and Location in Compensated Network
Matthieu LoosA thesis submitted for the degree of PhD in Engineering Sciences
Academic year 2013-2014
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 nec-essary 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.
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.
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 26
2.1 Solid Grounding . . . 28
2.2 Isolate Grounding . . . 30
2.3 Low Impedance Grounding . . . 32
2.4 High Resistance Grounding . . . 33
2.5 Resonant Grounding . . . 34
2.6 Examples of Industrial Grounding . . . 35
3 Single Phase to Ground Fault In Compensated Network 36 3.1 Steady State . . . 36
3.1.1 Isolated network . . . 36
3.1.2 Compensated network . . . 39
3.2 Transients . . . 43
3.2.1 Symmetrical components to study the transients . . . 43
3.2.2 Discharging frequency . . . 44
3.2.3 Charging frequency . . . 45
3.2.3.1 The charging frequency model . . . 46
3.2.3.2 Charging transient magnitude considering the fault resistance 47 3.2.4 Transient due to the fault resistance . . . 49
3.2.4.1 Neglecting the parallel resistance . . . 50
3.2.5 Transient due to inception time . . . 51
3.2.6 Extinction of the fault . . . 53
3.3 Intermittent and restriking earth fault . . . 54
3.3.1 Shape of an intermittent earth fault . . . 55
3.3.2 Shape of restriking earth fault . . . 56
4 Confrontations of the Theory with the Field 58 4.1 The topologies of the distribution . . . 58
4.2 The circulating current problem . . . 59
4.2.1 Asymmetric series impedance . . . 59
4.2.2 Network coupling . . . 62
4.2.3 Illustration with real recordings and simulations . . . 63
5 Summary 66 III Single Phase to Ground Fault Detection Algorithms 67 1 Introduction 68 2 Review of today fault detection devices 69 2.1 The Wischer principle . . . 69
2.2 The QU-method . . . 71
2.3 The Wattmetric function . . . 72
3 The faulty feeder C0 method algorithm 74 3.1 The capacitive behavior of the sound feeder . . . 74
3.2 The algorithm . . . 75
3.3 Disadvantages of the method . . . 78
4 The directional method algorithm 81 4.1 The observation . . . 81
4.2 The algorithm . . . 82
4.3 Specific topology . . . 86
4.3.1 Discussion about the active power flow . . . 86
4.3.2 Possible direction of the 4 relays in a closed ring . . . 87
5 Tests and simulations of the methods 89 5.1 Classic fault . . . 89
5.2 High impedance fault . . . 91
5.3 Coil effect . . . 93
5.4 Intermittent earth fault . . . 95
6 Summary 98
IV Fault Detection Prototype Development 99
2 The signal conditioning 101
2.1 High pass FIR filter - Purpose and design . . . 101
2.2 Circulating current issue . . . 102
2.2.1 The detection . . . 103
2.2.2 The first suppression technique . . . 104
2.2.3 The second suppression technique . . . 105
2.3 Current condition . . . 105
3 The C0 method 106 3.1 Integrating the current i0 . . . 106
3.2 Estimating C0 . . . 106
3.3 Error threshold computation . . . 109
3.3.1 Basis . . . 109
3.3.2 Feedback and updates from the tests . . . 111
3.4 Calculation of the error and its integration . . . 112
4 Device running criteria 114 4.1 Blocking the algorithm . . . 114
4.2 Stopping the algorithm . . . 115
4.3 Characterization of the fault . . . 115
4.4 Faulty phase determination . . . 115
5 Directional method 116 5.1 Implementation . . . 116
5.2 Feedback and updates from the tests . . . 118
6 Summary 120 V Fault Location in Compensated Network 121 1 Introduction 122 2 The needs of fault location in compensated network 123 2.1 Today’s fault location . . . 123
2.2 What fault location algorithm could bring . . . 125
3 State of the art of fault location and application 126 3.1 Charging transient . . . 126
3.2 Fault passage indicators . . . 127
3.3 Traveling waves . . . 128
3.4 Steady state . . . 129
4 Challenges of steady-state fault location 130 4.1 The compensated network problem . . . 130
4.2 Single-ended method . . . 132
4.2.1 Heterogeneous line . . . 133
4.3 Two-ended method . . . 135
4.3.1 Heterogeneous and tree structure . . . 136
4.3.2 Loop topology . . . 137
4.4 Loads and DGs impact on fault location . . . 139
4.4.1 Loads and DGs impact . . . 139
4.4.2 Loads and DGs model . . . 140
5 Summary 142 VI Fault Location Tool and Sensitivity Analysis in Compensated Net-work 143 1 Introduction 144 2 Fault location main problem 145 2.1 Parameters and measurements accuracy . . . 145
3 Graphical User Interface Tool 148 3.1 Purpose . . . 148
3.2 Structure . . . 148
3.2.1 Network description . . . 148
3.2.2 SimNet.m script . . . 151
3.2.3 RunSimNet and the GUI . . . 155
4 Sensitivity analysis 159 4.1 Purpose of the sensitivity analysis . . . 159
4.2 The parallel resistance importance . . . 160
4.3 Size of distribution network . . . 161
4.4 The single-ended measurements precision . . . 162
4.4.1 Today’s knowledge . . . 162
4.4.2 Improvement of Z0 knowledge . . . 164
4.4.3 Heterogeneous line . . . 165
4.4.4 The parallel resistance effect . . . 166
4.5 Two ended measurements precision . . . 167
4.5.1 The best symmetrical system . . . 168
4.5.2 The parallel resistance effect . . . 170
4.5.3 The loop advantage . . . 172
4.5.4 Heterogeneous line . . . 173
5 The load impact and bias error 174 5.1 The impact . . . 174
5.1.1 The single-ended algorithm . . . 174
5.1.2 The two-ended algorithm . . . 175
5.2 A solution . . . 177
VII Conclusions 181
1 General conclusions 182
2 Fault detection 183
3 Fault location 184
4 Future work and perspectives 186
VIII Appendices 195 A Network Information 196 B DSO Survey 198 B.1 The description . . . 198 B.2 Customer 1 . . . 203 B.3 Customer 2 . . . 206 B.4 Customer 3 . . . 210 B.5 Customer 4 . . . 213 B.6 Customer 5 . . . 216 B.7 Customer 6 . . . 218
2.1 Network representation of two feeders network with single phase earth fault . 26
2.2 Single phase earth fault representation with symmetrical components . . . 27
2.3 Representation of solidly grounded transformer . . . 28
2.4 Representation of a solidly grounded network with two feeders . . . 29
2.5 Single phase earth fault on phase A in a solidly grounded network . . . 30
2.6 The current is flowing through the shunt capacitance in case of single phase earth fault . . . 31
2.7 The voltage neutral is floating in isolated network . . . 31
2.8 The current flows are opposite for the sound and the faulty feeder . . . 32
2.9 Representation of a high resistive grounding in single phase to earth fault situation . . . 33
2.10 A phase angle of 90° is measured for a high resistive grounding system . . . 34
2.11 Representation of a compensated network in single phase to earth fault condi-tion . . . 34
3.1 The isolated network has capacitive current circulating through the healthy phases in case of single phase earth fault . . . 37
3.2 Steady state amplitude on the faulty feeder depends on the healthy feeders . 38 3.3 Fortescue representation of the zero-sequence current flows in case of EF . . . 38
3.4 Fortescue representation of the zero-sequence current flows in case of EF . . . 39
3.5 No phase angle between the faulty and sound feeder with a perfect Peterson coil 40 3.6 Phase angle appears between the faulty and sound feeder with a realistic Pe-terson coil . . . 40
3.7 Simplified zero sequence system . . . 41
3.8 Phase Angle of the faulty feeder depends on RN G . . . 42
3.9 Using the symmetrical components is equivalent to the distributed model for the transients consideration . . . 43
3.10 Representation of the discharge of the faulty phase . . . 44
3.11 Representation of the charge of the healthy phases . . . 45
3.12 Model of a network with three feeders to characterize the charging transients with symmetrical components . . . 47
3.13 Three charging frequencies are measured on a network with three feeders . . 47
3.14 Charging transient with a 0 Ω earth fault . . . 48
3.15 Charging transient with a 100 Ω earth fault . . . 48
3.16 Charging transient with a 1.66 kΩ earth fault contains only 50 Hz signal . . . 49
3.17 Slow increasing of the 50 Hz voltage and current with Rf ault=1.66kΩ . . . 49
3.18 Influence of the fault resistance . . . 50
3.19 Validation of the equation considering the parallel resistance . . . 51
3.20 Peterson coil effect on symmetrical components . . . 51
3.21 Transient current due to the Peterson coil is measured only on the faulty feeder 52 3.22 Decreasing exponential occurs only on the faulty feeder . . . 52
3.23 Decreasing of V0 and I0 after fault extinction . . . 53
3.24 50 Hz resonating zero-sequence system . . . 53
3.25 52 Hz resonating zero-sequence system . . . 54
3.26 Typical intermittent earth fault . . . 55
3.27 Typical intermittent earth fault with coil effect . . . 56
3.28 Typical restriking earth fault . . . 56
4.1 Pfalzwerke distribution network . . . 60
4.2 Asymmetry in the series phase impedance creates circulating current . . . . 61
4.3 Single conductors in parallel and trefoil position . . . 62
4.4 Zero-sequence voltage is measured during healthy operation due to mutual coupling . . . 63
4.5 Circulating current due to coupling with parallel asymmetric network . . . . 64
4.6 Circulating current before the single phase earth fault on feeder J03 and J07 65 4.7 Simulation of the load power on the zero sequence circulating current . . . . 65
2.1 The 7SN600 transient earth-fault relay from Siemens . . . 69
2.2 Detection of transients in the Wischer principle . . . 70
2.3 The EOR-D device of a-eberle . . . 71
2.4 Illustration of the QU method . . . 72
2.5 The Wattmetric function decision criteria . . . 73
3.1 A least square method is necessary to get a C0 value . . . 76
3.2 In case of low impedance fault, the error signal is very high . . . 76
3.3 High impedance fault with error signal . . . 77
3.4 Integration of the error signal to increase the sensitivity of the algorithm . . 77
3.5 Transient has bigger error than the steady state . . . 78
3.6 Transient does not exactly matches the capacitive model . . . 79
3.7 No problem to know which feeder is faulty . . . 79
3.8 Detection of the faulty feeder is not possible with four devices in a loop . . . 80
4.1 Active power depends on the current and voltage behavior . . . 82
4.2 Main power flow in a compensated network during single phase earth fault . 83 4.3 Instantaneous zero-sequence active power power for small impedance fault . 84 4.4 Instantaneous zero-sequence active power power for high impedance fault . . 85
4.5 Energy evolution of a low impedance fault . . . 85
4.6 Energy evolution of a high impedance fault . . . 86
4.7 Schematic active power flow in closed ring structure . . . 86
5.1 Simulation network to test the algorithm . . . 89
5.2 Zero-sequence current and voltage for a low impedance fault . . . 90
5.3 QU diagram of a classic single phase earth fault . . . 90
5.5 Energy in case of classic single phase earth fault . . . 91
5.6 Zero sequence current and voltage for high impedance fault . . . 92
5.7 QU diagram in case of high impedance fault . . . 92
5.8 Integration of the error signal for a high impedance fault simulation . . . 93
5.9 Energy in case of high impedance fault . . . 93
5.10 Zero sequence current and voltage with a coil effect . . . 94
5.11 Coil effect disappears with the high pass filter . . . 94
5.12 QU diagram with a coil effect is easy to detect . . . 95
5.13 Integration of the squared error with a coil effect . . . 95
5.14 Energy for direction determination with coil effect . . . 96
5.15 Simulation of an intermittent and restriking earth fault . . . 96
5.16 The feeder 1 is not on a straight line in the QU diagram . . . 97
5.17 The integration of the squared error works well with intermittent earth fault 97 5.18 The direction determination works correctly in case of intermittent earth fault 97 2.1 Integration of the current i0(t) without (left) and with (right) high-pass filtering compared to voltage signal U0 . . . 101
2.2 High pass filter characteristic for signal conditioning . . . 102
2.3 Illustration of circulating current from real recording before a single phase earth fault happens . . . 103
2.4 Healthy feeder can be detected as faulty without dealing the circulating current 104 2.5 Suppression of the 50 Hz component to delete the circulating current . . . 104
2.6 Deletion of the circulating component without filtering . . . 105
3.1 Illustration of the trapezoidal integration compared to a perfect integration . 106 3.2 Estimation of C0 in case of sound or faulty feeder . . . 108
3.3 Estimation of C0 in case of faulty feeder with unrealistic C0 value . . . 109
3.4 Threshold value depending on C0 value . . . 109
3.5 Minimum value of the threshold limited in case transient detection . . . 110
3.6 Evolution of the threshold depending on the current signal . . . 110
3.7 Relay picks up after the inception of the fault with Feeder 1 faulty and 3kOhm fault . . . 111
3.8 C0method values and threshold . . . 111
3.9 Updates make the relay picked up before the inception of the fault . . . 112
3.10 The threshold can be smaller in this case and detect the faulty feeder . . . . 112
4.1 Voltage is decreasing when the fault has disappeared . . . 114
5.1 Flowchart of the direction determination . . . 116
5.2 The three zones of direction and determination in case of LIF . . . 117
5.3 The three zones of direction and determination in case of HIF . . . 118
5.4 Zero sequence active energy with circulating current in a four feeders sound loop118 5.5 Zero sequence active energy without circulating current in a four feeders sound loop . . . 119
2.1 Flowchart explaining the procedure to locate the faulty section in compensated network with ring possibilities . . . 124
3.1 Model to determine the frequency of the charging transient . . . 127
3.2 Example of fault passage indicators for a radial feeder . . . 128
3.3 Effect of the fault used in the traveling wave fault location principle . . . 128
4.1 Connection of a parallel resistance to increase the fault current . . . 130
4.2 Example of signal increasing due to the connection of a parallel resistance . . 131
4.3 Example of current increasing due to the connection of a parallel resistance . 131 4.4 Injection of a signal from the transformer neutral . . . 132
4.5 Schematic of a fault location model using a single ended method . . . 133
4.6 Computation of the current and voltage on the faulty section . . . 134
4.7 Topology of a tree feeder . . . 134
4.8 Schematic of a fault location model using a two ended method . . . 135
4.9 Identification of the faulty branch with a two ended algorithm . . . 136
4.10 Procedure to isolate the faulty branch in a tree feeder and locate the fault . 137 4.11 Closed ring structure made of more than two feeders . . . 138
4.12 Impact of the distributed loads if the fault current is not significant . . . 140
4.13 There is no impact on the fault distance if the loads are beyond the fault . . 140
4.14 Method of load tap from [Altonen and Wahlroos, 2007] . . . 141
2.1 Standard error representation on a phasor measurement . . . 146
2.2 Bias error representation compared to the standard error . . . 147
3.1 Illustration of the PI model from the interface . . . 150
3.2 Positive sequence system node number . . . 152
3.3 Negative sequence system node number . . . 153
3.4 Zero sequence system node number . . . 153
3.5 Screenshot of the Graphically User Interface . . . 155
3.6 Algorithm selection - Popup button and list of fault locator . . . 156
3.7 Example of text box information . . . 156
3.8 Variance detailed example . . . 156
3.9 Checkbox display information . . . 157
3.10 Standard deviation edit box . . . 157
3.11 Algorithm option window . . . 158
3.12 The parallel resistance design button . . . 158
4.1 Additional questions are brought by the requirement of the fault locator . . . 159
4.2 The active system can make the fault location possible in compensated network 160 4.3 Comparison of single phase earth fault between compensated and solidly grounded network . . . 161
4.4 Standard deviation for three different C0 total . . . 162
4.5 Fault location accuracy with single-ended method and actual knowledge of the network . . . 163
4.6 Fault location accuracy with improvement of the zero sequence impedance in single ended method . . . 165
4.7 The ratio X/R is not important compared to the absolute value of the impedance . . . 166
4.9 Multiple measurements can help to improve the fault location . . . 167
4.10 Illustration of the zero sequence system two-ended method fault location . . 169
4.11 Voltage value of the three symmetrical systems depending on the parallel re-sistance . . . 170
4.12 Zero sequence system variance with two ended solution . . . 171
4.13 Positive sequence system variance with two ended method . . . 171
4.14 Negative sequence system variance with two ended method . . . 172
4.15 Compensation effect with the loop structure . . . 173
5.1 Impact of the loads on the single ended algorithm . . . 174
5.2 The zero sequence system is not influenced by the loads . . . 175
5.3 The positive sequence system is strongly influenced by the loads . . . 176
5.4 The negative sequence system is almost not affected by the loads . . . 177
5.5 Load impact integration in the faulty area estimation . . . 177
A.1 Network length and topology . . . 196
A.2 Position of the phases . . . 196
B.1 Illustration of fault location problem . . . 198
B.2 Voltage difference between the faulty position and the measurement position 199 B.3 Illustration of the parallel resistance . . . 200
B.4 PI model used for fault location . . . 201
B.5 Grid representation with measurements devices . . . 201
4.1 Survey of the German Distribution Network topology . . . 59
2.1 Wischer direction logical table . . . 70
4.1 The different indication of the direction protection in closed ring . . . 87
2.1 Default value of the standard deviation of the parameters . . . 146
3.1 Example of the network initialization text file . . . 149
3.2 Example of line characteristic in the text file . . . 149
3.3 Measurements node in the text file . . . 150
3.4 Loads information in the text file . . . 151
3.5 Distributed generation information in the text file . . . 151
4.1 Accuracy of the single ended method and contribution of each parameter . . 163
4.2 Single ended method accuracy if the knowledge on Z0 is improved . . . 164
4.3 Comparison of the symmetrical system for fault location . . . 168
4.4 Accuracy and contribution of each symmetrical system with two-ended method 168 4.5 Accuracy of the each symmetrical system with two ended method in a loop . 172 A.1 Line parameters . . . 197
B.1 Example of information provided by the fault locator . . . 199
B.2 Network information of the customer 1 . . . 203
B.3 Precision of the customer 1 . . . 204
B.4 Network information of the customer 2 . . . 206
B.5 Precision of the customer 2 . . . 208
B.6 Network information of the customer 3 . . . 210
B.7 Precision of the customer 3 . . . 211
B.8 Network information of the customer 4 . . . 213
B.9 Precision of the customer 4 . . . 214
B.10 Network information of the customer 5 . . . 216
B.11 Precision of the customer 5 . . . 217
B.12 Network information of the customer 6 . . . 218
B.13 Precision of the customer 4 . . . 218
Introduction
This PhD thesis has been sponsored by Siemens with the goal of developing a new pro-tection 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.
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 pre-sented 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
principle are presented with low impedance fault, high impedance but also circulating current problem.
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
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.
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 2013. 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 2013.
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.
Overview of Distribution Network
Grounding Practices and Single
Phase to Ground Fault Behavior in
Compensated Network
This first chapter of the thesis reviews the different techniques used to ground the distri-bution 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 sin-gle 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 dif-ference 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 distribu-tion 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.
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 his-torical, 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 strat-egy 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 rep-resentation with the symmetrical components simplifies any unbalanced three phase power systems into three balanced system [Fortescue, 1918]. The fault current will then depend
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 cur-rent characteristic in single phase to ground fault is then mainly defined by the transformer connection, the others symmetrical systems having an insignificant influence.
2.1
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 suffi-cient 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 Zl, the earth impedance ZE and a fault
impedance if there is one Zf.
If =
VLG
Zl+ ZE + Zf
(2.1) The series impedance can be considered in the symmetrical system as:
Zl =
Z1+ Z2+ Z0
3 =
2Z1+ Z0
3 (2.2)
Figure 2.4: Representation of a solidly grounded network with two feeders
Z0= K0Z1 (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 de-tection is then very easy for low impedance fault and the simple used of overcurrent prode-tection is enough.
0 50 100 150 200 250 300 −600 −400 −200 0 200 400 600 time [ms] Current [Amp] I a I b I c Fault inception
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: I1 = I2 = I0 = V0 X0C (2.4) Ic= 3I0 = 3V0 X0C (2.5) Regarding the equation 2.4, this is correct for the fault current but not for the
cur-rent in the feeder because the symmetrical systems have their own capacitances X1C,X2C
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
fer-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 V0 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.
20 30 40 50 60 70 80 90 100 time [ms] Faulty I o Sound I o V o
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
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.
0 50 100 150 time [ms] V 0 I0 Faulty I0 Sound
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.
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 hazardous-type applications because it emphasizes the personnel safety. This system limits the fault current to 25-50 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
pensated 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.
3.1.1 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 zero-sequence 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
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.
3I0sound=IA1+ IB1 (3.1)
3I0f aulty =IA2+ IB2+ If ault (3.2)
If = − IA2− IB2− IA1− IB1 (3.3)
3I0f aulty0 = − IA1− IB1= −3I0sound (3.4)
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.
20 40 60 80 100 120 140 160 180 time [ms] Faulty I o Sound I o V o Steady State
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 I0f aulty = Isound
0 .
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 ZT 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.
3.1.2 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 ωLN G − ωC0 (3.5) LN G= 1 ω2C 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 uncom-pensated current. Therefore, if the network is slightly overcomuncom-pensated, 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.
If =IN G+ IC0 (3.7) If =V0( 1 ωLN G − ωC0+ 1 RN G ) (3.8)
If is the fault current, IN G is the current circulating in the transformer neutral, IC0 is
the current due to the zero-sequence capacitance and RN G 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 I0 on a sound and a faulty feeder with the voltage
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. 0 20 40 60 80 100 120 140 160 180 200 time [ms] Faulty Io Sound Io V o Max Sound &
Fault feeders
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 im-perfection 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.
0 20 40 60 80 100 120 140 160 time [ms] Faulty I o Sound I o V o Max Sound feeder Max Faulty feeder
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 I0 on the faulty feeder and I0 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 LN G 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 C0sound=Psoundf eeder
C0. 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 V0 is applied, F1 will measure a current I0= V0
jωCsound
0
that has
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 C0soundand the Peterson coil. The variable x is equal to x = RN G
V0 IF 2 0 =Z(jω) (3.9) Z(jω) =(jωC0sound+ 1 3RN G + 1 3jωLN G) −1 (3.10) Z(jω) = 3jωRN GLN G −ω23Csound 0 LN GRN G+ jωLN G+ RN G (3.11) then |Z(jω)| =q 3ωRN GLN G (−ω23Csound 0 LN GRN G+ RN G)2+ (ωLN G)2 (3.12) and Arg(Z(jω)) = − π 2 + atan( ωLN G RN G(1 − ω23C0soundLN G) ) (3.13) if RN G=xωLN G (3.14) then |Z(jω)| =q 3xωLN G (−ω23Csound 0 x)2+ 1 (3.15) and Arg(Z(jω)) = − π 2 + atan( 1 x(1 − ω23Csound 0 LN G) ) (3.16)
The next figure shows a graphical representation of the impact of the parallel resistance
RN G on the phase angle between I0 on the faulty feeder and V0. This result comes from an
EMTP/ATP simulation using line distributed model and the theoretical faulty feeder comes
from the equation 3.16. XN G is the reactance of the Peterson coil. The angle is the phase
angle between the zero-sequence voltage V0and the zero sequence current I0 on the concerning
feeder. 0 5 10 15 20 25 30 35 40 −100 −80 −60 −40 −20 0 x=RNG/XNG
Phase Angle comparing to V0 [°]
Faulty Feeder Sound Feeder Eq. 1.18
Figure 3.8: Phase Angle of the faulty feeder depends on RN G
