impedance fault and the threshold is decreased to have a higher sensitivity. This is illustrated by the next figure Figure 3.10: The threshold can be smaller in this case and detect the faulty feeder 3.4 Calculation of the error and its integration With C 0, the instantaneous error ɛ(k) is calculated as defined by the equation: ɛ(k) = u 0 (k) q 0(k) C 0 err (3.17)

113 3. THE C0 METHOD 113 In case of sound feeder, the capacitive behavior is verified and the error created comes from a small amplitude difference coming from noise and from the quantification error and rounding due to the use on integers. Regarding a faulty feeder, the error consists in an amplitude, because no correct capacitance estimation can be found, but also a in phase angle difference. Therefore the faulty feeder has a much larger error signal than the sound feeder. Once this error is computed, the algorithm is calculating the equation (with the trapezoidal rules described above): k k0 ɛ(k)2 dt; the integral is used to remember every previous error made and the square value gives more weight to the extreme errors than to the smallest ones. The integral is done with the same trapezoidal method as for the current i 0 (k). This result is compared to the threshold defined by C 0 and if the integral exceeds this threshold, a faulty feeder is detected. Of course, even the error of the sound feeder is not exactly zero. It oscillates around zero and it will increase the integral but much slower than for a faulty feeder. To avoid drift, the integral is also reset every 2 to 5 periods.

114 4. Device running criteria 4.1 Blocking the algorithm In compensated network, when the fault is gone, voltage and current signals are decreasing slowly during several periods. This is due to the resonance of the zero sequence system between the Peterson coil and the line-to-earth capacitances Fault disappeared Voltage is decreasing Voltage [V] TBlock time [ms] Figure 4.1: Voltage is decreasing when the fault has disappeared It is not needed to run the algorithm when the fault is gone, a small error signal subsists when there is no fault. The algorithm can be paused i.e. it does not calculated the error signal and the integral any longer when the voltage has been decreasing for five periods, because this means that the fault is gone and no more feeder is faulty. Stopping the algorithm before this five cycles delay could make the method miss some intermittent earth fault. Once the voltage is going higher again, the algorithm is resumed. For every forty samples received - i.e. 20ms of data - the device looks for the highest absolute value and compares it with the previous ones, if the maximum voltage has been decreasing since minimum five cycles, the algorithm will stop estimating C0 and wait for a new higher voltage - higher than 105% or two times higher than 95%. If the voltage is still high but the current too low, the algorithm is also paused when the root means square value of the current is - < Amp secondary - and the algorithm is waiting for a higher current. 114

115 4. DEVICE RUNNING CRITERIA Stopping the algorithm The stop criterion is a zero sequence voltage below the start threshold. The stop threshold must be smaller than the start threshold because there must be some hysteresis. This avoids any disturbance if the voltage is near this limit. When the voltage is below this threshold, all the internal parameters are reset and the algorithm will start a new process when the voltage is reaching the start threshold again. To avoid the use of a data window which contains a voltage drop to zero in case of wrong switching-off of the line; a fast voltage drop detection is required to block the algorithm before it tries to estimate of C 0 on a disconnected line. Such voltage drops may be caused by a circuit breaker opening or any other phenomenon. If, in the window of 20ms, the last 5ms are near 4 N/4 zero, the algorithm will stop. The ten samples are computed as: N k=1 u 0(k 0 ) 2 < u0_stop2 2. The parameter u0_stop is the U0/UN Pickup setting minus the hysteresis: U0/UN pickup*0.95. The algorithm must be blocked before the voltage drops occurs. The capacitive model is not suited when the voltage drops and if the C 0 method tries to estimate a capacitance with a part of the voltage and current near zero, it will lead to an error. 4.3 Characterization of the fault Additional information can be indicated by the function detecting the fault. The function recognizes three kinds of fault: Temporary: A fault has been detected but the voltage has decreased and the fault is gone, the fault was only temporary. If the function has been blocked once due to a voltage decrease, the fault is considered as only temporary. Intermittent: If the fault disappears, the voltage will decrease and the function will be blocked. If the fault occurs again due to an intermittent earth fault and than disappears again, the function will be blocked several times and it will be detected as an intermittent earth fault. Continuous: If the fault does not disappear or if the fault reappears within 80 ms it is considered as a continuous earth fault. The function will never be blocked and the fault will be considered as a continuous earth fault after 1 second. 4.4 Faulty phase determination The device can also determine which phase is faulty if the phase measurements are provided. The algorithm measures the lowest rms voltage value and if the rms value is 90% below the rms value of the two others phases, then this phase is considered as the faulty one. The two highest phase voltage must have a rms value of minimum u0_start. This determination can be difficult when the fault impedance is very high because the phase voltage is decreasing or increasing very slowly.

116 5. Directional method 5.1 Implementation If the fault is in a forward direction, the measured active zero sequence energy is negative because U 0 and I 0 are opposite. This power is measured during a maximum of three periods. This power is integrated to measure the energy through the feeder. Then this energy is compared to a threshold. If the energy is below this threshold, the direction is considered as forward. If the average energy is above this threshold, the energy is considered as reverse. And if the average energy is between the two thresholds during three consecutive periods, then the direction is considered as unknown. The algorithm can be stopped when the energy has reached one threshold. The flowchart below details the way to determine the direction of the fault. u0(1 40) i0(1 40) Compute the active power: T 1 pa ( t) u0( ) i0( ) d T 0 Maximum 2 times Compute the active energy: T ea ea _ old pa ( t) dt 0 Is e a <- Threshold? No Is e a >Threshol d? No Reverse Yes Yes Forward Reverse Figure 5.1: Flowchart of the direction determination First the zero sequence power must be calculated: p 0 (k) = u 0 (k)i 0 (k) (5.1) 116

117 5. DIRECTIONAL METHOD 117 With the trapezoidal rules developed, the zero-sequence active power is computed: p a (k) = 1 T ˆ T k T p 0 (k) (5.2) And then the active zero sequence energy is calculated and compared to a threshold ˆ T e 0 (T ) = e0_old + p a (k) (5.3) 0 Some explanation can clarify the way to compute the active power equation 5.2. The active power of the sample k is the integration of the forty previous samples - one period if the sampling frequency is different than 20 ms - divided by the period. Because is is assumed that the p0 is almost zero before the earth fault, the first period received to determine the direction can be computed that way: p a (k) = 1 T ˆ k 0 p 0 (5.4) The vector pa must be placed in memory - named old_pa - and will be used for the next period: new_p a (k) = 1 T ˆ k 0 p0 + old_p a (last_sample) old_p a (k) (5.5) With this way to compute the active power, it will fit the equation 5.2 without memorizing too complex vector due to the use of a sliding window. The two next figures 5.2 and 5.3 illustrated the way to determine the direction. The direction determination starts at 46 ms in this figure. In case of low impedance fault, the average energy during the window 46ms -66ms is high enough to be detected as reverse or forward in both case. Energy p a (k) 3 x Sound Feeder Faulty Feeder Reverse zone Forward zone Forward direction! Reverse direction! Unknown zone time [ms] Figure 5.2: The three zones of direction and determination in case of LIF The importance of the synchronization with the inception of the fault can be explained with this picture. If the determination of the direction window starts earlier, the average energy will be much smaller and could be in the unknown zone. On contrary, if the window starts much later, the fault could be gone and the energy will be decreasing which will be measured as a negative energy by the device and could lead to a wrong determination. A high impedance fault shows a very small energy and therefore the average energy could be not high enough to determine safely the direction of the fault. The fault direction is then unknown in this case as illustrated by the figure 5.3.

118 5. DIRECTIONAL METHOD 118 Energy p a (k) 3 x Reverse zone Forward zone 2 Unknown zone Sound Feeder Faulty Feeder time [ms] Figure 5.3: The three zones of direction and determination in case of HIF 5.2 Feedback and updates from the tests The new way to determine the direction of the fault has shown really good results regarding the sensitivity. However, in some cases, false direction determinations occurs. In every case, the problem occurs when a loop with strong circulating currents is measured. The circulating current does not have the behavior of an earth fault and if the feeder is faulty, it could be detected as a sound one because of this behavior. This circulating current could have an active part compared to the zero sequence voltage produced by the fault. Because this current is circulating, one feeder will measure an active part which is positive and the other will measure it as negative. The determination of the direction is then disturbed by these currents. The next figure shows the zero sequence active energy if the circulating currents are not filtered. The signals come from real recording and the four feeders are connected in one big loop. The four feeders are sound, if there is no circulating current, all the active energy should increase to charge the healthy capacitance of the loop. The fault impedance is really high and the zero sequence current produced by the fault on the sound feeder has a smaller amplitude than the circulating current. 2 x Feeder 1 Feeder 2 Feeder 3 Feeder 4 Energy time [ms] Figure 5.4: Zero sequence active energy with circulating current in a four feeders sound loop If the circulating currents are suppressed by the signal processing as detailed in section 2.2, the zero sequence active energy measured is mostly due to the charging of the zero sequence capacitance of the sound loop. There is still a small drift because the circulating currents are not completely filtered; the threshold should take this into account and the detection window too. If no fault has been detected several cycles after the fault inception, the deletion of the

119 5. DIRECTIONAL METHOD x 10 5 Energy Feeder 1 Feeder 2 Feeder 3 Feeder time [ms] Figure 5.5: Zero sequence active energy without circulating current in a four feeders sound loop circulating current could not be as efficient as it was because of drifting, loads level changes, etc. Therefore, the algorithm should be stopped after five cycles.

120 6. Summary This chapter focuses on the technical aspect regarding the development of a prototype for fault detection and direction determination of single phase earth fault in compensated network. The constraints that occur when transferring from the Matlab code to the device has been described. The fine tuning concerning the threshold, the starting, stopping of the methods have been considered. Several problems have been noticed during the first test phase and the development especially regarding the starting time and the pick-up threshold. Feedback from these tests have been used to improve the sensitivity of both methods and reduced the number of wrong fault detection. The circulating current problem has been solved by an active filtering using the pre-fault value and considering the loads as constant before and during the fault. This method keeps a good sensitivity but cannot run the algorithm in case of permanent earth fault because the drift in the suppression of the circulating current could create errors after several periods. 120

121 Part V Fault Location in Compensated Network 121

122 1. Introduction Once a detection algorithm has been implemented in a prototype, the next part of the research concerns the fault location of single phase earth fault. The research has begun with a state of the art and a comparison of the existing methods but it quickly appears that it was important to define the goal of the fault location to take the right direction. A survey was then made among several operators which helped to understand the problems of a commercial fault location. This chapter introduces the theoretical concepts of the fault location made during this work. Many different solutions exist and come from the transmission power system. However there is some differences between the transmission and the distribution network. The first section describes the needs of fault location in the German compensated networks. It was important in this work to clearly understand what are the needs of the distribution system operators to design the adequate technique. A survey has also been made with several operators to understand their problem and the structure of their network with distributed generations, loops, etc. The second section gives a general state of the art in fault location. The standard [C , 2005] elaborated in 2004 by the IEEE society is mainly used because most techniques are summarized in it. Classic impedance method is presented and compared to traveling wave techniques. Some methods developed especially for the fault location in compensated networks are analyzed. Others have been developed during the nineties but no truly commercial application has appeared since. The experience built during this PhD work tries to explain the reasons of this lack. Then we shall explain how and why we have chosen a fault detection strategy based upon the steady state. The third section describes the challenges of the fault location choice using the steady state such as the current level, the equations and the different possible topologies. Explanations are provided for decision making in case of trees structure. The loads and the distributed generations could also be a problem because it is a current infeed/outfeed that the algorithms are not aware of. 122

123 2. The needs of fault location in compensated network 2.1 Today s fault location First of all, it is necessary to explain how a fault location is processed in a compensated network nowadays. When a single phase earth fault is detected on a feeder, either this fault is permanent or not. If it is not permanent then no action is taken because the fault can come from many short-life phenomena. Floating plastic bags or tree branches touching the overhead lines then burning are an common example. If the fault is permanent, a location of the fault must be performed to enable the repair. This fault location is made in two steps. Firstly an intervention team has to go along the line to locate the faulty section then secondly they precisely locate the position where the repair must be made. A section is a part of a line between two secondary substations, this section is homogeneous meaning the linear impedance is the same along the section (i.e. it is the same power line characteristics). Each section must be checked until the faulty one is found. The procedure to find it is extremely time consuming because the intervention team has to switch off and switch on manually some of the feeders. In Germany, many distribution system operators have the possibility to connect the faulty feeder with another feeder to create a temporary loop structure. The goal of this loop is to have two direction indications in the main substation so, by opening the loop at different position, it is possible to locate the faulty section. The advantage of this technique is to maintain the power in the whole network during the location of the faulty section. The procedure to locate the faulty section in a temporary closed ring is the following: 1. Detect the fault on the feeder 2. Connect the feeder to the other one to create a temporary loop structure 3. Disconnect the loop at another position 4. Check if the feeder is still faulty, if yes go to step 3 5. If not, the section disconnected from the former faulty feeder is the faulty one The following figure 2.1 describes the procedures with a flowchart diagram. Each switching on and off is usually done manually. Therefore a patrol has to drive to the secondary substation to connect or disconnect the feeder [saha et al., 2010, Nikander and Järventausta, 1998]. This procedure is then very time consuming and the whole procedure can take one or two workdays. New substations are sometimes connected to a central control room from which they can be 123

124 2. THE NEEDS OF FAULT LOCATION IN COMPENSATED NETWORK 124 teleoperated but even in that case the direction information coming from the protection devices are usually not sending the information back to the central unit. Therefore, a patrol still has some driving distance to do. Fault detection Close the ring Open the ring at a different position No Does the fault direction has changed? Yes Fault detection Figure 2.1: Flowchart explaining the procedure to locate the faulty section in compensated network with ring possibilities The following figure 2.2 illustrated the procedure in four steps. The ring is opened in different position until the fault direction is changing, the faulty section is then the feeder that has changed on the open loop Faulty section is located Figure 2.2: Schematic describing the faulty section location in a ring structure Once the faulty section has been detected, a so called chariot is brought to the secondary substation of the faulty section to make an accurate fault location. This concerns fault location in cables. This equipment creates pulses which allows the team to locate the fault

125 2. THE NEEDS OF FAULT LOCATION IN COMPENSATED NETWORK 125 precisely and to begin the repair by digging into the ground at the exact fault location if it is a underground cable. Fault location in overhead line can be easier if the field is more accessible. 2.2 What fault location algorithm could bring Bringing a fault location algorithm into the main substation will save a lot of time to the operators if the location can be faster than the whole process described above. However, it is not possible with today s structure and technologies to precisely locate the fault using only the measurement from one substation. There are many factors that impact the precision. Therefore, it has been assumed that the fault location will still be operated in two steps. This work has then been focused on the improvement of the first step i.e. finding the faulty section, because it is the most time-consuming one, due lots of travels and non-automated tasks.. An algorithm that would find the faulty section would save time to the intervention team because it will not have to drive and disconnect the sections many times. However, once the faulty section is detected, the precise fault location still must be done with the appropriate equipment. If this fault area is quickly located then the user will have to check only a few sections instead of the whole feeder. An efficient fault location to isolate the faulty section or to provide the user a faulty area where the fault has a great chance to be is the goal of this thesis. A short state of the art is presented and then a choice in the actual fault location solution has been made and a deep study of this solution is the outcome of this work with practical suggestions for future implementation.

126 3. State of the art of fault location and application The goal of this chapter is to provide very general information about the different fault location techniques. The presented methods have advantages and disadvantages and they were not deeply investigated in this work The steady state method is the one used in this work. Some reasons are given why it has been chosen but the others methods could be more investigated in the future and are clearly not rejected. 3.1 Charging transient During the 1990s, several works have been presented to locate the fault in compensated network using the charging transient [Welfonder, 1998, Lehtonen, 1992]. Depending on the network model used, an equation of the charging transient can be linked to the fault distance. For example, Welfonder has determined the equation of the frequency of this transient as (detailed in the section ): f charge 1 2π (1.5L T + dl d )2(C g,tot + C p,tot ) (3.1) The parameter L T is the inductance of one phase of the transformer, l d is the linear inductance of the faulty line, C g and C p are the total capacitance phase-to-ground and capacitance phase-to-phase of the network. According to this equation, if the frequency can be measured with enough accuracy and the parameters are known, then the fault location can be found because there is a relation with the distance in this equation. The model on figure 3.1 has been used to determine this equation. The left drawing illustrates the network with a three phases representation and a two-feeder compensated network. The right figure shows the simplified network developed by Welfonder to establish the relationship between the charging frequency and the network parameters. The parameters must then be very accurate so as the measurements of the charging frequency. However, even if some simulations show that there is obviously a relationship between the frequency and the distance the reality seems more complex than the model currently proposed if a distributed lumped model is used for fault simulation. Also, to confront this model with the reality some assumptions might be reconsidered: 1. This model assumes the lines are homogeneous which is often the case in transmission network but not in distribution network. 126

127 3. STATE OF THE ART OF FAULT LOCATION AND APPLICATION 127 Figure 3.1: Model to determine the frequency of the charging transient 2. The capacitive model is considered with only a series impedance on the faulty phase of the line. 3. The fault is purely resistive during the transient. To identify the charging frequency, several method can be used such as a simple FFT or more complex mathematical tools such as wavelet, differential or neural network algorithms [Imris, 2006, Hänninen et al., 1999][Eberl et al., 2000]. Despite this modeling problem that could be improved, experimental results and recordings have shown that the transients is not always present in single phase-to-earth fault. The fault can have a high impedance in which no charging frequency is measured. More often the fault is intermittent due to the effect of the Peterson coil. Such intermittence lasts only half a period of the charging transient, the fault is only a strike or a few milliseconds which makes very difficult to measure the charging frequency. On a set of 40 recordings received from Siemens, only 20% had a frequency higher than 50 Hz which could be considered as a charging frequency. It might be possible that a higher sampling frequency than the 12.8 khz - supposing that the charging frequency was higher than 6 khz - used in the recorder would have measured a higher charging frequency but this could have increased by 10% the signals with interesting frequency. Fault location using this system then depends on the network conditions and are not controlled by the user. Therefore, this solution was not chosen in this work. 3.2 Fault passage indicators A technique requiring much more equipments is the installation of several fault indicators along the feeder. The distribution network has a direction indication at each secondary substation [Management, 2013]. Using the transient measurement or based on a magnetic sensor [Bjerkan and Venseth, 2005], a direction indication is provided to the user. Usually a color is displayed on the device e.g. green means that the section is reverse and red means that the fault is forward. Unfortunately these devices are not equipped with any transmission system, so that a patrol has to drive at each secondary substation to check which direction

128 3. STATE OF THE ART OF FAULT LOCATION AND APPLICATION 128 has been detected. This technique is faster than the complete manual fault location because neither opening nor closing of secondary substations are required. An example of faulty section identification using fault passage indicators is illustrated by the figure 3.2. BB sbb 1 sbb 2 sbb 3 sbb 4 sbb 5 : Reverse : Forward Figure 3.2: Example of fault passage indicators for a radial feeder The costs of such system can vary depending of the network and the technology used. If the fault current is significant, the fault passage indicators can catch the magnetic flux from the fault current and indicates the direction. Such devices do not require any current or voltage transformers and can be relatively cheap. 3.3 Traveling waves This method needs a very high sampling frequency because it measures the electromagnetic wave reflection on the bus bar and on the fault location. The principle of the fault location is simple and is described by the figure 3.3. When the fault occurs, an electromagnetic traveling wave is produced by the fault, once it reaches a point where the medium has a different impedance, a reflection will occur. At this moment a first peak is measured by the device. This wave will reflect at the fault position due to the presence of the fault arc and will come back to the bus bar. The measurement of the time between the two peaks and the knowledge of the wave speed gives the fault distance. t0 t11 t12 t Figure 3.3: Effect of the fault used in the traveling wave fault location principle This solution is used in transmission grid [Crossley and McLaren, 1983, Lopes et al., 2011] but some papers are trying to implement it for application in distribution network as explained in [Borghetti et al., 2007]. One advantage compared to the others solutions is the immunity

129 3. STATE OF THE ART OF FAULT LOCATION AND APPLICATION 129 to power-frequency phenomena such as transformation saturation, power wings 1, fault type and source parameters of the system [saha et al., 2010]. Some methods use an additional measurement device to achieve a two-ended traveling wave method. The devices are then synchronized by GPS [Lopes et al., 2011]. The speed of the waves is different in cables and overhead lines which could decrease the accuracy if the speed is assumed to be the speed of light. The heterogeneity of the feeders creates multiple reflection between the secondary substations which could create difficulty in the algorithm. Teed circuits are difficult topology where multiple reflections appear but solutions are suggested [Evrenosoglu and Abur, 2005]. 3.4 Steady state This method uses the 50 Hz component of the network to find the fault location. An impedance based model of the faulty feeder is made for example using PI line model. When a fault occurs, measurements are taken and the fault distance can be found thanks to the relationship between the measurements and the parameters of the model. The accuracy of the steady state depends on the voltage drop along the line. Phasors are usually computed during the steady state of the fault. Different equations and techniques are available to compute the value in the literature. The first and simplest technique is the use of one single point of measurement. In this case every parameter of the feeder is required and a model of the fault must be developed. Indeed, the electrical loop used to determine the fault location equation consists in the feeder and in the return path from the ground. The second way is the use of multiple measurement points. It is necessary if there are several infeed in the network. The equations are then different and can use a path which does not need the ground impedance and a fault model. This work will focus on the steady state method. A model of the feeder has been created and studied. The following sections of this chapter describe the equations considered during this work and the associated problems. Then different strategies are presented depending on the topology of the network and on the faulty part. 1 moving power lines

130 4. Challenges of steady-state fault location 4.1 The compensated network problem The problem of compensated network compared to the other distribution network is the very small faulty current. Therefore the associated voltage drop is not high enough to enable an accurate fault location. This statement is demonstrated in the next chapter with a sensitivity analysis and Monte Carlo simulations. Another problem linked to the Peterson coil is that this small faulty current is not strong enough to avoid insulation recovery for example in underground cable. The fault is restriking when the voltage is increasing again and has a sufficient magnitude to break through the insulation. This phenomenon leads to intermittent and restriking earth faults which do not have steady-state fault current making the fault location impossible. Two solutions are suggested in the literature to use the steady-state method with compensated network. The first one proposes to change the compensation of the network by switching on a resistance in parallel to the Peterson coil [Eberl, 2004, Fickert et al., 2007]. The fault current will be increased because the impedance of the zero sequence system is smaller. Such resistance provides a fault current magnitude between 1 to 3 times the maximum load current of the feeder. Others resistances can provide much bigger fault current but there is a question of safety and damage on the equipment. This is enough to stabilize the fault and have a sufficient steady state to make a correct phasor estimation. The figure 4.1 illustrates the connection of a parallel resistance to make a steady state fault location. Figure 4.1: Connection of a parallel resistance to increase the fault current The impact of the parallel resistance are recorded and shown in the following figure 4.2. The figure illustrates the voltage on the faulty phase, it decreases quickly at the beginning of the fault and is quite stable until the parallel resistance is switched on. The fault is very stable even during the earth fault however it is important to notice that it is a recording made during a test field where the fault has been solidly connected to the ground. The behavior of a actual fault might be different. Also the voltage on the faulty phase during the fault 130

131 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 131 does not drop very much. This could be explained by a high fault resistance which limits the voltage drop. 2 x 104 Beginning of the fault Voltage phase 2 [V] Parallel resistance switched on Time [ms] Figure 4.2: Example of signal increasing due to the connection of a parallel resistance The small voltage drop during the fault has also an impact on the faulty current. The figure 4.3 shows a very small current increase of around 20 Amps primary compared to the 100 Amp of load before the fault occurs. Switching on the parallel resistance doubles the faulty current value but it is still small compared to the loads current. This is due to the small voltage drop. However, simulations of the parallel resistance clearly shows a stronger faulty current as it is discussed in the chapter VI. 150 Beginning of the fault 100 Current [A] Parallel resistance switched on time [ms] Figure 4.3: Example of current increasing due to the connection of a parallel resistance The second idea is to install an active element in the transformer neutral. The goal is to keep the compensation at 50 Hz and injects a current at higher frequency [Buigues et al., 2012, Dan and Raisz, 2010]. It has the advantage that the series impedance of the line will be larger because the line is mainly inductive - ωl f - which could make the fault location more accurate. However, the shunt capacitances are also smaller at higher frequency. Steady state, they could be neglected at 50 Hz but probably not at higher frequencies. The model of the line might not be always true. The injection source must be strong enough to stabilize the fault even if the 50 Hz signal is not stable. The injection is in the transformer neutral which will lead to a production of zero sequence current.

132 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 132 Figure 4.4: Injection of a signal from the transformer neutral Our fault location algorithm has been implemented using this method. A model of the network is built and simulations are run with thousands of different fault positions and fault impedances for a specific injected frequency. This builds a look-up table where the fault can be located once the voltage and current measurements have been made. There is almost no computation during the fault, all the computation is made during the setup of the fault locator. Values are then interpolated if they are between two simulated values. 4.2 Single-ended method The single-ended method uses only one measurement point which is the one available in the main substation. The three phases current and voltage are measured and the symmetrical components can be computed from them. The electrical circuit used to locate the fault is illustrated by the figure 4.5. The fault current is flowing through every symmetrical system and the fault. The distance is computed as the distance that creates the voltage drop on the circuit on each symmetrical system. The fault connects each system at this point. The equation of the fault location is then: V 0 dz 0 (I 0 dc 0V 0 2 ) + V 1 dz 1 (I 1 dc 1V 1 2 ) + V 2 dz 2 (I 2 dc 2V 2 ) = 3R f I f (4.1) 2 This equation has two unknown variables which are the fault resistance and the distance. The faulty current can be estimated based on the zero sequence current. I f = I 0 (4.2) More complex models can be made to consider the zero sequence current flowing through the capacitances of the faulty line but with the increasing of the faulty current by the parallel resistance, the capacitive current can be neglected. However, the model of the fault has to be a pure resistance because a complex impedance would add an unknown parameter to the equation and the system would have two equations for three unknown variables. Nevertheless, this assumption is plausible because it is generally accepted that the electrical arc consumes only active power over one period and therefore can be considered as a pure resistance. Shunt capacitances are considered in this model with a PI model depends on the kind of power line. The shunt capacitance can usually be neglected for overhead line but there influences must be evaluated for cables. This impact is deeply studied in the next chapter. The fault location equation can be divided into a real part and a complex part and simply solved by a matrix equation:

133 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 133 Figure 4.5: Schematic of a fault location model using a single ended method [ d R f ] [ real( 2i=0 Z = i (I i dc iv i 2 ) 3real(I f ) imag( 2 i=0 Z i (I i dc iv i 2 ) 3imag(I f ) ] 1 [ real( 2i=0 V i ) imag( 2 i=0 V i ) ] (4.3) The model with the shunt admittance needs an iterative computation of the fault distance to converge to the real distance value. For example, d begins with a value of 50 % and changes at each iteration Heterogeneous line The equation 4.3 assumes the line is homogeneous because the impedance is constant on the PI model. Additional equation is necessary is the line is not homogeneous because the voltage and current must be computed at the location where the section is homogeneous. This is illustrated by the following figure 4.6. The faulty is not known on the faulty feeder therefore, the fault location must be tested on several section before finding the faulty section. Here the algorithm tests the first section then the second, etc. until a result is possible. The equation to compute the voltage and current at the end of the section is simply a computation of the voltage drop and the current leaking into the shunt capacitance. The

134 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 134 V&I Step 1: Test FL d>1 Step 2: V&I Test FL d>1 Step 3: V&I Test FL d<1 Figure 4.6: Computation of the current and voltage on the faulty section following equation gives the equation for the zero sequence system where i is the end of the i th section Tree structure V0 i = V0 i 1 Z0(I i 0 i 1 Ci 0 V 0 i 2 ) (4.4) I0 i = I0 i 1 Ci 0 (V 0 i + V 0 i 1 ) 2 (4.5) Specific topology might require additional measurements to locate the fault on every part of the feeder. This problem occurs in case of a treed feeder. This feeder has a main power line in which secondary substations distribute the power in several direction called branches. The following figure 4.7 illustrates the topology of a tree feeder. BB F1 F2 : V & I F3 Figure 4.7: Topology of a tree feeder The problem with the single-ended method is the case where the fault is on one of the branches F1, F2 or F3. The algorithm finds several solutions where the fault might be. If the fault is at a position smaller than any branch length than the fault could be on any branch. Therefore no distinction can be made until additional measurements are installed in

135 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 135 the network. To locate the fault in one position, only two current measurements have to be installed on the two branches. By checking this current value, it is possible for the algorithm to detect if the branch is faulty or not. 4.3 Two-ended method Some topologies or the addition of a voltage and current measurements create the possibility to use a two-ended method. In this case, a different electrical path is available to find the fault distance using the steady state. This path is very interesting because it uses only one symmetrical system and does not need any model of the fault because the circuit does not integrate it. Figure 4.8: Schematic of a fault location model using a two ended method The equation of such fault location is then: V1 bb = V fault 1 + dz 1 (I1 bb dc 1V1 bb ) (4.6) 2 V1 end = V fault 1 (1 d)z 1 (I1 end (1 d)c 1V1 end ) (4.7) 2 The unknown variables of these two equations are the complex value of the voltage at the fault location and the real part of the distance. A complex part is computed and represents the errors made on the voltage measurements. This part is not important for the fault location but it could still be considered as a precision information. The equations presented represent the positive sequence system. However, any symmetrical system can be used for the fault location and the equations are the same. Of course using one symmetrical system will require the respective parameters and measurements of this system.a huge advantage of this method is that it does not need any model of the fault current or impedance. Only the accuracy on the measurements, parameters and PI model impacts the error on the result. All this sensitivity is analyzed in the next chapter. A simple matrix equation can compute the distance.

136 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 136 [ V fault 1 d ] = [ 1 Z 1 (I bb 1 2 ) 1 + (1 d)z 1C 1 2 Z 1 (C 1 V1 end dc 1 V end 1 dc 1V bb 1 ) ] 1 [ V bb 1 V end 1 + Z 1 (V end 1 C 1 dc 1 V end 1 ) ] (4.8) The model with the shunt admittance needs an iterative computation of the fault distance to converge to the real distance value. Also, one difficult tasks with two ended method is to bring the information at the same place where the fault location can be computed. This requires a synchronization of the signals and communications link. The fault voltage is not necessary in our application but its value can be checked to be realistic or not. The distance is normally a real quantity but errors on the variables will solve the equation in a complex value. Only the real part represents the distance to the fault. However the complex part can be checked, perfect case should lead to a null complex quantity or a very small one. Big value should indicate strong error and suggests that the computed distance is probably not the real distance to the fault Heterogeneous and tree structure Regarding the non homogeneity of the power lines in distribution network, the technical developed for the single ended measurement can be applied in the two ended method. The voltage must be computed for the both end of the considered section. Voltage at the beginning and at the end of the line must be used for the respective beginning and end of the section. The tree feeder has the same problem as the single ended method. It is not possible to know on each branch the fault is. However, a method can be used to find the faulty section if there is only one branch per secondary substation. It is not possible to locate the fault with a two ended algorithm but the isolation of the faulty section can be made. V&I V&I Step 1: Step 2: Test FL d>1 V&I V&I Test FL d>1 V&I Step 3: V&I Test FL d<1 V&I Figure 4.9: Identification of the faulty branch with a two ended algorithm The figure 4.9 illustrates the procedures to identify a fault which is not on the main feeder but on the branch.

137 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 137 Once this branch has been detected as faulty, the voltage and current at the secondary substation feeding this branch can be computed. This value can be used to apply a singleended algorithm on the branch if the branch is very long and contains several sections. If the feeder had several branches starting from the same secondary substation then additional measurements must be installed to identify which branch is faulty. If the feeder has only one branch per secondary substation then it is theoretically possible to isolate the faulty section and apply a single-ended method to locate the fault. The following figure 4.10 illustrates the procedure. V&I V&I Step 1: Step 2: Test FL d>1 V&I V&I Test FL d>1 V&I Step 3: V&I Test FL d<1 V&I Figure 4.10: Procedure to isolate the faulty branch in a tree feeder and locate the fault The fault location must be applied on each section of the main power line. If no fault has been located on this main power line it means that the fault is on one of the branches connected to it. According to the measurements at both ends, the computation of the voltage at the substation feeding the faulty branches will be equivalent if it is computed from the bus bar measurement and from the end measurement. This is not true for the others node because an over or under estimation of the voltage drop will happen from one side. Indeed, if we assume the fault is on the first branch of the figure 4.10 instead of the second branch, then, the voltage at this node computed from the end will not match the voltage at this node computed from the main substation. The voltage from the end will be much bigger because it does not considered the fault current flowing through the second section. The measurements value are true only for this specific faulty branch Loop topology One specific topology of the distribution especially in Germany is the loop structure. This structure has a strong advantage for the two-ended method [Nikander et al., 2003]. The two measurements are in the same main substation which avoid the cost and the installation of a communication link between the two ends of the feeder. The synchronization is also very simple. The voltage measurement is also the same for both devices which simplifies the equations.

138 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 138 V 1 = V fault 1 + dz 1 (I1 bb dc 1V 1 ) (4.9) 2 V 1 = V fault 1 (1 d)z 1 (I1 end (1 d)c 1V 1 ) (4.10) 2 The equation is then much simpler and the synchronization error is almost non-existent which such strategy. The equation when the line is homogeneous is only a current ratio. Indeed, the current will be distributed depending on the fault position. I1 end C 1V 1 2 d = I1 bb + (4.11) Iend 1 C 1 V 1 The series impedance is not present in this equation therefore an error on this parameter does not impact the result of the fault location. Some distribution system operators have loops with more than two feeders. The voltage at the end can be calculated but it is sometimes measured, this can be done using two sound feeders. There is a redundancy in such system to compute this voltage because there are several electrical paths Figure 4.11: Closed ring structure made of more than two feeders In such configurations, the fault location is made in two steps; the first one is the detection of the faulty feeder inside the closed ring and the second one is the location of the fault. The detection of the fault can be made using the directional algorithm if there are direction indicators on both end of the feeders. If such devices are not available then the strategy is to assume that the fault is on one feeder, to run the algorithm and to check if the result is coherent. The equation below is an example of fault location formula if the fault is on the feeder 1 with a closed-ring structure made of four feeders as illustrated by the figure The positive sequence is used and the shunt admittances are neglected for the sake of clarity but can be considered in the final algorithm. V1 bb = V fault 1 + dz 1 I1 bb (4.12) V1 bb = V fault 1 + (1 d)z 1 (I2 bb + I3 bb + I4 bb ) + Z x I x (4.13) The subscript x is one of the assumed sound feeders. In this case, x will take the value 2, 3 and 4. One of this equation will result in a distance between 0 and 1 while the other

139 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 139 ones will not. The selection of the faulty feeder is based on this result. This feeder should be the one with the best (i.e. having the least standard deviation) measurements. If the feeders seem equivalent, the position could be run with every sound feeder and a least square method will minimize the error on the location. 4.4 Loads and DGs impact on fault location In compensated network, the fault current is small and a parallel resistance must be switched on to increase the faulty current. However, the faulty current will be increased up to one to three times the maximum load current on a feeder. Therefore, the impact of the loads cannot be neglected for fault location and a model must be used. Also the distributed generation can be considered here as a negative load where current is an output instead of an input. The difference made in this work is that the distributed generation can be impacted by the single phase earth fault and therefore the infeed current from the sources can change before and during the earth fault. The loads are not affected by the single phase earth fault because they consume phase to phase current which does not change during single phase-toearth fault Loads and DGs impact The impact of the loads on the fault location concerns a current flow that is not modeled in the network which leads to wrong voltage drop estimation. The problem appears if the loads are distributed along the feeder because there is a current flow that cannot be measured. By assumption, the fault locators using the positive and negative sequence symmetrical systems are impacted by the loads. The zero sequence system does not have any load connected because the transformer connection is a delta wye in Europe which blocks the circulation of zero sequence current between the two voltage levels. The following figure 4.12 illustrates the problem of the fault location if the faulty current is not high enough to neglect the load current. The loads consumes current which reduces the current along the feeder. Therefore the voltage drop is smaller beyond each load as illustrated. If the algorithm is not aware of this load information, it assumes that the current is constant along the feeder and hence that the voltage drop remains constant. Therefore the estimated position of the fault is closer than it is in the reality. However, this error only occurs if the loads are between the measurements and the fault. If the fault is closer than the loads, the faulty current is overestimated if the zero sequence current is not used but the voltage drop is correct. Overestimating the fault current leads only to a underestimation of the fault resistance but does not impact the distance. This is illustrated by the figure This condition is often not realistic in distribution network because the network is made of several secondary substations where the loads or low voltage networks are connected. The loads must be then considered as distributed along the power line. The quantification of their impact is studied in the next chapter regarding the sensitivity of the methods and their errors. The best solution to avoid any error due to the load is to measure it and transmit the synchronized measurement to the fault locator. Such a solution is extremely expensive and therefore not realistic except in a long term fully integrated smart grid. This work wants to be more practical and pragmatic and suggests others strategies. Some model of the loads must be made to estimate the current flowing into them.

140 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 140 BB Voltage V bb Estimated fault position V fault distance Figure 4.12: Impact of the distributed loads if the fault current is not significant BB Voltage V bb Estimated fault position V fault distance Figure 4.13: There is no impact on the fault distance if the loads are beyond the fault Our fault location algorithms uses the steady-state signal and considers an impedance based load. The reality can be different because the load consumption is not always depending on the voltage value especially with the increasing part of non-linear electronics loads. However due to the use of the steady state and to the short amount of time required for the fault location, the load is supposed constant during the whole process and can be modeled as a simple impedance. More investigations could be done in future work on fault location in distribution network Loads and DGs model Some papers present different methods to estimate the loads in a distribution network. The first method consists in the estimation of the equivalent load tap somewhere along the feeder depending on the prefault value [Altonen and Wahlroos, 2007]. The authors assume evenly distributed load along the feeder. A fictional load tap having the value of the prefault is introduced at a distance s from the substation. This distance s depends on the actual voltage drop along the line. This method is illustrated by the figure The measured prefault current and a model of the power line gives the slope of the dashed blue line. This blue line is stopped where it reaches the voltage at the end of the feeder. This

141 4. CHALLENGES OF STEADY-STATE FAULT LOCATION 141 Figure 4.14: Method of load tap from [Altonen and Wahlroos, 2007] method requires the voltage at the end of the line to know the tap distance s defined by the equation below with the numerator being the actual maximum voltage drop of the feeder and the denominator is the fictional voltage drop if the entire load would have been tapped in at s. s = U drop(real) U drop(s=1) (4.14) This method reduces the error made by the load if the tap is between the fault and the bus bar because it estimates a current flow for the loads which the classic algorithm does not consider. However, if the load tap is beyond the fault location then the error is the same because the equation is the same. This method is not perfect because it does not consider the real current flow. Others methods assume the load position is known and only a model of it is necessary [Herrera-Orozco et al., 2012, Nunes and Bretas, 2010]. These models improve the fault location but they do not consider the fluctuations of the loads or the distributed generation along the time. Others papers use the ultimate solution consisting in measuring of the distributed generation to consider it in the fault locator [Orozco-Henao et al., 2012]. The problem with these models is that they do not consider any time dependance of the loads which can change from 0% to 100% during a working day depending on their nature. Therefore, this work has been focused on the development of a strategy taking those fluctuations into account and which is the subject of the next chapter.

142 5. Summary This chapter presents the general information required to understand the fault location problem in compensated network. The need of a fault locator by the distribution system operators has been discussed and the goal of the fault locator has been clearly defined. Firstly the problem of fault location is discussed. The purpose of a fault location algorithm is explained as well as the benefits it could bring to the operators of compensated network. The main argument is a time saving to locate the faulty section of a feeder. A more accurate fault location is particularly useful if digging to repair the cable is necessary. A short state of the art regarding fault location algorithm is detailed. The specific charging transient in isolated and compensated network has been described for fault location purpose. Then the traveling waves problems have been introduced followed by the steady-state theory. Each theory has pros and cons regarding the accuracy of the fault location and its implementation. Comparing the different methods, we have chosen the steady state fault location method. The challenges of the steady state method have been detailed for different algorithms using either a single measurement or several ones. The topology of the faulty feeder influences the algorithms because some decisions must be made. Tree feeder requires additional current measurement if a single-ended method is used. Two-ended methods can identify a faulty branch in theory but location inside a branch is not always possible. Then the loop structure is considered and the advantages of this topology are explained with the use of a two-ended method. We have shown the advantages of combining this topology with a two-ended method. Last, a short discussion has been then made on the modeling and on the impact of the loads. 142

143 Part VI Fault Location Tool and Sensitivity Analysis in Compensated Network 143

144 1. Introduction This last chapter describes the work made to locate the fault in a compensated network. The work has been focused on the accuracy of the existing algorithms and not in the developments of new methods or power line models. It has been assumed and demonstrated that the models are not the main issue but that the present problems of the fault location comes from the knowledge on parameters and measurements. The main problem with the fault location is its accuracy. The distance found has to be as close as possible to the real distance. If not, the user will not be able to improve costs and restoration time. In fault detection, the accuracy is not important because it is only a difference between a faulty and a healthy model which is significant to work properly. Fault location requires an accurate model of the network and also accurate measurements. Each error will change the distance found. The impact of the errors will be deeply studied in the next chapter with a sensitivity analysis. This section considers the algorithms that are used in this work and the line model studied to locate the fault. A discussion about the implementation of the method in the real distribution is also made based on the interviews the author has had during his PhD thesis. Firstly algorithms are usually accurate enough if the parameters and the measurements are well known. The problem is that the users do not know exactly the parameters. Considering all the possible errors, the fault locator will be less accurate even if the equations are correct. Therefore the performance of the algorithm should not be made on the exactness of the model but more on the sensitivity with the different parameters using Monte Carlo simulations or a probabilistic law. Secondly, due to the demonstrated complexity of the fault location, a tool has been suggested to understand the improvements which could be brought in a compensated network to achieve the required accuracy for an operational fault location. Then a sensitivity analysis is presented. It has been made to understand the weaknesses of the steady-state fault locator in compensated network. We have studied the impact of the fault current magnitude, the power lines model, the single-ended and two-ended algorithm comparison, topologies, etc. These results are followed by suggestions depending on the topology and on the actual the accuracy to have an efficient fault locator. 144

145 2. Fault location main problem Many papers are publishing new methods for fault location and different models but a few are really implemented in the distribution network. The problem often lies in the non consideration of the errors coming from the measurements and on the parameters. An accurate fault location requires a as good as possible knowledge on parameters such as the series impedances and precise measurements of the voltage and current. However, according to a survey amount German distribution system operators and available ion the appendix B, many distribution system operators state they do not know the value of their zero sequence series impedance. 2.1 Parameters and measurements accuracy The fault location with the steady state values require lot of information from the network. The topology. The algorithm has to know which method is able to locate the fault depending on the actual lines layout. If there are branches, decisions must be made to select the faulty branch and use additional methods to estimate the fault location in this branch. The voltage and current. Depending on the method, the three symmetrical components must be known which requires a measurement on the three phases. The parameters of the faulty lines. The series impedance and shunt admittances for each section for the three symmetrical system are required for the algorithms. The distribution system operators usually know very well the positive sequence. The negative sequence is the same because there are no rotating part in a distribution network and consequently is the same as the positive value. The loads and DGs are not considered because only the network part is necessary with this method. Loads and DGs bring others errors that will be explained further. However, the zero sequence parameters are not known and when they have to use them, the operators apply a coefficient to the positive sequence impedance as in equation 2.3. The information has to be very accurate otherwise the method cannot work properly. Indeed, the idea behind the fault location is to build a model of the system where the distance parameter is the only unknown. However, if the others parameters have errors, then applying a perfect model leads to errors on the distance. This work separates the errors in two different kinds. The first kind is the standard error coming from the errors made during the measurements of the current and voltage but also from the power lines parameters. These errors come from the noise on the signals and the accuracy limits of the measurement devices.it means that if several measurements are 145

146 2. FAULT LOCATION MAIN PROBLEM 146 made on a parameter, the value will be spread around a mean value. The parameters have a standard error because it is possible to measure several times their value and obtained a Gaussian distribution of the impedance and admittance. An example of standard error is represented by the figure 2.1. This error is uniformly distributed on the real and complex axis but different shape like an ellipse can be investigated in the future. Indeed, magnitude and phase errors can be different. The errors are considered as a percentage of the nominal value therefore the relative error depends on the measured magnitude. The figure 2.1 shows that if the current magnitude is smaller, then the relative error will be larger (but the fault current is small in compensated network). This is important to know because it means that the larger is the value, the better is the accuracy. This problem is also due to the quantization error of analog-to-digital converters(which is at least +/- 1/2 bit), and has a larger relative impact on small values. Imag(I) Error I 1% Error I 30% Real(I) Figure 2.1: Standard error representation on a phasor measurement Regarding the standard error, each parameter has a standard deviation. This deviation has been set by default for the variables in the table 2.1. The measurements of the current and voltage are very accurate and an error of 1 percent has been considered. A discussion could be made about the analog-to-digital conversion regarding the zero sequence measurement because some protection devices have a sensitive measurement for this value. However a conservative value has been kept. The positive series impedance is also well known depending on the manufacturer and the position of the cable, it is often used by the distribution system operators. The network has no rotating part therefore the negative system is equal to the positive. The shunt admittance is a more difficult parameters to estimate therefore an accuracy of 20 percent has been considered. Most of the values considered are inspired from [Philippot, 1996] and on a survey made with several distribution systems operators. Zero V 0 I 0 Z 0 C 0 std (% rated value) Positive V 1 I 1 Z 1 C 1 std (% rated value) Negative V 2 I 2 Z 2 C 2 std (% rated value) Table 2.1: Default value of the standard deviation of the parameters The next error is the bias error. This is an error due to a model problem. Even if the

147 2. FAULT LOCATION MAIN PROBLEM 147 parameters, voltage and current are measured many times, an error still exists because the model is not the reality. Some examples that are deeply investigated in the next sections are the use of series model for the fault location instead of a PI model or neglecting the loads effect. Neglecting the shunt capacitances of a line depends on the amount of current circulating through them compared to the fault current. This is the same for the loads, even if the parameters are correct, neglecting them creates a bias error because some current will flow in unknown nodes. This kind of errors is represented on the figure d real bias d estim mean 2 σ length [pu] Figure 2.2: Bias error representation compared to the standard error

148 3. Graphical User Interface Tool 3.1 Purpose Many solutions for fault location in distributed network using the steady state are proposed in the literature. All of them can be applied to compensated network but their accuracy is difficult to predict if you do not consider the error as described above, the standard for fault location considers only the precision on the bias error which is a small part of the error in these conditions. The impact of each parameter depends on the network parameter and others variables. Therefore, an interface has been developed to select the best algorithm depending on the network topology and on the knowledge that the user has on the parameters and on the measurements. The purpose of this interface was first to help understanding the algorithms of single-ended and two-ended method and how they are impacted by the measurements and parameters accuracy and also the model of the network. Then a second purpose appeared: to indicate to the user where to put its effort in order to obtain a fault locator of a defined accuracy. 3.2 Structure To fully understand the purpose and the added value of this Graphical User Interface, this section describes every steps required to run it. First the network parameter and topology must be indicated then the sensitivity is computed for each algorithm implemented and the result is plotted. Several actions are then possible to understand the weaknesses of the considered method Network description Network.txt is the file that describes the whole network and gives all the information the simulator needs. The network description is divided in several parts. The name of the text file has to be Network.txt. This can be changed in the readnetwork.m script file by changing the code line: fid = fopen( network.txt, r ); Each part of the network is separated by a % xxx (% is also a comment instruction; % must be followed by a space to be a comment) where xxx is the title of the part. The syntax in this text file does not follow any rule from any existing language. Network initialization This part contains the general information about the network: 148

149 3. GRAPHICAL USER INTERFACE TOOL 149 % Network initialization (Ltfo & Rtfo are secondary side and couple Dy) UnetDSO(Volt) Lpet(mH) 2763 Rpar(Ohm) 10 Ltfo(mH) 0.65 Rtfo(Ohm) Rfault(Ohm) 0.1 BusbarNode BB Table 3.1: Example of the network initialization text file UnetDSO(Volt): This is the rated voltage of the distribution network. In the text box above, the network is a 12 kv network. This value must be entered in Volt. Lpet(mH): This is the inductance of the Peterson coil. Rpar(Ohm): This is the value of the parallel resistance that is switched on once the faulty feeder has been detected. Ltfo(mH): This value is important to simulate the network. This is the inductive part of the transformer in the secondary side. Rtfo(Ohm): This value is the real part of the transformer impedance. Rfault(Ohm): This is the value of the fault resistance that will be simulated in the network. The higher is the fault resistance and the larger is the error on the fault locator. BusbarNode: This is a string value which gives the reference to the algorithm. Therefore it knows where to place the Peterson coil and transformer. The line characteristic The second part is the line characteristics. % Line (every parameter is in per unit length) % Start with feeder connected to the bus bar < Node 1 > < Node 2 > <R0 (Ohm)> <L0 (Ohm)> <Y0 (µf) > BB F BB F <R1 (Ohm)> <L1 (Ohm)> <Y1 (µf) > <Pos X> <Pos Y> Table 3.2: Example of line characteristic in the text file The line characteristic contains 10 variables: Node 1: This is the node at the left of the line, this is a string variable. The bus bar in this network is at the left hence this is the node closest to the bus bar. At least one of the node among all the lines must be the BusbarNode defined in the network initialization. Node 2: This is the node at the right of the line, this is a string variable. R0 (Ohm): This is the value of the real part of the series impedance of the line in the zero-sequence system. X0 (Ohm): This is the imaginary part of the series impedance of the line in the zerosequence system.

150 3. GRAPHICAL USER INTERFACE TOOL 150 Y0 (µf): This is the zero-sequence shunt admittance value of the PI model. This value is the sum of the left and right admittance of the PI model. R1 (Ohm): This is the value of the real part of the series impedance of the line in the positive-sequence system. X1 (Ohm): This is the imaginary part of the series impedance of the line in the positivesequence system. Y1 (µf): This is the positive-sequence shunt admittance value of the PI model. This value is the sum of the left and right admittance of the PI model. R+jX Node 1 Node 2 Y Figure 3.1: Illustration of the PI model from the interface Pos X: This is the coordinates of the line in the plot graphic of the GUI. This value is used to compute the line length. Two values must be entered separated by a space. The first value is the x-axis position of the Node 1 and the second value is the x-axis position of the Node 2. The values are in kilometers. The resolution of the algorithm goes down to 10 meters, below the display will not be efficient for the user and the algorithm cannot reach such accuracy. Pos Y: This is the y-axis position for the line. Two values have to be entered by a space. The values are in kilometers. Examples of line parameters are shown in the text box at the beginning of this section. Measurements node The following part is the placement of the measurement points. There are the current and voltage measurements. The current measurements: They are defined by introducing a Node 1 different than the Node 2. The script will understand that this is the measurement of the current flowing from the Node 1 to the Node 2. The voltage measurements: To measure the voltage at a node, the Node 1 must be the same as the Node 2. The algorithm understands this is a voltage measurement. It is very important to keep the line % Measurement points the same because this sentence is a criteria for the script to stop encoding the line characteristics. % Measurement points (if node 1=node 2, it is a voltage measurement, if not it is current) < Node 1 > < Node 2 > BB BB BB F11 Table 3.3: Measurements node in the text file

151 3. GRAPHICAL USER INTERFACE TOOL 151 The load information The next step is the load description. The line % Loads must be kept as it is because it is the stop criteria for the measurements points encoding. % Loads % Indicate the node where the load is connected, its active power and its reactive power < Node > < P [kw] > < Q [kva] > F F Table 3.4: Loads information in the text file The load has three parameters: Node: This is the node where the load is connected. P [kw]: This is the active power of the load. Q [kvar]: This is the reactive power of the load. The distributed generation information The last step is the distributed generation. The line % Distributed Generation and % EndOfFile must not be changed because it is a stopping criteria. The distributed has exactly the same parameters as the loads: Node: This is the node where the DG is connected. P [kw]: This is the active power of the DG. Q [kvar]: This is the reactive power of the DG. % Distributed Generation % Indicate the node where the DG is connected, its power and short circuit value < Node > < P [kw] > < Q [kva] > F Table 3.5: Distributed generation information in the text file SimNet.m script Once the text file has been read, the simulation of the network can happen. The script will create structured variables containing the network information. If there are DGs, a Newton- Raphson method [Tinney and Hart, 1967] will be run, this is the NR_tool.m script. Once this is done, a simulation of the network for fault position every 500m or at the middle of the section if it is smaller than 1 km will be done. This is the BuildNet.m script. After the computation of the voltage for each node, the current is computed in the Sim- Net.m script according to the measurements indicated in the text file. Then every fault location algorithm is tested. Once all the fault location have been made for every position, the script fills two four-dimension variables containing the standard deviation (vard) and the bias error (meand). The first dimension is the section number as it is encoded in the text file, the second dimension is the position of the fault in this section, the third is the variance contribution regarding the symmetrical measurements and parameters

152 3. GRAPHICAL USER INTERFACE TOOL 152 and the last dimension is the algorithm. To add an algorithm, it is necessary to add one dimension to vard(x,y,z,n+1). NR_Tool.m By solving a matrix equation of the network and introducing the power produced by each generation, the load flow is solved with an iterative process and the angle between each generation and load can be found. BuildNet.m This script is the building of the admittance matrix of the whole network. The admittance matrix is computed using the symmetrical components in series which simulates a single phaseto-earth fault. The node order is shown at the next three pictures. Please refer to the script file for the node name. Rfault (NbNode+1) (Nodenb) (Nodenb) (1) (Nodenb) (Nodenb) (2*NbNode+2) Figure 3.2: Positive sequence system node number The negative sequence system is connected in series with the zero sequence node and the positive sequence node. Therefore, the fault node on the negative sequence system is connected to the ground of the positive sequence system and the ground of the negative system is connected to the fault of the zero sequence system. The logic is to start the number from the bus bar and complete one symmetrical system before starting to count on the next work. Therefore the node number starts with NbNode+2 for the negative sequence system. The next figure shows the node number and references for the zero sequence system. This is the last system to be referenced therefore the values are between two and three times the number of nodes. The ground of this system is also the reference for the computation therefore it is not referenced. Once the admittance matrix is built, the voltage is equal to V=A -1 I where I is the current sources (there is only one in case of non active network).

153 3. GRAPHICAL USER INTERFACE TOOL 153 (2*NbNode+2) (Nodenb+1+NbNode) (Nodenb+1+NbNode) (NbNode+2) (Nodenb+1+NbNode) (Nodenb+1+NbNode) (3*NbNode+3) Figure 3.3: Negative sequence system node number (3*NbNode+3) (2*NbNode+3) (2NbNode+2+Nodenb) (Ground) Figure 3.4: Zero sequence system node number The fault location algorithm Each algorithm is different however they have the same basis in the Matlab code. Two functions are in each script of the fault location algorithm. The first function computes the bias error and the standard deviation error, the bias error is computed by running the algorithm with the real parameters and the real measurements, the result is then compared with the real fault position and the difference gives the bias error. This error comes from a modeling error by neglecting the loads or some network parameters. The variance error has been computed by Monte Carlo simulations at the beginning of the study but a linearization of the equations have shown very closed results. Therefore this error is computed by application of the following equation which means that the variance on the distance is the sum of the variance weight by its impact on the distance.

154 3. GRAPHICAL USER INTERFACE TOOL 154 σd 2 = σre 2 d Vbb ( ) 2 + σ 2 d Im Re Vbb ( ) 2 + σ 2 d Re Vbb Im Vend ( ) 2 Vbb Re Vend + σim 2 d Vend ( ) 2 + σ 2 d Re Im Ibb ( ) 2 + σ 2 d Im Vend Re Ibb ( ) 2 Ibb Im Ibb (3.1) + σre 2 d Iend ( ) 2 + σ 2 d Im Re Iend ( ) 2 + σre 2 Iend Im Z ( d ) 2 Iend Re Z (3.2) + σim 2 d Z ( ) 2 + σ 2 d Re Im Y ( ) 2 + σ 2 d Im Z Re Y ( ) 2 Y Im Y (3.3) To compute the sensitivity regarding each parameter, the fault location is computed for each derivative. The subsections are explaining the principle of each algorithm. 7SA522 The algorithm is a single ended algorithm, it uses all the symmetrical system and it solves the following equation: d(z 0 I 0 + Z 1 I 1 + Z 2 I 2 ) + 3R f I f = V 0 + V 1 + V 2 (3.4) Rf and d are unknown but the equation is complex therefore the real part and the imaginary part provides a single solution to this problem (Rf and d are real value). Before applying this equation, the algorithm is computing the voltage and current for the section where the fault might be. Every section is tested and the section where the fault is between 0 and 1 is the faulty section. 1 is the length of the section. Single-ended - SE This method considers the shunt capacitance and therefore reduces the bias error compared to the 7SA522 method. The equation is then iterative: V 0 dz 0 (I 0 dv 0 C 0 ) + V 1 dz 1 (I 1 dv 1 C 1 ) + V 2 dz 2 (I 2 dv 2 C 2 ) = 3R f I f (3.5) The shunt admittance depends on the distance that is why an iterative calculation must be done. Two-ended - 2E 2E means Two-ended method and the number after the 2E_ means the symmetrical system used. The 2E_0 means the zero-sequence system used with 2-ended measurements, 2E_1 means 2-ended method using the positive sequence system and 2E_2 means 2-ended method using the negative sequence system. Firstly, the algorithm will check if there are two measurements available for the fault location. Then it looks at the topology of the feeder, if it has branches, loops, etc. this is the frow_build script which is made in the first function because this result is used often and it is sent to the FL function. Once the feeder structure is found, the fault locator will determine the voltage and current at each side of the tested section. Once the voltage at both end is known, the iterative fault location is made with the following equation: { V 1 = V f + dz(i 1 dv 1C 2 ) V f = V 2 + (1 d)z(i 2 (1 d)v 2C 2 ) (3.6)

155 3. GRAPHICAL USER INTERFACE TOOL 155 V 1 and V 2 are the voltages from both side of the faulty section, Z is the series impedance of this faulty section, Y is the shunt admittance and I 1 and I 2 are the currents from both side. This equation is applied on one of the symmetrical system, if the fault location occurs in the zero sequence system, the voltage, current, impedance and admittance will be in the zero sequence system RunSimNet and the GUI The GUI interface has been done to ease the understanding of fault location algorithm and the use of the tools. The center of the interface provides a general view of the system with color indicating the accuracy of the fault locator. Buttons have been implemented to change the parameters and see the impact they could have in the reality. General information is given on the left side with variance per section and a small legend. Figure 3.5: Screenshot of the Graphically User Interface The interface has several buttons that are described in this section. All the functions are written in the script RunSimNet.m. The following sections describe each option of the interface. Start - Push button This button will start the whole process for the fault location. It will read the network.txt file to create the network, then it will compute the voltage at each node and it will make the fault location at many positions in the network to calculate the accuracy of the fault locator. Once the computation is done, the network is displayed with the results. Algorithm selection - Popup button This button provides a list of the algorithms available in the tool. The algorithms have already been described in the section A general view is also available; this view mixes the algorithms in the network representation and selects only the best algorithm for the specific fault position.

156 3. GRAPHICAL USER INTERFACE TOOL 156 Figure 3.6: Algorithm selection - Popup button and list of fault locator The information box - Text box This text box on the left of the window provides the information about the algorithm accuracy. Once an algorithm is selected, its worst accuracy on each section is displayed. Figure 3.7: Example of text box information Different informations can be displayed, for example, if the variance details button is used, the contribution of each parameters and measurements is displayed to provide additional information to the user about his fault location strategy. The variances details - Push button The variance button will make a cross appear and the user has to select a fault position in the network. Figure 3.8: Variance detailed example

157 3. GRAPHICAL USER INTERFACE TOOL 157 Once the position has been selected (by left clicking on it), the tool will draw the area where the fault might be (blue circle) and details the variance contribution for each parameters. The goal of this button is to show to the user the parameters or the measurements that are the most sensitive to improve significantly the algorithm accuracy. Display CT/VT - Checkbox This check box displays the loads, DGs and the current/voltage measurements. A legend is also plotted on the bottom left. Figure 3.9: Checkbox display information The standard deviation settings - Edit box This area gives the user the opportunity to edit the standard deviation of the parameters. Each time the accuracy is changed, the fault location will be computed for every position in the network. The new result is then displayed. The goal is to show the user the impact of each inaccuracy in his network; this is also helped by the text box on the left. Figure 3.10: Standard deviation edit box Algorithm options The bottom box has an option regarding the loads in the fault location algorithm. The user can edit the load level in the network, the load in the text file is the nominal value but the loads can run at different level and this is what the user can change. The bias error will be smaller in this case because the current flowing through the loads is smaller than in the first calculation.

158 3. GRAPHICAL USER INTERFACE TOOL 158 Then another box can be checked to give the algorithm the possibility to use the prefault current and the knowledge the algorithm has about the loads to reduce the load impact. This box is called load estimation because it is only an estimation of the loads depending on the knowledge available for the algorithm. Figure 3.11: Algorithm option window The parallel resistance analysis This is another option for the user. He can edit the value of the parallel resistance and see the impact of a larger or smaller parallel resistance. Also a design rpar button can be clicked and the algorithm will test one hundred different values of parallel resistance and the result will be displayed to the user for each algorithm. This option consumes lot of computation resources. Therefore the user can optimize his own parallel resistance with the accuracy he needs. Figure 3.12: The parallel resistance design button

159 4. Sensitivity analysis The Graphical User Interface has helped to study the sensitivity of different algorithms to the parameters standard deviation. This section studies the impact of the parallel resistance value on the fault locators performance. The influence of the precision on the measurements and on the parameters is also demonstrated. Suggestions are then made regarding the efforts a distribution system operators have to make to improve fault location. 4.1 Purpose of the sensitivity analysis The purpose of the sensitivity is to answer the two last questions of the following flowchart. What method? What has an impact? Steady state Parameters info + Detune the network How much the detuning? + Additional measurements Where? How many? Figure 4.1: Additional questions are brought by the requirement of the fault locator Indeed, the steady-state solutions have been chosen to locate the fault in the compensated network. However, as it will be proven in the next sections and has been demonstrated in the chapter V, using only the algorithm does not provide a sufficient accuracy for a commercial fault locator. Therefore the network has to be decompensated and some measurements or parameters must be measured more precisely. However, the topology of a network is very specific therefore the actions for the decompensation and the improvement of the measurements will not have the same effect on different network. This tool provides a clear information of 159

160 4. SENSITIVITY ANALYSIS 160 the impact of each effort made. It helps to size the parallel resistance and get the best fault location with minimum cost. 4.2 The parallel resistance importance Since the beginning of the fault location research project, the needs to locate a single phase earth fault in a compensated network have increased. There were two suggestions for the fault location: using the transient or the steady state. The transient is due to the charging of the healthy phase capacitances. Experiences gained thanks to the recordings used for the fault detection development have shown very few identifiable charging transient because of high impedance fault or very short earth fault. This is probably caused by the good compensation of the network which extinguishes the fault. The sampling frequency of the fault locator could also be a problem. Then the steady state has been investigated to be used as classic fault locators do. However, in compensated network the steady state is not always stable because the Petersen coil extinguishes the fault which makes the fault intermittent. Even if the fault is continuous, simulations have proved that the fault current is not very high. The information coming from the fault is then too small to obtain a sufficient accuracy for the location. The figure 4.2 below shows a Monte Carlo simulation of the distance computed by a fault locator using the steady state in a compensated network (extremely detuned). The result clearly shows the need of a parallel resistance. If the network is normally compensated (95% in this case), the standard deviation of the fault is larger than the length of the line, this means the fault will be located anywhere on the line due to the error on the measurements and parameters. However, if the decompensation is significant (i.e. the parallel resistance is 2 times less impedant than the coil), the standard deviation is reduced to 10% of the line length. Number of samples from the MonteCarlo tests Estimated distance [pu] Parallel resistance [%X ] ng 1000 Figure 4.2: The active system can make the fault location possible in compensated network The steady state solution can then be improved by an active method on the network. The goal consists in the decompensation of the network which increases the fault current and therefore the information about the fault. The single phase earth fault will have higher current amplitude and should be more stable. More energy will be available for the location and the fault location could be accurate enough to locate the fault in some places. The general accuracy of a fault locator shows the importance of the parallel resistance. It is also important to understand the evolution of the parameters contribution on the overall

161 4. SENSITIVITY ANALYSIS 161 distance error with the parallel resistance value. The understanding and the interpretation of this can be made further in the document but it is specific to the algorithms. The downside of increasing the faulty current is of course the safety and the damages on the power system. A compromise must be made between increasing the accuracy and avoiding the damages on the grid. These effects are very difficult to quantify but if the operators know a fault current limit, the tool is able to compute the minimum value of parallel resistance that can be used to stay below this limit. For the rest of the analysis, the parallel resistance has been set to produce a fault current two times bigger than the maximum load current on the feeder. 4.3 Size of distribution network The size of a network has an impact on the magnitude of the fault current especially the size of the total zero-sequence capacitance. In a perfectly compensated network, the fault has no current because the Petersen coil and the total zero-sequence capacitance make impedance infinite. However, in reality a network cannot be perfectly compensated and the difference between the total zero sequence capacitance and the inductance of the Peterson coil creates an excess of capacitive or inductive current that flow through the fault. In solidly grounded network, the fault current is very high because the impedance is very small (impedance of the transformer + impedance of the line to the location + fault impedance). The current magnitude depends on the voltage source and the impedances. The next pictures 4.3 show the difference of current flow in a compensated and in a solidly grounded network. The switching of the parallel resistance creates a network which is between these two states. Figure 4.3: Comparison of single phase earth fault between compensated and solidly grounded network Simulations have been made with three different networks with an identical topology but different zero sequence capacitance with short overhead lines (few km) or underground cable difference. The simulations was made with ATP-EMTP with the same parallel resistance. The fault location is the same; the difference is the capacitance of the network sound part.

162 4. SENSITIVITY ANALYSIS 162 The next figure 4.4 shows the standard deviation in per unit, it indicates that there is no significant difference between the three networks and therefore the compensation factor is not important due to the parallel resistance. It is justified because most of the fault current is flowing through the parallel resistance and not in the Peterson coil. Different results might be obtain in the standard deviation if there is a difference on the distance to the fault or on the line parameters Standard deviation [pu] Small [IC0 = 14.7 Amp] Medium [IC0 = 39.2 Amp] High [IC0 = 91.9 Amp] Figure 4.4: Standard deviation for three different C0 total 4.4 The single-ended measurements precision The voltage and current measurements are always impacted by the noise and the precision of the devices. The goal of this section is to identify the contribution of the voltage and current accuracy on the fault location. V 0 dz 0 (I 0 dv 0C Today s knowledge ) + V 1 dz 1 (I 1 dv 1C 1 2 ) + V 2 dz 2 (I 2 dv 2C 2 ) = 3R f I f (4.1) 2 The single-ended algorithm uses every symmetrical system to locate the fault; therefore the error on each system has an impact to the distance standard deviation. This implies to have a good precision on each measurement made in the substation. Moreover the knowledge on the positive, negative and zero sequence parameters of the faulty line must be accurate. Unfortunately, the zero-sequence parameter is often not known by the distribution system operators and a bad approximation is made to estimate its value. Using these assumptions (detailed in section 2.1), a simulation has been made by the tool on a theoretical network with the parameters available in appendix C. The bias error is not considered for this test and only the measurements from the bus bar have been used for the fault location. The standard deviation on the distance to the fault goes from 0.3 km to 15 km. It is interesting to notice that the accuracy on the fault location is decreasing with the distance from the bus bar. The results for a test network are illustrated on the figure 4.5. Several tests have been made to study the accuracy of the fault location in a classic singleended method. The conclusions of these tests are the same along the whole line because the zero sequence impedance has an impact that contributes to 76% of the total error (with 13 % for V 0 and 10 % for V 1 ) if the fault is near the bus bar and a contribution of more than

163 4. SENSITIVITY ANALYSIS 163 Figure 4.5: Fault location accuracy with single-ended method and actual knowledge of the network 99 % if the fault is at the end of the line. An example of the detailed contribution of each parameter and measurement is shown on table 4.1. The variance contribution shows that the zero sequence impedance contributes the most to the total error. The accuracy is also rather poor: the algorithm indicates an area of 2.2 km for the fault (with a confidence of 95%). The result is extremely bad if the fault is at the end of the line: the area is 15 km which is half the feeder length. In a city, the section length can reach several hundreds of meters which is too small for the accuracy of this single ended method. Zero sequence Positive sequence Negative sequence 4σ 2.2 km V 1 % 1 % 0 % I 0.19 % 0.02 % 0.01 % Z % 0.01 % 0.01 % C 0 % 0 % 0 % Table 4.1: Accuracy of the single ended method and contribution of each parameter Depending on the user needs for fault location, an improvement can be made by a better estimation on the zero sequence impedance. System operators often do not measure this value and effort could be put on this task depending on the cost of a measuring campaign. One remaining problem with the zero sequence impedance is the dependence of the ground itself which is varies according to weather condition, etc. Therefore the measure of Z 0 can not be as accurate as the positive impedance. The equation has been simplified according to some assumptions. The negative sequence voltage is very small compared to the positive and zero sequence voltages, this is one reason why its impact is neglected in the table 4.1. Also Z0 is often larger than the positive and negative impedance, therefore a deviation of 1% of Z0 has more impact on the denominator

164 4. SENSITIVITY ANALYSIS 164 than the others impedance, even if the precision is the same and if the currents are assumed equal (neglecting loads and capacitive current). V 0 dz 0 I 0 + V 1 dz 1 I 1 + V 2 dz 2 I 2 = 3R f I f (4.2) V 0 dz 0 I 0 + V 1 dz 1 I 1 dz 2 I 2 = 3R f I f (4.3) d = V 0 + V 1 3R f I f Z 0 I 0 + Z 1 I 1 + Z 2 I 2 (4.4) d = V 0 + V 1 3R f I f I 0 (Z 0 + Z 1 + Z 2 ) (4.5) In conclusion, the main problem with a single ended method is the accuracy on the zero sequence series impedance. As stated above, the majority of the distribution system operators do not know this value and estimate it if necessary which might lead to error even greater than 20 %. The fault location using single-ended method is therefore almost impossible with these conditions. The precision might be sufficient at the beginning of the line and using fault location on short line might not be interesting. The general accuracy depends also on the network but the error is so important on this parameter than it can be a general conclusion of this study Improvement of Z0 knowledge If the precision on Z 0 is a problem, it is interesting to understand what could be the accuracy when the precision on the zero sequence impedance is the same as on the positive and negative symmetrical systems. Therefore the next problems to solve can be anticipated and the user could know if it is worth the effort to measure it. The table 4.2 provides the results at the same position as the table 4.1 but with a standard deviation of 1 % for Z 0 instead of 20 %. The accuracy of the algorithm is much better and is improved with a reduction of the faulty area by a factor 7. The series impedances are no longer the main problem to the fault location. Of course, it depends on the network topology and in this case it strongly depends on the position of the fault in this network. At the end of the feeder, the positive sequence voltage has 59% contribution, the zero sequence current 18 % and its impedance 21 %. At the beginning of the feeder, the problem is for 55 % on the zero sequence voltage and 43 % on the positive sequence voltage. Zero sequence Positive sequence Negative sequence 4σ 0.33 km V % % 0.30 % I % 0.33 % 0.33 % Z % 0.32 % 0.32 % C 0% 0 % 0 % Table 4.2: Single ended method accuracy if the knowledge on Z0 is improved However, the accuracy of the fault locator still depends on the distance to the fault. Two times the standard deviation on the distance of the fault goes from 0.14 km to 1.6 km depending if the fault is near or far away from the bus bar. The improvements put could be only on the parameters that mostly impact the fault at the end of the feeders. Unfortunately,

165 4. SENSITIVITY ANALYSIS 165 the contribution is well spread among many parameters when the fault is far away from the substation. Therefore, efforts must be put to improve the precision of variables which could be difficult. The practical maximum accuracy available has been reached for the single-ended fault location algorithm. Other algorithms could be found but any single-ended method will always need every symmetrical system. Usually this method is improved with a better modeling but it has been shown that the first problem is the variables precision. The figure 4.6 shows the accuracy of the fault location algorithm on the total network. Figure 4.6: Fault location accuracy with improvement of the zero sequence impedance in single ended method The results are much better and they could be used for a real fault location; even if the algorithm is not able to identify the faulty section, a large part of the feeder will be declared as healthy and hence can be skipped for further investigations. However, as stated about the zero sequence impedances, the earth impedance plays a role and is difficult to measure and therefore will always limitthe accuracy of the fault locator Heterogeneous line Distribution networks can present very complex topologies for many reasons compared to the transmission grid. One difficulty can be an heterogeneous line. Indeed, the single-ended algorithm remains the same but more tests are required in case of heterogeneousity as detailed in the section 4.2. Two questions were to be answered with this test. The first was to know if the heterogeneity could impact the fault location if the ratio X/R is changing and if the absolute impedance value is changing. A simulation has been made to understand the impact of different X/R ratio along a feeder. The impact of the zero sequence impedance is the strongest one therefore the ratio has been changed on this parameter. The zero sequence impedance starts with a first section having a ratio of 4.82, the second section has a ratio of 2.41 but with the same absolute impedance value and the last section has a ratio of 4.82 but with resistance and reactance two times smaller for the same length.

166 4. SENSITIVITY ANALYSIS 166 The result shows that the ratio does not change the size of the faulty area but the absolute value of the impedance is important. The fault location is more accurate if the impedance is higher because it creates a higher voltage drop per kilometer and therefore reduces the relative error. The X/R ratio has no impact on this voltage drop if the absolute value of the impedance is the same. The figure 4.7 shows the result on the Matlab user interface developed during this PhD. The last section shows a stronger color with an heterogeneous line which indicates a worst precision than the homogeneous line. Figure 4.7: The ratio X/R is not important compared to the absolute value of the impedance This conclusion can be a disadvantage for the cables because they have a smaller impedance per kilometer compared to the overhead lines. The operation of a fault locator will then change from section to section and a strange case might occur where the fault could be located with a relatively good accuracy on the feeder except in some parts. Therefore, the limitation of a fault locator could be the line with the smallest impedance The parallel resistance effect The parallel resistance is necessary for fault location in compensated network. This resistance improves the precision of the fault locator by increasing the fault current. More current leads to an increased voltage drop and therefore changes the contribution of each parameter. The figure 4.8 shows the variance contribution of the parameters and measurements contributing for more than 99 % of the total error (the rest is neglected). A very small parallel resistance creates a very high fault current and the error is mainly due to the zero sequence series impedance. Then if the parallel resistance increases, the voltage on the positive sequence and zero sequence system begin to have an impact on the total error of the fault position. The voltage drop is smaller if the fault current is decreasing meaning that an error on the voltage measurement will deviate the solution significantly. The variance of the zero sequence impedance is almost constant and independent of the parallel resistance value. This information is important because it means that it is not useful to decrease the parallel resistance value below 300 Ohms because the variance will be constant,

167 4. SENSITIVITY ANALYSIS V 0 V 1 Variance I 0 Z R// [Ω] Figure 4.8: Variance contribution of the main parameter for single ended method versus the parallel resistance it is much more important to improve the knowledge on Z 0 before increasing the fault current (without considering the stability of the fault). 4.5 Two ended measurements precision The active method increases the faulty current but not as high as a solidly grounded network which reduces the accuracy of the fault locator in compensated network. In the context of smart grids, communication between the devices of a network will be much easier. This communication could be extremely helpful in the context of fault location because it brings additional information. If a fault location is not accurate enough with a single measurement point, extra measurements along the feeder can improve the accuracy. For example, the measurement of the voltage and current on both sides of a feeder permits the use of another algorithm which needs only one symmetrical system instead of three. In the case of a loop, the voltage is the same on both ends and the current measurement can easily be done in the same substation. If both measurements are available, then the standard deviation on the distance can be reduced by a factor 10 as the figure 4.9 below illustrates it. This figure is a test on a loop structure where a two-ended method is applied and a single-ended method is applied starting from one side and then from the other side. Standard deviation [pu] ended Mean of both single ended results Single ended one side Single ended from the other side distance [pu] Figure 4.9: Multiple measurements can help to improve the fault location

168 4. SENSITIVITY ANALYSIS 168 The result simply illustrates the performance of the two ended method in this situation and proves that the use of several measurements can help to improve the fault location The best symmetrical system Using a two-ended method gives the opportunity to choose the symmetrical component to use. Each symmetrical system has pros and cons which is described by the table. Advantages Disadvantages Zero No load impact Z0 less known Positive Better knowledge of the parameter Load impact Negative Better knowledge of the parameter and no generators Load impact Table 4.3: Comparison of the symmetrical system for fault location The loads have no influence on the zero sequence system because the connection of the transformer made an infinite impedance for the load in this system. This is a strong advantage if the load is important and creates strong bias error which would require a lot of information about the loads along the feeder. The impact of the loads is the strongest on the positive sequence system if we assume that the loads are constant impedances (i.e. no rotating machine). The voltage on the positive sequence is close to one per unit compared to the negative sequence where the voltage on the bus bar is near a tenth of per unit which means that the current flowing to the loads is much more important in the positive sequence system. The fault current is the same in every system therefore the contribution of the loads current at the measurement point is also much more important in the positive sequence system. Regarding the parameters, as discussed above, the positive and negative sequences are well known and usually measured but the zero sequence system is not and is impacted by the earth impedance. A test has been made on a radial feeder with a voltage measurement at the end of the line. The result is shown by the table 4.4 with the size of the faulty area and the contribution of each parameter and measurement. This test is made on a radial feeder and does not consider the result on the loop structure. Positive Negative Zero 4σ 0.2 km 0.2 km 3.3km V 38.15% 39.26% 0.15% I 39.52% 32.69% 0.14% Z 21.43% 28.04% 99.71% C 0.9% 0% 0% Table 4.4: Accuracy and contribution of each symmetrical system with two-ended method The accuracy of the positive and negative sequence systems is very good using the twoended method, the faulty area has the same order of magnitude as a section length. The contribution of each variable is well distributed except for the shunt capacitance because a small part of the current is flowing through them. This result indicates that improvements will require efforts in every measurement and parameter. The figure 4.10 shows the result for two times the standard deviation using the zero sequence system.

169 4. SENSITIVITY ANALYSIS 169 Figure 4.10: Illustration of the zero sequence system two-ended method fault location The zero sequence system is not so accurate due to the knowledge problem on the impedance. Indeed the error on the faulty area using this symmetrical system is mainly due to Z 0. The relation of the faulty area size is also dependent of the fault distance from the main substation. The fault location equation could help to understand this behavior. d = V 1 V 2 ZI 2 Z(I 1 I 2 ) (4.6) V 1 and I 1 are respectively the voltage and the current at the beginning of the line and V 2 and I 2 the voltage and the current at the end of the line. If there is no current at the end of the line, I 2 = 0, the equation becomes: d = V 1 V 2 ZI 1 (4.7) The zero sequence system shows that the voltage is responsible for 12 % of the total error if the fault is at the beginning of the line and the impedance contributes for 87 %. The positive sequence system contributes for 97 % on the voltage at the beginning of the feeder and for 95 % at the end with an increase of the impedance. For the negative sequence system the figures are 38 % on the voltage, 44 % on the current and 18 % on the impedance if the fault is at the beginning of the line and this evolves to 31 % for the voltage, 49 % for the current and 20 % for the impedance at the end of the line. Depending on the symmetrical system, the contribution of each parameter is very different. If the distance is longer the current will decreased because the impedance is higher. However, the numerator is not the same if the fault is near the bus bar or at the end of the line but a smaller current reduces the voltage drop on the same impedance which makes the voltage drop per per unit of impedance smaller if the fault is farther. This explanation assumes that the voltage on the bus bar is the same if the fault is near or at the end of the power line. This is almost true if the fault current is not very high. If it is too high, the voltage drops on the transformer cannot be neglected.

170 4. SENSITIVITY ANALYSIS 170 Therefore, the accuracy of the two-ended method on a radial feeder is the best if the fault is in the middle because the errors are compensating the most. The improvement of the two-ended method will then depend on the symmetrical system used. Also some improvements could be mathematically done by coupling the equation of the positive and the negative systems to have a impedanceless method. However, the first problem that the operators would probably face is the practical implementation of an additional voltage measurement at the end of the feeder The parallel resistance effect The impact of the parallel resistance on the different parameters and measurements is studied for the three symmetrical systems. To understand the evolutions of the symmetrical systems with the decompensation, an evolution of the voltage on the main substation and at the end of the line is represented by the figure The negative sequence voltage remains small and slightly increases if the fault current is very strong. The positive sequence voltage is mostly constant in the main substation but decreases at the end of the line because of the voltage drop mainly produced by the fault current. The zero sequence voltage is very close to the positive sequence in magnitude if the network is well compensated but it decreases much stronger if the fault current is increasing. The voltage difference between the beginning the main substation and the end of the feeder is higher because of the higher value of the zero sequence impedance Voltage [V] V 2 bb V 2 end V 0 bb V 0 end V 1 bb V 1 end R // [Ω] Figure 4.11: Voltage value of the three symmetrical systems depending on the parallel resistance The zero sequence system sensitivity is shown on the figure The series impedance does not depend on the parallel resistance value. One explanation could come from the equation where Z is constant value, a variation has the same impact independently of the others variables. The current should have the same impact as the series impedance but the variance on the measurements is 400 times smaller than on the impedance which makes its contribution very small compared to the rest of the variables. Regarding the voltage, its contribution is constantly increasing with the parallel resistance value. If the parallel resistance is larger, less current can circulate through the fault and the voltage difference between the main substation and the end is getting smaller. Therefore an error on one of the voltage measurements will have more impact on the voltage difference (which is smaller) which is increasing the error on the distance.

171 4. SENSITIVITY ANALYSIS Variance V 0 I 0 Z 0 Y R// [Ω] Figure 4.12: Zero sequence system variance with two ended solution The positive sequence system is shown on the figure 5.3 is mainly about the voltage problem. As it is shown in the figure 4.11 the voltage difference is very small if the parallel resistance and the voltage value are both large. This value also depends on the angle between the two phasors which is not represented in this figure. This angle depends on the load current and the line parameters. Therefore the results could be very different depending on the loads if they are significant compared to the fault current. The small decrease of the voltage at 1000 Ohms might be a particularity of the system because the error contribution does increase significantly for higher resistance values. 10 V 1 Variance I 1 Z 1 Y R// [Ω] Figure 4.13: Positive sequence system variance with two ended method Regarding the contribution of each variables in the negative sequence system represented in the figure 4.14, the total error is much smaller than the others systems. The negative sequence voltage is much smaller on both end which makes a deviation less important on the voltage difference (e.g. a deviation of 1 % of the voltage on the bus bar will not change that much the result on the distance). The contribution of the impedance is constant as explained above for the others systems. The last significant contribution is the current which is the most important variable for the distance error, this evolution comes from an hyperbolic dependance of the fault current with the parallel resistance value. This analysis of the active system influence on the parameters is clearly not general and depends on a lot of variables where each case needs a specific investigation. However, these

172 4. SENSITIVITY ANALYSIS x V 2 Variance 1 I 2 Z 2 Y R// [Ω] Figure 4.14: Negative sequence system variance with two ended method figures provide a good information on how to design a parallel resistance and the efforts that could lead to an improvement of the fault location The loop advantage The fault location as it is made nowadays often uses the loop structure to temporarily keep the service and locate the faulty section. This loop could be used temporarily to apply a fault location algorithm with a two-ended method using the measurements from the same substation. These measurements could be easily synchronized because one device can be connected to the two measurements. The table 4.5 shows the result for each symmetrical system of the two-ended method if the feeder is a loop that has two measurements from both feeders in the main substation. The feeders are homogeneous in this test. The method with a closed ring structure shows extraordinary results regarding the size of the faulty area. Theoretically, the precision is less than the meter. The error mainly comes from the shunt capacitances which are not very well measured with a standard deviation estimated at 20 %. This parameter was not significant in the previous test because the current flowing through the capacitance is very small but the accuracy with a loop is so good that this small current matters. Therefore the current has also an impact because the loop structure is simply a ratio of the current from both side due to a compensation from both side. Positive Negative Zero 4σ 1.7e-3 km 8e-5 km 1e-4 km V 0.76 % 0.04 % % I % 1.87 % % Z 0 % 0.07 % % C % % % Table 4.5: Accuracy of the each symmetrical system with two ended method in a loop The series impedance has no effect. Indeed, if the loop is homogeneous, a compensation effect occurs which makes any error on the impedance insignificant. The compensation effect is described by the figure 4.15 to explain why the loop has a better accuracy than the twoended radial method. This effect also applies on the voltage because the error is the same on both end since there is only one voltage measurement. The error created by the impedance

173 4. SENSITIVITY ANALYSIS 173 from one side will be exactly the same on the other side which cancels its impact on the fault position. The error will increase or decrease the voltage at the fault position. However this value is not important for the fault location. V&I Error on Z (10% bigger than reality) This has no impact of the distance result C Vf Vbb Vf V&I d fault Length loop Figure 4.15: Compensation effect with the loop structure This effect can also be explained by the equation below. The series impedance is not in the equation due to the compensation effect. The voltage is in the equation if the shunt capacitances are not neglected in the model but, because the error on the capacitance is bigger than on the voltage, the impact of the capacitance is more important in the total error. I1 end C 1V 1 2 d = I1 bb + (4.8) Iend 1 C 1 V 1 An accuracy of a few meters is excellent for the purpose of the fault location. However, this precision could not be met in practice for many others reasons such as modeling error, non perfect homogeneity of the line, loads, etc. still this method seems to be the best one to implement Heterogeneous line The compensation effect works well if the line is homogeneous but this effect is not 100 % effective if the line is heterogeneous because the impedance is not completely compensated in the equation. The result will strongly depend on the error made on the measurements of the different series impedance in the feeder. A test of heterogeneity has been made by changing the ratio X/R of the section F51-F52 from 4.8 to 1.9 and of the section BB-F51 from 4.8 to 6.9 on the zero sequence system. This modification increased the distance from 5e-4 km to 0.69 km, for the zero sequence system where the impedance has a strong standard deviation due to the bad knowledge the operators has. Therefore a small deviation creates large error on the distance. If another symmetrical system is used, the modification increases the faulty area to 0.04 km instead of km with compensation for the positive and negative sequence system. The results are still very good with these systems. Again, the ratio is not important but the absolute value that produces a voltage drop along the line is the most important. The error will be larger if the difference of absolute value is significant between both the two sides of the fault.

174 5. The load impact and bias error The connection of the parallel resistance increases the faulty current to 1 to 3 times the maximum load current. This magnitude is not enough to neglect the influence of the loads on the fault location. There is a big difference between the loads in transmission network and distribution network. In transmission network, the loads are usually located at the end of the long power lines at different nodes in the meshed network. In distribution network, the loads are located along the lines every 100 meters to several kilometers. Therefore, there is current infeed in different position in the feeder in compensated network that are not monitored. Such currents are not measured, only the total loads consumption on the feeder can be measured in the main substation. 5.1 The impact The loads will perturb the algorithm but they will not increase or decrease the faulty area because the error is no due to the imprecision on a measurement or a parameter. This can be assimilated to a modeling error which leads to a bias error. The bias errors are difficult to estimate because they are due to the deviation of the model from the reality which is difficult to quantify The single-ended algorithm The single-ended algorithm uses the three symmetrical systems which implies a load impact in the negative and positive sequence system. Three loads of a total of 1.5 MW with 0.3 MVar have been connected along the feeder BB-F43. The load on F41 is 500 kw and 200 kvar, the one on F42 is 1000 kw and 100 kvar. The results on this line are illustrated on the figure 5.1. The bias error is represented by small vertical purple bar along the feeder. However, this error being too small to be represented significantly it has been exaggerated to illustrate the consequence of distributed load on a single-ended method. Figure 5.1: Impact of the loads on the single ended algorithm 174

175 5. THE LOAD IMPACT AND BIAS ERROR 175 The bias error goes from 0 m to 1.4 km which is 11% of the faulty area for a feeder of 29 km. As it is observed on the figure 5.1, the bias error occurs beyond the loads as it has been explained in the previous chapter 4.4. The load on F41 is small so that the bias between F41 and F42 is very small. If the fault is between the measurements and the first load then there is no bias error. The simulation tool validates thus the theory developed. If there are many loads along a feeder that are equally distributed then the bias error will progressively increase with the distance. This can shift the faulty area and the fault has a strong probability to be outside this area. Such a result could be understood by the user as a malfunctioning of the device but it is simply due to the fact that the algorithms do not considered everything in the network. To avoid such malfunctioning, the algorithm has to know what are the currents flowing through the loads. However this idea requires a high investment in measurements and communications which can be dreamt in future smart grids but is not economically realistic today The two-ended algorithm The two-ended method is not impacted in the same way as the single-ended method because it computes current flows coming from the both end and this method uses only one symmetrical system. First, in Europe the loads are connected with delta wye connection which makes their impedance infinite in the zero sequence system. Therefore, fault location with the two-ended method using the zero sequence system is not affected by the loads. The figure 5.2 shows that there is no bias error due to the load. Figure 5.2: The zero sequence system is not influenced by the loads In addition to the line BB-F43, two loads of 1 MW have been added on the loop BB-F52. The bias error is represented by purple vertical bars along the lines; they are visible on the branches F31-F34. They are not due to the loads but to the fact that the algorithm does not

176 5. THE LOAD IMPACT AND BIAS ERROR 176 take the branches into account. A decision algorithm must be implemented to provide several faulty areas when the fault might results in different positions if no additional information is given. The positive sequence system is the most affected system when we use the two-ended method. The voltage is near 1 per unit creating an important load current that is not considered in the algorithm. The bias error can reach 4 km, this is very important compared to the size of the area. Therefore, using the positive sequence system without taking the loads into account will lead to a wrong location of the area. The purple bars representing the bias error can be seen in different parts of the network in the figure 5.3. The loop structure shows a strong bias error on the first sections due to the large value of the load. However the bias error is much smaller on the section F51-F52 because the load F51 and F52 are quite similar in rated power. This creates again a compensation effect similar to the series impedance but this effect is not predictable unlike for the series impedance because the loads are changing with the time and this effect can happen or not without which is impossible to know if there are no load measurements. Figure 5.3: The positive sequence system is strongly influenced by the loads The negative sequence system is not much affected by the loads as the figure 5.4 shows it. The bias error is not much than 10 meters because the negative impedance of the load has been considered the same as the positive sequence (assuming that the load contains no rotating machines) and the negative voltage is very small which creates a very small negative current in the load. If we would add rotating machines the load current would be almost 3 times bigger which does not change much the conclusions because it remains much lower than the faulty current. The negative sequence system seems to be the best system with load if a two-ended method is possible in the network. Such a good result might focus the perspectives of this work in the line modeling of the system which could be the most significant error in the reality.

177 5. THE LOAD IMPACT AND BIAS ERROR 177 Figure 5.4: The negative sequence system is almost not affected by the loads 5.2 A solution If the negative sequence system cannot be used for any reason, we have thought about a solution to consider the bias error without knowing the loads. We have at least to provide the position of the loads to the algorithm. Those are known by the operators because loads are at the secondary substations. Moreover the rated values of the transformers give an indication of the maximum value of the loads. This knowledge gives the algorithm the opportunity to compute a fault location with full load and no load. This idea is illustrated by the figure 5.5. V&I FL result w/out load estimation V&I FL result w/ few load information V&I FL result with full load measurement Figure 5.5: Load impact integration in the faulty area estimation This will result in two different positions that are the extreme bias error caused by the

178 5. THE LOAD IMPACT AND BIAS ERROR 178 loads. The distance between those two positions is then added to the faulty area to increase it and be sure that the bias error is integrated in this area. The problem is that it can strongly increase the size of the area. Therefore the prefault conditions can be used to limit the maximum load current assuming that a single phase earth fault does not change the load consumption. One more step could be done to reduce the size of the faulty area is to integrate any additional information from the loads for example consumption curve, real-time consumption, etc.

179 6. Summary This chapter concludes the fault location study. The first part of this chapter consisted in the details of a graphic user interface tool developed in Matlab to understand and illustrate the fault location precision and problems. This tool has many part such as standard deviation estimation, lot of different algorithms, parameters settings and options. The goal was to be very flexible to be adapted to the needs of an external user. A Newton-Raphson has also been implemented to allow the network to integrate distributed generation and understand the impact of loads and generations in fault location. Thanks to this tool, a sensitivity analysis has been performed to identify the weaknesses of each considered fault location method. General tests were considered such as the size of the network and the parallel resistance value. Tests clearly indicate the need of a parallel resistance to improve the precision of the algorithm. However the size of the network and the amount of capacitances does not seem important in the fault location precision because the parallel resistance increases significantly enough the fault current. The single-ended algorithm is not accurate because the zero sequence series impedance is often not known by the operators. However, our analysisshows that a much better precision could be achieved if this impedance was better known. The limiting variables were then the voltage on the positive and zero sequence system. However the contribution depends greatly of the position of the fault and the line parameters if the knowledge on Z0 is solved. Therefore it might be difficult to improve the precision in this case because all the parameter should probably be measured more accurately. Then the parallel resistance impact on the contribution of each variables have been considered. The contribution of the zero sequence series impedance is constant or slightly decreasing if the fault current is decreasing but the most important variables are the zero sequence and the positive sequence voltages which are significantly increasing with the parallel resistance value. The heterogeneousity of the feeder has then been studied. The main conclusions are that the absolute value of the impedance is influencing the precision of fault locator. Feeders with very small series impedance produce smaller voltage drop which reduce the precision of the fault locator. The two-ended method has also been investigated and has shown good result in radial structure for the positive and negative sequence. The zero sequence system has still the problem of the series impedance accuracy which makes the method not efficient with this system. The loop structure has proved excellent precision because of a compensation effect on the series impedance. The best case is an homogeneous loop where the fault location equation is only a ratio of the measured current from both end. Then the bias error was investigated with the load impact. The single-ended method and the two-ended method using the positive sequence system are very sensitive to the loads and therefore require estimation methods which increases the size of the faulty area. The negative 179

180 6. SUMMARY 180 sequence system has a very small voltage, therefore the loads on the negative sequence system consume very small current compared to the fault current. The precision of the fault locator is then not impacted.

181 Part VII Conclusions 181

182 1. General conclusions Three years of research were necessary to deliver this document. The work has been followed up by the industrial partner Siemens AG and supported by the BEAMS Department. This collaboration led to very practical results. Even if there is only one document, it can be divided in two almost independent parts because the knowledge of one is not necessary for the understanding of the other one. The first part of the thesis concerns the detection of single phase earth fault in compensated network. The beginning of the project has started by understanding the phenomena occurring in a compensated network during single phase earth fault. This thesis also brings some mathematical development and simulations to illustrate the network behavior. Then algorithms have been suggested, implemented and tested in simulations and on real recordings. The main strategy for the algorithms is to consider the sound feeder as a pure zero sequence capacitance and not the faulty feeder. This has led to two methods using both the transients signal and the steady state for the greatest sensitivity regarding the fault impedance. One of the outputs of this work is a prototype which is now almost the new transient protection of Siemens for the compensated and isolated network. A patent has also been taken to protect the algorithms. Fault location using the steady state was investigated after the fault detection. It has appeared that compensated networks have a too small fault current to locate precisely the fault. This is also due to a lack of knowledge coming from the operators who do not measure the zero sequence series impedance and therefore do not know all the parameters required for a precise fault location. A last reason why steady state fault location is not possible in compensated network is the intermittence of many fault because of the Peterson coil effect. This intermittence does not provide a sufficiently stable signal to compute the current and voltage phasors for a proper location. Therefore, one solution is the addition of an active system to the network that is able to increase the fault current. We propose to switch on a resistance in parallel to the Peterson coil. This solution significantly improve the fault location but many parameters can still be improved. A simulation tool has then been developed to determine which parameters are reducing the precision and select the best algorithm depending on the topology and on the network condition. This tool will be further developed after this PhD to be used inside Siemens. 182

183 2. Fault detection Two solutions have been proposed and implemented for the single phase-to-earth fault detection problem in compensated network. The solutions consider the capacitive behavior of a healthy feeder compared to the non-capacitive behavior of a faulty feeder. The transients are playing an important role in the fault detection because the fault can be intermittent or very weak. However both methods use all information from the transient and from the 50 Hz signals to be the most sensitive. Contrary to the Wischer relay that used only the transient signal, our methods are very sensitive because they use the rising transient during high impedance faults. The first method consists in an estimation of the zero sequence capacitance of the monitored feeder. An integration of the current is made and a least square method estimate the slope the signals on a q0-u0 diagram. Once this estimation has been made, each sample is compared to the perfect capacitive behavior. The deviations of the samples from the perfected capacitive behavior is integrated and a threshold is set. If this threshold is reached meaning the deviation from a perfect capacitive behavior is large enough then a fault is detected. This method has shown good result regarding the sensitivity during high impedance faults however the fine tuning of the threshold was very difficult. It has finally been set by using a theoretical rule and also a feedback from the tested recordings during the implementation of the prototype. Low impedance with strong transients have shown differences in the perfect capacitive model which largely increases the error signals and makes the detection more difficult. A dynamic threshold has then been implemented to deal with this problem. The second algorithm is also considering the capacitive behavior of the healthy feeder but details the behavior of the faulty feeder as producing a negative active power in the zero sequence system whereas the sound feeder consumes active power. Based on these conclusions, the fault detection has the advantage of being directional unlike the first method. The method uses the voltage and current zero sequence signals to calculate the zero sequence active energy which is an integration of the zero sequence active power. This energy makes the detection of the fault very quick and sensitive because a lot of faulty information can be accumulated for the detection. The common problem of these algorithms was the circulating current. The non-capacitive behavior of this current with a 50 Hz frequency was disrupting the algorithms because it does not satisfy the assumptions made during the creation of the algorithms. Therefore the algorithms consider such a behavior as faulty. However this problem has been solved using appropriate filters and the devices can now be used in network operating with loop structure and having such circulating currents. 183

184 3. Fault location The fault location was the most difficult part of this work because there were many possibilities of fault location strategies and the problem is more complex than fault detection with many parameters. The primary decision was to chose which location method to use and try to improve. A short comparison of the methods has been presented and the steady state at 50 Hz has been chosen. The sampling frequency and the experience got with the recordings for the fault detection prototype development are some reasons why the transients have not been selected to locate the fault. The heterogeneity of the power lines was also an argument to use steady-state fault location instead of traveling waves. The goal of the fault location had to be defined. It appears that fault location in compensated network is made in two steps. The first step is to locate the faulty section which is a part of the feeder between two secondary substations. The length of a section ranges between 100 meters and several kilometers. Once the faulty section is found, some materials are brought to the closest secondary substation and a very accurate fault location (+/- 1 m) is done to know where the digging has to be made. The first step takes between several hours to one or even 2 days and is done by driving along the faulty feeder and switching on and off different secondary substations. It is very time consuming and if an algorithm is able to directly select one or two section with strong probability of being faulty, it will save a lot of time and money to the operators. Therefore the efforts have been put to develop such an algorithm. The intermittence of the fault is a problem encountered with steady state fault location, the fault must be stable for at least several periods to have a good estimation of the voltage and current phasors. The installation of a parallel resistance has been proposed to stabilize the fault current. This resistance is switched on in parallel to the Peterson coil which changes the compensation factor resulting in a much bigger faulty current that improves the accuracy of the fault locator. The main problem discovered during this work is not about the algorithm already developed in the literature but it is more about the nature of the compensated network and the distribution network characteristics. Indeed the small fault current and the line parameters make the voltage drop from the bus bar to the fault position relatively small. Therefore the errors made on the measurements and on the parameters make any algorithm unable to locate the fault accurately enough. The error on the fault location does not come from a model error but is due to the precision of the measurement devices and the insufficient knowledge that the operator has on its network. Consequently a tool has been developed with a graphical user interface to estimate the accuracy of different fault location algorithms in a specific distribution network. The user is allowed to change the precision on the parameters, on the measurements, the value of the decompensation, etc. the goal is to indicate if the fault location with current algorithms is 184

185 3. FAULT LOCATION 185 possible on his network and if it is not then the operator can understand which actions could be taken to obtain a useful fault location. The results of this tool even if they depend on the network structure and on the parameters provided some general conclusions. The zero sequence system has the weakness of the series impedance which is not known by the operators. Therefore the single-ended method and the two-ended method using this system are not very accurate. However a two-ended method using the positive or the negative sequence system has a relatively good accuracy if the loads are not considered. The loads create current infeed which the algorithms are not aware of, leading to strong bias errors when we use the positive sequence. The negative sequence is almost not impacted by the loads because of its very small voltage. If a two-ended method technique can be used then the negative sequence system seems to be the most accurate. The topology has also a great influence in the precision. The loop structure creates a compensation effect which boosts the fault location precision to a very interesting level. The errors on the parameters are not even more the main problem in this case and others error must be considered as the modeling error.

186 4. Future work and perspectives Even if the fault detection has led to a useful device, some work can still be done. Some details will be found with the experience from the fields and the sensitivity will probably be impacted. Some additional mechanisms such as a better dynamic threshold or stopping criteria could enhance the algorithms. New solutions could be found in the problem of circulating currents which is still reducing the sensitivity. A more efficient filtering system could be investigated for this purpose. The fault location topic has not been solved in this work but strong tools have been developed to identify the problems depending on the topology, the current way of operating a distribution network, the measurements accuracy, etc. Tests of these simulations on a real network could provide lot of information about the fault location and demonstrates the possibility to implement such system. The effect of the parallel resistance and the increasing of the faulty current should be more investigated. For example, it is supposed that the increasing of the faulty current will stabilize the fault and might transform an intermittent earth fault into a permanent earth fault. This effect must still be proven; Also the simulation tool has been developed for compensated network but it can be adapted to of other network and others applications than the fault location problem. Six months will be spent after this thesis to develop a more commercial product of this simulator. 186

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192 Bibliographical contribution Technical reports 1. Loos, M.. Detection of earth faults in compensated networks. October pages report. Siemens-ULB October 2010 meeting. 2. Loos, M. Intermittent & Restriking Earth Fault - Recording from EDF and Eon-Sweden. 17 pages report. November Technical study for Siemens. 3. Loos M., QU-algorithm and QU2-Algorithm. 7 pages report. November Technical study for Siemens. 4. Loos, M. Study of the QU-method using phases measurement and the q(t) analysis. 22 pages report. January Technical study for Siemens. 5. Loos, M. EF in compensated network - Development of algorithm based on the knowledge of Co. 18 pages report. January Siemens-ULB February 2011 meeting. 6. Loos, M. Transient Effect caused by Earth Fault in Compensated Network. 34 pages report. February Siemens-ULB February 2011 meeting. 7. Loos, M. Using a sampling frequency of 2 khz for the new algorithm to detect EF in compensated network. March pages report. Technical study for Siemens. 8. Loos, M. Description of a new algorithm to detect EF in compensated network. April pages report. Siemens-ULB April 2011 meeting. 9. Loos, M. Tests of a new algorithm to detect EF in compensated network. April pages report. Siemens-ULB April 2011 meeting. 10. Loos, M. High circulating current, Problems and solutions. May pages report. Techinal study for Siemens. 11. Loos, M. Presentation of a new algorithm to detect EF in compensated/isolated network. June slides. Presentation to Siemens department as Siemens intern. 12. Loos, M. C0 estimation algorithm Prototype Implementation and test. July pages report. Internship report for ULB. 13. Loos, M. Directional information with the ULB algorithm. November pages report. Siemens-ULB November 2011 meeting. 192

193 BIBLIOGRAPHY Loos, M. Technical improvements on the prototype C0 method and directional method. September pages report. Siemens-ULB September 2011 meeting. 15. Loos, M. Fault location algorithm - Method comparison. January pages report. Siemens-ULB January 2012 meeting. 16. Loos, M. Fault location algorithm - Parameter study. March pages report. Siemens-ULB April 2012 meeting. 17. Loos, M. The needs and the topology of fault location in compensated network. June pages report. Siemens-ULB June 2012 meeting. 18. Loos, M. Tool development for fault location optimization. 24 pages report. September Siemens-ULB September 2012 meeting. 19. Loos, M. Tool development for fault location optimization. 32 pages report. December Siemens-ULB December 2012 meeting. 20. Loos, M. Fault Location Algorithm Specifications Report. 38 pages report. March Siemens-ULB 2013 March meeting. 21. Loos, M. Adaptation of the Pfalzwerke network to the tool. 20 pages report. June Siemens-ULB 2013 June meeting. 22. Loos, M. Fault Location Simulators Specifications. 17 pages report. June Siemens-ULB June meeting. Development Specification 1. Loos, M. Development Specification Firmware; 7SN64 / Earth Fault Detection. 95 pages. February Survey 1. Loos, M. and Werben, S. Fault location in compensated network - Information and questions for the attention of Distribution System Operators. April pages survey. Patent 1. Loos, M. and Maun, J.-C. Method and protective device for identifying a ground fault in a polyphase electrical energy supply network having a compensated or isolated star point. Europe PCT/EP2011/ Issued October 28, 2011.

194 BIBLIOGRAPHY 194 Conference papers 1. Loos, M. and Maun, J.-C. and Werben, S. Circulating Currents in Closed Loop Structure, a New Problematic in Distribution Networks. Presented at IEEE PES GM Poster session. 2. Loos, M. and Maun, J.-C. and Werben, S. Multiple Measurements to Locate Single Phase Earth Fault in Compensated Network. Presented at ISGT Europe Paper session. 3. Loos, M. and Maun, J.-C. and Werben, S. and Kereit, M. Detection of single phase earth fault in compensated network with C0 estimation. Presented at CIRED Poster session. 4. Loos, M. and Maun, J.-C. and Werben, S. and Kereit, M. Fault Direction Method in Compensated Network using the Zero Sequence Active Energy Signal. Presented at IEEE EUROCON Paper session. 5. Loos, M. and Maun, J.-C. and Werben, S. and Kereit, M. Fault Locator Comparison Tool and Designer for Distribution Network. Presented at IEEE PES GM Poster session.

195 Part VIII Appendices 195

196 A. Network Information The network used to test the detection algorithm is a 12kV distribution network with a Peterson coil of mh with a equivalent parallel resistance of Ohm which is 20 times the coil impedance. There are three feeders, the line can be overhead or undergound. Figure A.1: Network length and topology The following figure shows the position of the phases. Figure A.2: Position of the phases The next table shows the the symmetrical parameters of each feeders. 196