ABSTRACT SMITH, JUSTIN WADE. Model Based Fault Locating on Distribution Feeders. (Under the direction of Dr. Mesut E Baran.) As electric power systems grow in complexity and size, ensuring system reliability and continuity has become a major concern. Failure to locate faults quickly can result in prolonged outage times, customer safety concerns and lost revenues. Over the past few decades distribution networks have evolved into large and complex networks capable of carrying thousands of customers. As of late, utilities have displayed particular interest in distribution fault location technology to reduce such widespread impacts. This thesis aims to develop a modern distribution fault locating algorithm. The proposed fault locating algorithm is a model based algorithm that uses a short circuit model of the feeder to locate the fault. In the short circuit model, a fault is placed at every node and the observed fault current at the substation is recorded in tabular format. During an actual fault condition, the algorithm compares the recorded fault current at the substation to the short circuit modelling data. This comparison allows the fault locator to identify the exact node in the network that is faulty. In many cases, the short circuit model will indicate that there are several unique nodes with the same fault current magnitude. This problem is overcome with a proposed sub-algorithm called the localization algorithm. This algorithm uses protective device data and load flow data to determine the protective device that has interrupted the fault. By knowing the protective device that has interrupted the fault, the fault can be localized to a specific region of the network. To test the fault locating algorithm, four different test cases are proposed. Three test cases are performed using a Progress Energy Carolinas feeder model. Detailed fuse, recloser and substation breaker models are inserted into the feeder model to test popular protective schemes such as fuse saving and fuse blowing. Finally, the Stewart Street 12.47kV feeder is tested using DEW models provided by Allegheny Power. The Stewart Street feeder is much larger than the Progress Energy Carolinas feeder model and contains hundreds of nodes and tapped loads. The proposed localization sub-algorithm directly relies on the accuracy of the load flow solution. In the final test case, we assume the load to be a gaussian random variable by which the known load is perturbed about a mean load operation point. This approach introduces load uncertainty and measures the fault locating algorithm’s sensitivity to load variability. Model Based Fault Locating on Distribution Feeders by Justin Wade Smith A thesis submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Master of Science Electrical Engineering Raleigh, North Carolina 2013 APPROVED BY: Dr. Subhashish Bhattacharya Dr. Mesut E Baran Chair of Advisory Committee Dr. Srdjan Lukic DEDICATION To my parents Jeffrey W. Smith and Cindy A. Smith. Without you, none of this would have been possible. You gave me strength when I had nothing left and encouragement when I couldn’t carry on. This one is for you. To my grandfather Harold W. Smith who never got to see my thesis completed. To my friend Asa Gray, who encouraged me. His hard work and dedication showed me that the best things in life are the hardest to get. ii BIOGRAPHY Justin Wade Smith was born in Salisbury, North Carolina, United States of America. Justin attended high school at Northwood High in Chatham County, North Carolina and graduated in 2004. He received a Bachelor of Science in Electrical Engineering from North Carolina State University in 2009. Upon completion of his bachelors degree he joined the graduate school at NCSU working towards his Master of Science degree in Electrical Engineering with an emphasis on power system protection and fault locating under the direction of Dr. Mesut Baran with the NSF FREEDM Systems Center. iii ACKNOWLEDGEMENTS I would like to thank my advisor Dr. Mesut E. Baran, and my other committee members, Dr. Subhashish Bhattacharya and Dr. Srdjan Lukic. I would also like to acknowledge Larry Alesi at Schweitzer Engineering Laboratories(SEL) for his guidance. Much of my knowledge in the field of power system protection can be attributed to the mentorship and dedication of Mr. Alesi. He is true mentor and friend. I would like to thank Bette Gray of Rodanthe, N.C. for helping me chase my dreams. My family could not have been blessed with a greater friend. I would like to thank my friends Nick Parks and Jon McDonald. Their support and friendship led me to success. I would also like to thank my friends at Progress Energy Carolinas: Ronald ”Chip” Moore, Juan Yancey and Lawrence Roberts. iv TABLE OF CONTENTS LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Chapter 1 Introduction . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . 1.2 Challenges of Distribution Fault Locating . 1.3 Proposed Solution: Model Based Algorithm 1.4 Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 2 4 Chapter 2 Modern Distribution Fault Locating Algorithms . . . . . . . . . . . 2.1 Introduction to Distribution Fault Locating Algorithms . . . . . . . . . . . . . 2.2 Technique with Two-port Network Section Representation(Das Method) . . . . 2.2.1 Overview of Das Method . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 Fault Detection and Classification . . . . . . . . . . . . . . . . . . . . . 2.2.4 Developing an Equivalent Radial Network . . . . . . . . . . . . . . . . . 2.2.5 Load Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.6 Estimating nodal pre-fault voltages and currents . . . . . . . . . . . . . 2.2.7 Estimating Voltages and Currents at the Remote End and at the Fault 2.2.8 Calculating the Distance to the Fault: Single Line to Ground . . . . . . 2.2.9 Assessment of the Das Algorithm: Advantages and Disadvantages . . . 2.3 Girgis Apparent Impedance Method . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Overview of Girgis Method . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Direct Determination of Distance to the Fault . . . . . . . . . . . . . . . 2.3.3 Assessment of the Girgis Algorithm: Advantages and Disadvantages . . 2.4 Fault Locating using Digital Fault Recorder Data(Saha Algorithm) . . . . . . . 2.4.1 Overview of Saha Method . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Fault Loop Impedance Determination . . . . . . . . . . . . . . . . . . . 2.4.3 Determination of the Faulty Node . . . . . . . . . . . . . . . . . . . . . 2.4.4 Distance to the Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.5 Assessment of the Saha Algorithm: Advantages and Disadvantages . . . 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 5 5 6 6 6 10 11 12 15 18 19 21 21 21 26 27 27 27 30 34 38 39 Chapter 3 Model Based Fault Locating . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Sampled Data Conditioning . . . . . . . . . . . . . . . . . . 3.3 Steady State Fault Current Extraction . . . . . . . . . . . . 3.4 Fault Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Sliding Fault Resolution . . . . . . . . . . . . . . . . 3.4.2 Selecting Possible Fault Locations from Fault Tables 3.4.3 Fault Identification and Fault Table Selection . . . . . . . . . . . . 40 40 41 43 44 46 47 47 v . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 49 50 52 53 56 58 59 61 62 64 Chapter 4 Fault Locator Test Results . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction to the Notional Feeder, Stewart Street Feeder and Test Cases . . . 4.2 Notional Feeder Fault Tables and Short Circuit Data . . . . . . . . . . . . . . . 4.3 Test Case 1: Notional Feeder Testing With No Localization . . . . . . . . . . . 4.3.1 Introduction: Test Conditions and Procedure . . . . . . . . . . . . . . . 4.3.2 FLA Testing for Line-to-Ground Faults . . . . . . . . . . . . . . . . . . 4.3.3 FLA Testing for Line-to-Line Faults . . . . . . . . . . . . . . . . . . . . 4.3.4 Test Case 1 Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Test Case 2: Localization using Load Flow and Protective Devices . . . . . . . 4.4.1 Introduction: Test Conditions and Procedures . . . . . . . . . . . . . . 4.4.2 FLA Testing for Line-to-Ground Faults . . . . . . . . . . . . . . . . . . 4.4.3 A-Ground Fault at Node 17 . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 A-Ground Fault at Node 7 . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.5 Limitations of the Localization Algorithm: A-Ground Fault at Node 16 4.5 Test Case 3: Fault Locating on Fuse Saving or Fuse Blowing Schemes . . . . . 4.5.1 Introduction: Notional Feeder with Fuse Blowing Coordination . . . . . 4.5.2 Introduction: Fuse Blowing Scheme Test Conditions . . . . . . . . . . . 4.5.3 FLA Testing for Line-to-Ground Faults: Fuse Blowing . . . . . . . . . . 4.5.4 Line-to-Ground Fault at Node 17 . . . . . . . . . . . . . . . . . . . . . . 4.5.5 Line-to-Ground Fault at Node 6 . . . . . . . . . . . . . . . . . . . . . . 4.5.6 Introduction: Notional Feeder with Fuse Saving Coordination . . . . . . 4.5.7 Introduction: Fuse Saving Scheme Test Conditions . . . . . . . . . . . . 4.5.8 FLA Testing for Line-to-Ground Faults: Fuse Saving . . . . . . . . . . . 4.5.9 Line-to-Ground Fault at Node 10 . . . . . . . . . . . . . . . . . . . . . . 4.5.10 Line-to-Ground Fault at Node 6 . . . . . . . . . . . . . . . . . . . . . . 4.5.11 Limitations of the FLA on Fuse Blowing or Fuse Saving Coordinated Feeders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Notional Feeder Test Results Summary . . . . . . . . . . . . . . . . . . . . . . . 4.6.1 Test Case 1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Test Case 2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Test Case 3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Test Case 4: Fault Locating on Large Scale Feeders . . . . . . . . . . . . . . . . 4.7.1 Introduction: Stewart Street 12.47kV Feeder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 65 66 67 67 67 68 69 70 71 71 72 75 77 79 79 80 80 80 83 85 85 85 86 88 . . . . . . . 90 91 91 91 91 93 93 3.5 3.6 3.7 3.8 3.4.4 Calculation of Fault Currents in the Fault Table: Fault Resistance Localization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.1 Localization Using Protective Devices . . . . . . . . . . . . . . . . 3.5.2 Zones of Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 Localization using Fuse Characteristics . . . . . . . . . . . . . . . . 3.5.4 Estimating Fault Current Through the Fuse . . . . . . . . . . . . . Localization using Load-Flow Rejection . . . . . . . . . . . . . . . . . . . 3.6.1 Calculating Best Matched Device from Load Flow Rejection . . . . Combining Localization Data for Best Match . . . . . . . . . . . . . . . . 3.7.1 Final Ranking of Each Possibility . . . . . . . . . . . . . . . . . . . Localization Flow Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi . . . . . . . . . . . . . . . . . . . . . . 4.8 4.7.2 Introduction: Test Conditions and Procedures . . . . . . . . . . 4.7.3 Fault Tables for the Stewart Street Feeder . . . . . . . . . . . . . 4.7.4 Load Flow Analysis on the Stewart Street 12.47kV Feeder . . . . 4.7.5 MATLAB Fault Modelling of the Stewart Street 12.47kV Feeder 4.7.6 Fault at Pole P4622 on the Stewart Street 12.47kV Feeder . . . . 4.7.7 FLA Test Results for P4622 Fault . . . . . . . . . . . . . . . . . 4.7.8 Fault at Pole P4266 on the Stewart Street 12.47kV Feeder . . . . 4.7.9 FLA Test Results for P4266 Fault . . . . . . . . . . . . . . . . . 4.7.10 FLA Test Results Summary for Stewart Street Feeder . . . . . . Sensitivity Analysis: System Load Perturbations . . . . . . . . . . . . . 4.8.1 Introduction: Sensitivity Analysis . . . . . . . . . . . . . . . . . 4.8.2 System Load Perturbations: Test Conditions and Procedures . . 4.8.3 System Load Perturbations on Test Case 1-No Localization . . . 4.8.4 System Load Perturbations on Test Case 2 . . . . . . . . . . . . 4.8.5 System Load Perturbations on Test Case 3-Fuse Saving . . . . . 4.8.6 System Load Perturbations on Test Case 3-Fuse Blowing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 95 95 96 98 103 105 109 111 112 112 112 114 116 118 120 Chapter 5 FLA Testing Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A Notional Feeder Load Flow Data . . . . . . . . . . . . . A.1 Notional Feeder Real Power Flow Data . . . . . . . . . . . . A.2 Notional Feeder Reactive Power Flow Data . . . . . . . . . A.3 12kV Capacitor Bank Data . . . . . . . . . . . . . . . . . . A.4 Transformer Bank Data . . . . . . . . . . . . . . . . . . . . A.5 Source Impedance Data . . . . . . . . . . . . . . . . . . . . A.6 Line Impedance Data . . . . . . . . . . . . . . . . . . . . . . A.6.1 Positive Sequence Line Impedance Data . . . . . . . A.6.2 Negative Sequence Line Impedance Data . . . . . . . A.6.3 Zero Sequence Line Impedance Data . . . . . . . . . A.6.4 Positive and Zero Sequence Shunt Capacitance Data A.7 Relay Settings and Fuse Characteristics . . . . . . . . . . . A.8 Fuse Characteristics . . . . . . . . . . . . . . . . . . . . . . Appendix B Modelling of the Notional Feeder using MATLAB . . . B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . B.2 Modelling of Lines . . . . . . . . . . . . . . . . . . . . . . . B.3 Modelling of System Loads . . . . . . . . . . . . . . . . . . B.3.1 Load Modelling Under Fault Conditions . . . . . . . B.4 Modelling of Sources . . . . . . . . . . . . . . . . . . . . . . B.5 Modelling of Capacitor Banks . . . . . . . . . . . . . . . . . B.6 Modelling of Multi-Winding Transformers . . . . . . . . . . B.7 Modelling of Feeder Transformer . . . . . . . . . . . . . . . vii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 . 127 . 127 . 129 . 130 . 130 . 130 . 131 . 131 . 132 . 133 . 134 . 135 . 136 . 138 . 138 . 138 . 141 . 142 . 143 . 143 . 144 . 145 Appendix C Distribution Fault Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 147 C.1 System Fault Currents and Voltages via Numerically Computed Thevenin Equivalents and Sensitivity Matrices . . . . . . . . . . . . . . . . . . . . . . 147 C.1.1 Thevanin’s Theorem and Superposition Principle . . . . . . . . . . . 148 C.1.2 Pre-Fault and Faulted Systems in DEW . . . . . . . . . . . . . . . . 151 C.1.3 Forming the Phase Thevanin Matrix . . . . . . . . . . . . . . . . . . 155 C.1.4 System Fault Characteristics . . . . . . . . . . . . . . . . . . . . . . 158 C.1.5 3-Phase Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 C.1.6 Phase-to-Phase-Ground Faults . . . . . . . . . . . . . . . . . . . . . 162 C.1.7 Phase-to-Phase Faults . . . . . . . . . . . . . . . . . . . . . . . . . . 164 C.1.8 Single Line-to-Ground Faults . . . . . . . . . . . . . . . . . . . . . . 166 C.2 Verification of DEW Fault Current Calculation: Example Feeder . . . . . . 167 C.2.1 Validation with MATLAB Simulink Model . . . . . . . . . . . . . . 173 Appendix D Supplemental FLA Simulation Results for Stewart Street 12.47kV Feeder174 D.1 Pole P4622 Supplemental Recorded Results . . . . . . . . . . . . . . . . . . 174 D.2 Pole P4266 Supplemental Recorded Results . . . . . . . . . . . . . . . . . . 178 viii LIST OF TABLES Table 3.1 Table 3.2 Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Fault Table for Figure 3.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Increased Resolution Fault Table for Figure 3.7 . . . . . . . . . . . . . . . 47 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 4.25 4.26 Notional Feeder Fault Table for SLG Faults on A Phase. . . . . . . Line-to-Ground Simulation Results for Test Case 1 . . . . . . . . . Phase-to-Phase Fault Simulation Results for Test Case 1 . . . . . . Percent Mismatch Table for Protective Device Localization. . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Percent Mismatch Table for Protective Device Localization . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Percent Mismatch Table for Protective Device Localization . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Percent Mismatch Table for Protective Device Localization . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Percent Mismatch Table for Protective Device Localization . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Percent Mismatch Table for Protective Device Localization . . . . Percent Mismatch Table for Load Rejection Localization . . . . . . Substation Bus Load Flow Solution for Stewart Street Feeder. . . . Pre-Fault Load Flow Values . . . . . . . . . . . . . . . . . . . . . . Fault Analysis Calculated Parameters . . . . . . . . . . . . . . . . MATLAB Model Parameters . . . . . . . . . . . . . . . . . . . . . Pre-Fault DEW Load Flow Values . . . . . . . . . . . . . . . . . . Success-Failure Rate on Node 10, Test Case 1(No Localization) . . Success-Failure Rate on Node 17, Test Case 1(No Localization) . . Success-Failure Rate on Node 4, Test Case 1(No Localization) . . . Success-Failure Rate on Load Perturbation Test for Node 10 Fault Success-Failure Rate on Load Perturbation Test for Node 17 Fault Success-Failure Rate on Load Perturbation Test for Node 10 Fault Fuse Saving Feeder Coordination. . . . . . . . . . . . . . . . . . . . Table 4.27 Success-Failure Rate on Load Perturbation Test for Node 17 Fault Fuse Saving Feeder Coordination. . . . . . . . . . . . . . . . . . . . Table 4.28 Success-Failure Rate on Load Perturbation Test for Node 10 Fault Fuse Blowing Feeder Coordination. . . . . . . . . . . . . . . . . . . Table 4.29 Success-Failure Rate on Load Perturbation Test for Node 17 Fault Fuse Blowing Feeder Coordination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . with . . . with . . . with . . . with . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 69 69 74 74 76 77 82 82 84 84 87 87 89 89 96 98 100 102 107 114 115 115 117 117 . 118 . 119 . 120 . 121 Table A.1 Table A.2 Relay Settings for Substation Breaker A and Substation Breaker B . . . . 135 Relay Settings for Recloser A and Recloser B . . . . . . . . . . . . . . . . 135 Table C.1 Table C.2 Fault types and their frequency of occurrence[23]. . . . . . . . . . . . . . . 159 L-G Voltage Results of DEW vs. MATLAB Powerflow Script . . . . . . . 168 ix Table C.3 Table C.4 Current Results of DEW vs. MATLAB Script . . . . . . . . . . . . . . . . 169 MATLAB Simulink Fault Current Results . . . . . . . . . . . . . . . . . . 173 Table D.1 Table D.2 Other Likely Fault Possibilities for P4622 . . . . . . . . . . . . . . . . . . 177 Other Likely Fault Possibilities for P4266 . . . . . . . . . . . . . . . . . . 180 x LIST OF FIGURES Figure 1.1 Figure 1.2 Figure Figure Figure Figure Figure Figure Figure Figure 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 2.9 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 12kV Radial Feeder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FLA High Level Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 Radial Distribution Feeder[25]. . . . . . . . . . . . . . . . . . . . . . . . . Flow Chart for Determining fault type[25]. . . . . . . . . . . . . . . . . . Line section Bus M and Bus R. . . . . . . . . . . . . . . . . . . . . . . . Radial Distribution Feeder[25]. . . . . . . . . . . . . . . . . . . . . . . . . Voltage and Current relationship between M and R[25]. . . . . . . . . . . Consolidated loads at the remote end, Node N[25]. . . . . . . . . . . . . . Fault between Nodes x and x + 1(= y)[25]. . . . . . . . . . . . . . . . . . Fault locator load model as constant impedance with system load model as constant power [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simple Feeder with no laterals or taps . . . . . . . . . . . . . . . . . . . . Single line-to-ground fault sequence networks. . . . . . . . . . . . . . . . B-to-C Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sequence Network Diagram for a Phase-to-Phase Fault. . . . . . . . . . . Simple Substation with Two Parallel Feeders during Pre-Fault Conditions. Simple Substation with Two Parallel Feeders during Fault conditions. . . Cascaded Line Sections of Distribution Feeder. . . . . . . . . . . . . . . . Faulted Distribution Feeder[1]. . . . . . . . . . . . . . . . . . . . . . . . . Circuit Representation of Network for a Fault located between 1 and k. . Circuit Representation of Network for a Fault located between k and k + 1. Tapped Load inserted between node 2 and node k. . . . . . . . . . . . . . 7 8 9 10 13 15 16 High-Level Overview of FLA. . . . . . . . . . . . . . . . . . . . . . . Handling of Raw Data Passed to the Fault Locator. . . . . . . . . . Sampling of Fault Current Recorded at 64 Samples Per Cycle . . . Bus Voltage During a Ground Fault. . . . . . . . . . . . . . . . . . . RMS value of the 60Hz Fundamental during Line-to-Ground Fault. Algorithm for detecting steady state fault current. . . . . . . . . . . Generic 6 Node Feeder. . . . . . . . . . . . . . . . . . . . . . . . . . Phase-to-Phase evolving into a 3-Phase fault[13]. . . . . . . . . . . . Generic 6 Node Feeder with Fuses and Overcurrent Relay. . . . . . Operating Times for a 8620 A Fault Through Current. . . . . . . . Observed Current during Fault Conditions for Figure 3.9. . . . . . . Zones of Protection for Figure 3.9. . . . . . . . . . . . . . . . . . . . FLA Fuse Localization Algorithm. . . . . . . . . . . . . . . . . . . . Superimposed Currents Through Faulted Fuse. . . . . . . . . . . . . Fault Current Estimation Algorithm in FLA. . . . . . . . . . . . . . Current Rejection after Recloser Lockout. . . . . . . . . . . . . . . . Load Flow Rejection Algorithm in the FLA. . . . . . . . . . . . . . xi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 22 23 28 28 31 32 33 34 35 36 39 41 42 42 43 44 45 45 50 51 52 53 54 54 56 58 59 60 Figure 3.18 FLA Localization Algorithm Flow Chart. . . . . . . . . . . . . . . . . . . 64 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 Figure 4.32 Figure 4.33 Simulation Testing Procedure using MATLAB Simulink. . . . . . . . . . 67 Test Case 1 Notional Feeder One-Line Model. . . . . . . . . . . . . . . . 68 Test Case 2 Testing Procedure. . . . . . . . . . . . . . . . . . . . . . . . . 70 Notional Feeder One-Line Model with added Reclosers and Breakers. . . 72 Test Case 2: Substation Phase A RMS current during a fault at Node 17. 73 Test Case 2: Substation Phase A RMS current during a fault at Node 7. 75 Fault Locator Ranking of Fault at Node 16. . . . . . . . . . . . . . . . . 78 Fuse Blowing Scheme on Notional Feeder. . . . . . . . . . . . . . . . . . . 79 Fault Locator Observed Fault Current for Fault at Node 17. . . . . . . . 81 Fault Locator Observed Fault Current for a fault at Node 6. . . . . . . . 83 Fault Locator Observed Fault Current for a Fault at Node 10. . . . . . . 86 Fault Locator Observed Fault Current for a Fault at Node 6. . . . . . . . 88 Fault Locator Observed Fault Current for Node 8 Fault(Fuse Blowing Coordination). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Stewart Street 12.47kV Feeder Modelled in DEW. . . . . . . . . . . . . . 93 Test Procedure for Stewart Street Feeder using DEW. . . . . . . . . . . . 94 Reflected Fault Current at the Substation Bus for a Fault at Pole P4622. 95 Pre-Fault Short Circuit Model. . . . . . . . . . . . . . . . . . . . . . . . . 97 Faulty Short Circuit Model. . . . . . . . . . . . . . . . . . . . . . . . . . 97 Post-Fault Short Circuit Model. . . . . . . . . . . . . . . . . . . . . . . . 98 P4622 Node Location in Stewart Street 12.47kV Feeder Modelled in DEW. 99 Reflected Fault Current at the Substation due to the fault itself. . . . . . 100 Observed Fault Current at FUSE654421506 during loaded conditions. . . 101 Observed Fault Current at Substation during loaded conditions. . . . . . 101 Possible Fault Locations in Stewart Street 12.47kV Feeder for a fault at P4622. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Best Matched Locations for a fault at P4622 as calculated by the FLA. . 104 P4266 Node Location in Stewart Street 12.47kV Feeder Modelled in DEW.105 Upstream Fuse(FUSE1052482746) Load Flow Solution. . . . . . . . . . . 106 Pre-Fault Voltage at P4266. . . . . . . . . . . . . . . . . . . . . . . . . . 106 Reflected Fault Current at the Substation due to the fault itself. . . . . . 107 Observed Fault Current at upstream fuse(FUSE1052482746) during loaded conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Possible Fault Location in Stewart Street 12.47kV Feeder for a fault at P4266. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Best Matched Locations for a fault at P4266 as calculated by the FLA. . 110 Normally Distributed Per-Unit Load Power. . . . . . . . . . . . . . . . . 113 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24 Figure Figure Figure Figure Figure Figure 4.25 4.26 4.27 4.28 4.29 4.30 Figure A.1 Figure A.2 SandC T-Speed Fuse Minumum Melt Characteristics. . . . . . . . . . . . 136 SandC T-Speed Fuse Total Clearing Time Characteristics. . . . . . . . . 137 Figure B.1 Figure B.2 Nominal PI Line Model[28]. . . . . . . . . . . . . . . . . . . . . . . . . . 139 Line Model Block in MATLAB Simulink[28]. . . . . . . . . . . . . . . . . 140 Figure 4.31 xii Figure Figure Figure Figure Figure Figure Figure Figure B.3 B.4 B.5 B.6 B.7 B.8 B.9 B.10 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure C.1 C.2 C.3 C.4 C.5 C.6 C.7 C.8 C.9 C.10 C.11 Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure . . . . . . . . . . . . . . . . 143 143 144 144 145 145 146 146 System Thevanin Equivalent Component Model. . . . . . . . . . . . . . Power System containing a source, load buses and bus F . . . . . . . . . Power System before a fault occurrence at bus F. . . . . . . . . . . . . Open switch replaced by voltage source. . . . . . . . . . . . . . . . . . . Closed Switch Replaced by Two Sources. . . . . . . . . . . . . . . . . . Circuit during pre-fault conditions. . . . . . . . . . . . . . . . . . . . . Calculation of currents due to the fault itself. . . . . . . . . . . . . . . . Converting the network to a thevanin equivalent. . . . . . . . . . . . . . Pre-Fault system showing several loads and bus N(future faulted bus). Faulted System with Fault applied at Node N. . . . . . . . . . . . . . . Pre-Fault system with scaled loads and test load inserted at the faulted bus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.12 Test load inserted on Phase A of the faulted node. . . . . . . . . . . . . C.13 Test load inserted on Phase B of the faulted node. . . . . . . . . . . . . C.14 Test load inserted on Phase C of the faulted node. . . . . . . . . . . . . C.15 Fault Root Causes and Percent Occurrence[7]. . . . . . . . . . . . . . . C.16 Model of a 3 Phase Fault. . . . . . . . . . . . . . . . . . . . . . . . . . . C.17 Model of a Phase-Phase-Ground Fault. . . . . . . . . . . . . . . . . . . C.18 Model of a Phase-Phase Fault. . . . . . . . . . . . . . . . . . . . . . . . C.19 Model of a Phase-to-Ground Fault. . . . . . . . . . . . . . . . . . . . . C.20 Simple Radial Feeder with three load buses. . . . . . . . . . . . . . . . C.21 DEW Event Report showing the current seen at the substation for a bolted 3-Phase fault at Bus 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 149 149 150 150 151 151 152 152 153 . . . . . . . . . . 155 156 157 158 158 160 162 164 167 168 Figure D.1 Figure D.2 3-Phase Dynamic Load Representing Exponential Load Functions. System Thevanin Equivalent. . . . . . . . . . . . . . . . . . . . . . Three Phase MATLAB Simulink Source. . . . . . . . . . . . . . . 12kV Capacitor Bank. . . . . . . . . . . . . . . . . . . . . . . . . . Three Winding Transformer. . . . . . . . . . . . . . . . . . . . . . MATLAB Multi-Winding Transformer Block. . . . . . . . . . . . Per Phase Representation of 3-Phase Feeder Transformer. . . . . . MATLAB Three Phase Transformer. . . . . . . . . . . . . . . . . Worst Other FLA. . Figure D.3 Worst Figure D.4 Other FLA. . . . . . . . . . . . . . . . . . . 172 Matched Locations for a fault at P4622 as calculated by the FLA. Likely Fault Locations for a fault at P4622 as calculated by the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matched Locations for a fault at P4266 as calculated by the FLA. Likely Fault Locations for a fault at P4266 as calculated by the . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 175 176 178 179 Chapter 1 Introduction 1.1 Introduction Modern utilities are required to transmit and distribute electric power over vast regions dependably while keeping costs low for its customers. As electric power systems grow in complexity and size, ensuring system reliability and continuity has become a major concern. Failure to locate faults quickly can result in prolonged outage times, customer safety concerns and lost revenues. Over the past few decades, distribution networks have evolved into large and complex networks capable of carrying thousands of customers. As of late, utilities have displayed particular interest in distribution fault location technology to reduce such widespread impacts. With the addition of fault locators, utilities are able to reduce the search radius substantially. This improvement has allowed utilities to expedite restoration time and reduce economic impact. 1.2 Challenges of Distribution Fault Locating Currently most of the research being performed in the field of fault location has been focused on transmission networks[1]. Transmission networks are generally very simple, homogeneous throughout and contain few tap lines or branches. The simplicity of transmission system topology greatly reduces the complexity of the algorithm. Many transmission fault locating algorithms have been shown to be accurate using basic fault locating techniques and methods([10],[30]). Unlike transmission networks, distribution systems contain various conductor sizes in addition to many load taps, laterals, and branches. Fault locating on such complex topologies presents many challenges not present in transmission systems. An example of a modern radial distribution feeder is shown in Figure 1.1. One of the challenges of fault locating on distribution networks is the presence of significant system loading. Unlike transmission networks, distribution systems contain many tapped loads 1 Figure 1.1: 12kV Radial Feeder. between the fault locator and the fault itself. Modern distribution networks make it infeasible to place measurement devices at every branch on the network. This implies that system load conditions throughout the network remain an unknown quantity. Therefore, distribution fault location algorithms must be robust enough to handle load uncertainty. Many modern distribution fault locating algorithms use apparent impedance at the substation to calculate the location of the fault. In many distribution networks there exist multiple nodes that have the same apparent impedance during fault conditions. This problem results in multiple calculated possibilities throughout the network. As a result, fault locating algorithms must be able to localize and rank these possibilities from most to least likely. 1.3 Proposed Solution: Model Based Algorithm The proposed fault locating algorithm(FLA) is a model based algorithm(MBA) that uses a short circuit model of the feeder to locate the fault. In the short circuit model, a fault is placed at every node and the observed fault current at the substation is recorded in tabular 2 format(fault tables). During an actual fault condition, the algorithm compares the recorded fault current at the substation to the short circuit modelling data. This comparison allows the fault locator to identify the exact node in the network that is faulty. A high level overview of the FLA is shown in Figure 1.2. Figure 1.2: FLA High Level Overview. In many cases, the short circuit model will indicate that there are several unique nodes with the same fault current magnitude. This problem is overcome with a sub-algorithm in the FLA called the Localization Algorithm. This sub-algorithm uses protective device data and load flow data to determine the protective device that has interrupted the fault. By knowing the device that interrupted the fault, we can de-rank all other possibilities as a poor choices. 3 1.4 Glossary of Terms MBA : Model Based Algorithm, which is the proposed algorithm in this paper. Short circuit models are used to locate the faulty node. FLA: Fault Locating Algorithm IEEE: Institute of Electrical and Electronics Engineers NF: Notional Feeder, which refers to the test network built by Progress Energy Carolinas in MATLAB Simulink. PEC: Progress Energy Carolinas, referring to the utility based in Raleigh, NC. P.U.: A per-unit quantity, expressed as a quantity on a defined system base unit. DFT: Discrete Fourier Transform, referring to the family of techniques based on signal decomposition into sinusoids. DFR: Digital Fault Recorder. RMS: Root Mean Square, referring to the process of calculating the quadratic mean, representing the measure of the magnitude of a varying function[12]. EPRI: Electric Power Research Institute SandC: Refereeing to the fuse and protective device manufacturer. DEW: Referring to the fault analysis and load flow software package. The Stewart Street 12.47kV feeder was built by Allegheny Power and tested in the software package. ASPEN One-Liner: Software fault analysis and coordination tool used to check protective device coordination. 4 Chapter 2 Modern Distribution Fault Locating Algorithms 2.1 Introduction to Distribution Fault Locating Algorithms Fault locating on transmission and distribution networks requires the algorithm to quickly and accurately calculate the location of the fault. Transmission systems by comparison tend to be much simpler, containing few lateral taps and homogeneous conductor sizing. Experimental data has shown that modern fault locating algorithms on transmission system to be very accurate([10],[30]). Distribution systems present a unique challenge for fault locating due to lateral taps(single and multiphase laterals), complex topologies, load uncertainty and nonhomogeneous nature of the system. This set of challenges makes distribution fault location distinctly different from transmission[25]. The algorithms presented in this section attempt to confront many of the challenges of distribution fault locating. Each algorithm is assessed and derived in full detail to show its strengths and weaknesses. At the end of each algorithm derivation, a section is included to review the advantages and disadvantages of each. 2.2 Technique with Two-port Network Section Representation(Das Method) The following method developed by Ratan Das([25]), uses fundamental voltages and currents available via measurement devices at the substation. The author’s method addresses many of the known problems with distribution fault location including: non-homogeneous cabling, system loading, fault impedance and multi-estimate conversion. In the following sections, a detailed assessment of the method is performed to illustrate advantages and dis-advantage of 5 the Das method. 2.2.1 Overview of Das Method The alogrithm proposed by Das uses fundamental voltages and currents at the substation bus provided by utility measurement equipment. The location of the fault is estimated by computing the apparent reactance from the fundamental voltage and current phasors at Bus M in Figure 2.1. Once all possible fault locations have been identified, estimates of the voltages and currents at the fault and remote end are calculated. The final step of the algorithm is to estimate the distance to the fault from the beginning of the line segment. The Das fault locating algorithm can be decomposed into seven major steps. • Data Acquisition. • Preliminary estimate of the faulted line section. • Modification of the radial model(Equivalent Model Development). • Load Modelling. • Estimation of voltage and currents at the fault and at the remote end. • Estimating the distance to the fault from the line origination node. • Converting multiple fault locations into a single estimate. 2.2.2 Data Acquisition After a fault is detected, the fundamental frequency voltage and currents at the substation bus(Node ”M”) are saved. The data saved includes the pre-fault(fault has not occurred) and fault(fault has occurred) voltage and current phasors. Once a fault has been detected, pre-fault voltage and current are saved 1 cycle before the fault occurrence. Fault data is saved 3 cycles after the fault occurrence to minimize infeed by motors. 2.2.3 Fault Detection and Classification The first step in many fault locating algorithms is detecting that a fault has occurred. The Das algorithm uses current thresholds or pickup values to declare that a fault has occurred. After the fault has been detected, the algorithm attempts to classify the fault condition as one of the following types: 3-phase, Line-to-Line, Line-to-Ground or Line-to-Line-to-Ground. The flow chart in Figure 2.2 is used to determine the fault type and the faulty phase A, B or C. 6 It must also be noted that zero sequence currents are used to discriminate between phaseto-phase faults and phase-to-phase-to-ground faults. If the zero sequence current threshold is exceeded, this indicates the presence of a ground fault. Figure 2.1: Radial Distribution Feeder[25]. Estimating the Faulted Line Section After the fault has occurred, a preliminary estimate of the faulted line section is made. To make this estimate, detailed knowledge of the line parameters in needed along with the fault voltages and currents. We first consider a Phase A-to-Ground fault F between nodes x and x + 1 = y in Figure 2.1. If load is neglected, the apparent impedance from node M to the fault is defined as: Zm = Vam Iam (2.1) We can define the apparent reactance as: Xm = Im 7 Vam Iam (2.2) Figure 2.2: Flow Chart for Determining fault type[25]. Let us define the line segment between Bus M and Bus R as the line segment in Figure 2.3. And the sequence impedance matrix for the line segment between Bus M and Bus R: Z00 Z01 Z02 Z012 = Z10 Z11 Z12 Z20 Z21 Z22 (2.3) Assuming de-coupled terms(equal self and mutual impedances): Z0 0 Z+ Z012 = 0 0 0 0 0 Z− (2.4) Where Z00 = Z 0 , Z11 = Z + and Z22 = Z − . We also assume that the negative and positive sequence impedances are equal for this line segment: Z + = Z − 8 Figure 2.3: Line section Bus M and Bus R. We can transform the sequence impedance matrix to the phase impedance matrix using the following transform: Z0 0 1 Zabc = T 0 3 0 0 0 0 3T −1 Z+ 1 1 Z+ (2.5) Where T is: 1 T = 1 α2 1 α (2.6) α α2 Where α2 = 16 120◦ . This yields the following result: Zabc = 2Z (1) Z (0) 3 + 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 2Z (1) Z (0) 3 + 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 2Z (1) Z (0) 3 + 3 Zaa Zab Zac = Zba Zca Zbb Zcb Zbc Zcc (2.7) We can now define the self impedance of phase A, Zaa as: Zaa = 2Z (1) Z (0) + 3 3 (2.8) The author defines the modified reactance as: Im (Zaa ) = Xaa = 2X (1) X (0) + 3 3 (2.9) If the modified reactace is less the apparent reactance than the fault must be located beyond 9 the remote node. To illustrate this point, if: ( Xaa < Xm : Fault is Beyond Node R Xaa > Xm : Fault is Between Node M and Node R If the fault is beyond the remote node of the first line section, the next section is added to the first to obtain the total modified reactance defined by the following general summation: Xtotal = N (1) X 2Xn n=1 ( Xtotal < Xm 3 (0) + Xn 3 (2.10) : Fault is Beyond Current Line Section Xtotal > Xm : Fault is Located on Current Line Section This general procedure is continued into Xtotal > Xm , indicating the faulted line section. Given the large size of distribution feeders, there is likely more than one possible fault location. If this occurs, all possible fault locations are recorded and analysed individually. In later sections, ranking of these possibilities from most likely to lease likely is discussed. 2.2.4 Developing an Equivalent Radial Network Once all possible fault locations have been established, the radial feeder model with laterals is converted to a network without laterals. All lateral loads between Bus M and the fault are consolidated at the tap origination. To illustrate this point we refer back to our radial distribution feeder shown in Figure 2.1 with lateral taps K and L. To eliminate laterals K and L, they are lumped with all other loads connected to x − 1. The final result is shown in Figure 2.4. Figure 2.4: Radial Distribution Feeder[25]. 10 2.2.5 Load Modelling System loading on distribution networks can introduce large errors when calculating distance to the fault along a faulted line segment. To mitigate this, the effects of loads are taken into account in the Das algorithm. It is assumed that system load is dependent on voltage. We begin our analysis of system loading by considering the following static exponential load model for real and reactive power consumed by the load: P (V, αp ) = P0 Q(V, αq ) = Q0 V V0 αp V V0 αq (2.11) (2.12) The above equations represent the consumed load at various voltages based on a nominal power and voltage. The terms αp and αq terms represent the real and reactive power sensitivity to changes in voltage. To illustrate the sensitivity terms, we begin by defining a relative sensitivity function[31]: F Sα = F Sα = ∂F F0 ∂α α 0 x0 ∂F ∂α α0 x0 F0 (2.13) (2.14) For Active Power: P SV = P SV = ∂P P0 ∂V V0 V0 ∂P ∂V V0 P V0 0 (2.15) (2.16) For Reactive Power: Q SV Q = SV = ∂Q Q0 ∂V V0 V0 ∂Q ∂V 11 V0 V0 Q0 (2.17) (2.18) If we take a derivative of the load model in Equation 2.11 active power with respect to voltage we get: ∂P P0 = αp ∂V V0 V V0 αp −1 (2.19) Evaluating V = V0 we get: ∂P ∂V = αp V0 P0 V0 (2.20) ∂P P0 ∂V V0 (2.21) ∂Q Q0 ∂V V0 (2.22) Solving for αp : P αp = S V = We can also do the same for αq : αq = Q SV = We can see intuitively that the coefficients αp and αq represent the load sensitivity to voltage. Therefore, the apparent power absorbed by the load is: S(V, αp , αq ) = P0 V V0 αp + jQ0 V V0 αq (2.23) Using Equation 2.23 formulation, a voltage dependent impedance value can be derived to represent the load at various voltages. The values of G0 and B0 are calculated at nominal voltage and corresponding value of Yload can be calculated at any voltage. This relationship is extremely important when calculating load currents under fault conditions: " Yload (V, αp , αq ) = G0 2.2.6 V V0 αp −2 + jB0 V V0 αq −2 # (2.24) Estimating nodal pre-fault voltages and currents A vital part of the Das algorithm is the compensation for system loading. The algorithm compensates for system load by calculating the nominal load impedance and applying it to Equation 2.24. After the nominal pre-fault load impedance is calculated, the appropriate impedance at any voltage can be calculated. With this result we can easily calculate the load impedance under faulted conditions and compensate for the effects of load. To calculate the load impedance under pre-fault conditions, the following parameters are needed: pre-fault load voltage, prefault power factor(assumed to be known), percent of the total load at the load node(assumed 12 to be known). The pre-fault voltage is solved for by using a two-port network representation of each distribution line. Using the two-port model, we can begin at the measurement node and calculate the corresponding current injection and voltage at each node. Before calculation of pre-fault values, the algorithm suggested by Das estimates the loads at all nodes up to the fault using a database. The following formulation is used: Sload= Connected Load at Node X ∗ Total Pre-Fault Load Total Connected Load (2.25) The total pre-fault load is measured before the fault occurred by using the voltage and current phasors measured by the fault locator. It can be see from the above equation that the measured pre-fault load is apportioned to each node based on the percent loading of the node. After the apparent power is calculated at each node(Equation 2.25), the load admittance can be calculated: Y0 = V02 Sload −1 (2.26) The above equation illustrates a very important point of this algorithm, the load impedance cannot be calculated until the pre-fault load voltage V0 is solved for1 . Beginning at the measured node, we can calculate the load voltage at each node using the following two-port network relationship: Figure 2.5: Voltage and Current relationship between M and R[25]. 1 It is assumed that αp and αq are known from the power database 13 The two port equation for Figure 2.5: " # Vr Irm " = Dmr −Bmr Cmr #" −Amr Vm # Imr (2.27) Where Dmr , Cmr , Bmr and Amr are as follows: Dmr = cosh (γmr Lmr ) (2.28) sinh (γmr Lmr ) s Zmr (2.29) Cmr = Bmr = Zmr sinh (γmr Lmr ) (2.30) Amr = cosh (γmr Lmr ) (2.31) s are the propagation constant and characteristic impedance of the The terms γmr and Zmr line, respectively. We can can calculate each of these terms by using the resistance, reactance, conductance and suseptance per unit length of the line. γmr = p (rmr + jxmr ) (gmr + jbmr ) s s Zmr = (rmr + jxmr ) (gmr + jbmr ) (2.32) (2.33) rmr −→ resistance per unit length xmr −→ reactance per unit length gmr −→ conductance per unit length bmr −→ suseptance per unit length For short cable lengths in distribution systems the following approximation can be made: Amr = Dmr = 1 14 s Bmr = Zmr γmr Lmr γmr Lmr s Zmr Cmr = Resulting in a two-port model for a short distribution line: " Vr # Irm " = 1 −Bmr Cmr −1 #" Vm # Imr (2.34) All pre-fault voltages and currents are solved for up until the faulty line section(node x) using the two-port in Equation 2.34. Once the faulty line section has been reached, all loads beyond the fault are consolidated at the farthest remote node (node N). Using another two-port equation similar to Equation 2.34, we can solve for the remote end voltage and current. Using a cascaded two-port model, we can form a cascaded line section equivalent for all nodes from x to N . This forms a equivalent two port model between the beginning of the faulted line section(Node x) to the remote node(Node N ). " Vn −In # " = De −Be Ce −Ae #" Vx # Ixf (2.35) Where De , Ce , Be and Ae are cascaded line section equivalent constants from node x + 1 to N. Figure 2.6: Consolidated loads at the remote end, Node N[25]. 2.2.7 Estimating Voltages and Currents at the Remote End and at the Fault The next step requires the voltages and currents at the fault to be calculated. When the fault occurs, the fault locator at Node M records the currents and voltages for later use. Since we have a two-port model representation of each line up until the fault, we can easily calculate 15 the voltage at the beginning of the faulted line section(Node x). Also, as expected, the loads are present during the fault and must be accounted for. Recall that Equation 2.24 allows us to calculate the load current at any voltage, even during fault conditions. Beginning at Node M , the two-port network model and Equation 2.24 can be used to calculate currents and voltages present at Node R. Using the two-port network model for R to x − 1 and the load model for Node x − 1 we can calculate the voltages and currents at node x − 1. This process is completed until you reach the beginning terminal of the faulted line section, Node x. Figure 2.7: Fault between Nodes x and x + 1(= y)[25]. After the values of Vx and Ixf have been solve for, we can begin the process of calculating the distance to the fault from Node x. The fault is considered to be s length from Node x and 1 − s from Node x + 1(= y). Therefore, we break the two-port model of the line segment x to x + 1 into two two-port models: one from x to F and the other from F to x + 1(= y). " Vf # = If x " Vx+1(=y) If n # " " = 1 −sBxy sCxy −1 #" Vx # (2.36) Ixf 1 −(1 − s)Bxy −(1 − s)Cxy 1 #" Vf If n # (2.37) With the above equations, the current flowing through the fault If is still unknown, along with the remote end voltage and current. We can relate the currents at the remote node N and the If n current by: " Vn −In # " = De −Be Ce #" −Ae Vx+1(=y) If n # (2.38) Where De , Ce , Be and Ae are cascaded line section equivalent constants from node x+1(= y) to N . If we substitute Equation 2.37 into 2.38, we get: 16 " # Vn " = −In #" De −Be −Ae Ce 1 −(1 − s)Bxy −(1 − s)Cxy 1 #" # Vf (2.39) If n The above equation represents a very important relationship between currents flowing around the fault and the remote end load voltage and current. If we simplify 2.39, we get: " # Vn " = −In Ka + sKb Kc + sKd Ke + sKf Kg + sKh #" # Vf (2.40) If n We can substitute If n = −If x − If to eliminate If n : " # Vn " = −In Ka + sKb Kc + sKd Ke + sKf Kg + sKh #" # Vf " Kc + sKd − If −If x # (2.41) Kg + sKh And substituting 2.36: " # Vn " = −In Ka + sKb Kc + sKd Ke + sKf Kg + sKh #" 1 −sBxy −sCxy 1 #" Vx Ixf " # −If # Kc + sKd (2.42) Kg + sKh We can substitute In = Yn Vn and re-arrange: " Vn # " + If −Vn Yn Kc + sKd Kg + sKh # " = Ka + sKb Kc + sKd Ke + sKf Kg + sKh #" 1 −sBxy −sCxy 1 #" # Vx Ixf (2.43) Reducing: " 1 Kc + sKd #" −Yn Kg + sKh Vn If # " = Ka + sKb Kc + sKd Ke + sKf Kg + sKh #" 1 −sBxy −sCxy 1 #" Vx # Ixf (2.44) Solving for Vn and If while neglecting second order terms: " Vn If # 1 = Kv + sKw " Km + sKn sKp Kq + sKr Kv + sKu #" Vx Ixf # (2.45) Equation 2.45 represents the relationship between currents and voltages at the beginning of the faulted line and the voltages and currents for the remote end load under fault conditions. Equation 2.45 broken into equation form: 17 1 [Vx (Km + sKn ) + sKp Ixf ] Kv + sKw (2.46) 1 [Vx (Kq + sKr ) + (Kv + sKu ) Ixf ] Kv + sKw (2.47) Vn = If = 2.2.8 Calculating the Distance to the Fault: Single Line to Ground For a single line to ground resistive fault, the fault voltage is described as: Vf = If Rf (2.48) The fault voltage and current can be broken into corresponding sequence components: (0) (1) (2) Vf + Vf + Vf Vf = (0) = Rf (1) (2) If If + If + If (2.49) Taking the imaginary parts of both sides: Im (0) Vf (0) (1) + Vf (1) (2) + Vf (2) If + If + If =0 (2.50) Referring back to Equation 2.37 and Equation 2.47, these equations can also be broken into sequence components: (0) (0) = Vx(0) − sBxy Ixf (1) (1) = Vx(1) − sBxy Ixf (2) (2) = Vx(2) − sBxy Ixf Vf Vf Vf (0) If (1) If (2) If = 1 (0) (2) (2.53) (1) h i (1) Vx(1) Kq(1) + sKr(1) + Kv(1) + sKu(1) Ixf (2.55) (2) h i (2) Vx(2) Kq(2) + sKr(2) + Kv(2) + sKu(2) Ixf (2.56) 1 (2) (2.52) (2.54) Kv + sKw = (1) (0) 1 (1) (2.51) h i (0) Vx(0) Kq(0) + sKr(0) + Kv(0) + sKu(0) Ixf Kv + sKw = (0) Kv + sKw After substituting Equations 2.54-2.57 and Equations 2.51-2.53 into Equation 2.49 while neglecting higher order terms we obtain the solution for the distance to the fault: 18 s= 2.2.9 KAR KCI − KAI KCR (KCR KBI − KCI KBR ) + (KDR KAI − KDI KAR ) (2.57) Assessment of the Das Algorithm: Advantages and Disadvantages The method proposed by Ratan Das, is a excellent fault location method with many advantages over other competing algorithms. In this section, a discussion of the advantages and disadvantages of the Das algorithm are compared to other apparent impedance techniques used in distribution fault location. Fault Resistance An excellent attribute to the Das algorithm is its ability to compensate for fault resistance. The author choose a 23 mile long, 25kV radial feeder to preform tests. The tests performed were single line-to-ground faults with fault resistances varying from 5Ω to 50Ω. The Das algorithm shows that for a SLG fault of 5Ω, the error is less than 1.7%. For a 50Ω fault, the error was shown to be less than 2.2% [1]. However, it can be easily shown that the Das algorithm does not work for a bolted fault(Rf = 0Ω) using Equation 2.49. Das does note this drawback: ”...it is practically impossible to have a fault with exactly zero resistance.”[25] Load Compensation One of the major problems of distribution fault location is compensating for the effects of loads. The Das algorithm does this by developing a voltage dependent load model that is calculated under pre-fault conditions. In order to develop the load model, information about the load is taken from a load database. This implies that the utility using the fault locator must have monitoring equipment at the load or available load flow study data. The drawback of using a load flow table is common for fault locators without communication systems such as SCADA to report real time load data. In [8], it was shown that inaccurate load studies can lead to significant errors in fault location with the Das algorithm. In Figure 2.8, a radial distribution feeder was modelled with constant power loads. The load were assumed to be constant impedance loads by the fault locator, resulting in large errors. The author of [8] concluded that the performance of the Das algorithm is not guaranteed without load behaviour studies preformed. 19 Figure 2.8: Fault locator load model as constant impedance with system load model as constant power [8]. Estimation of the Faulted Line using the Loop Reactance Method One of the notable drawbacks of this method is that a estimation of the faulted line section is obtained via the Loop Reactance method. The loop reactance is summarized by Equation 2.9. Under no or light load conditions, the loop reactance can be used to estimate the faulted line section with acceptable accuracy. Although for heavily loaded feeders, the loop reactance can provide inaccurate results for estimation of the faulted line section. In [9], for heavily loaded feeders the error between actual reactance to the fault and estimated reactance to the fault were greater than 73%. Under light load conditions the reactance method performed much better with a error of 28%. Under no load conditions the error was 2%.Therefore we can conclude the under lightly loaded conditions, the loop reactance method may provide acceptable results. However on heavily loaded feeders this can lead to a incorrect preliminary estimation of the faulted line section. Localizing Multiple Fault Possibilities One of the major drawback of impedance based methods is multiple possible locations of the fault and the Das algorithm is no exception. Das recommends the use of FCIs(Faulted Circuit Indicators) to isolate the correct location of the fault from a list of possibilities. However, given the size and complexity of large distribution feeders this may not be an acceptable solution 1 most notably where the load current is a substantial part of the fault current at the remote end of a long feeder 20 for a utility. Also, careful attention must be given to the placement of the FCIs in order to maximize their effectiveness. 2.3 Girgis Apparent Impedance Method The Girgis Apparent Impedance method was developed by Adly Girgis and uses symmetrical components to determine a distance to the fault from the measurement point(usually the substation)[26]. The proposed algorithm addresses some of the issues with fault location such as fault impedance, and fault localization. However, this algorithm does not address issues such as: unbalanced mutual coupling and non-homogeneous lines. 2.3.1 Overview of Girgis Method The Girgis method uses fundamental frequency voltage and current phasors available at the substation bus to determine the distance to the fault. Before the distance to the fault can be calculated, the fault type is needed: Line-to-Ground, Line-to-Line, Line-to-Line-to-Ground, or 3-phase. To classify the fault type, changes in current magnitude are observed, indicating the faulted phase(s). Once the fault type has been determined, the algorithm uses symmetrical components to determine the distance to the fault. If the solution yields multiple fault locations the algorithm will use localization techniques to determine the most likely candidate. Therefore, we can break the Girgis algorithm into three easy steps: Fault Classification, Solution and Localization. 2.3.2 Direct Determination of Distance to the Fault To begin our analysis of the Grigis algorithm we consider a simple feeder with no laterals or taps in Figure 2.9. A single line-to-ground fault is placed d distance from the measurement bus. We will begin our analysis be assuming the system to be unloaded, and the only current flowing at the time of the fault is due to the fault itself. (0) If a 1 1 1 If a (1) 1 If a = 1 α α2 0 3 (2) 1 α2 α 0 If a (2.58) Evaluating Equation 2.58 above yields: (0) (1) (2) If a = If a = If a = If a 3 (1) (2.59) (2) (0) The above equation directly implies that the positive(If a ), negative(If a ) and zero sequence(If a ) 21 currents are equal during the fault. Using this implication, we must connect the positive, negative and zero sequence networks in series as shown in Figure 2.10. The positive, negative (1) (2) (0) and zero sequence impedance of the line are represented in the figure as ZL , ZL , and ZL (i) respectively. The source voltage is also broken into sequence components Vs . Figure 2.9: Simple Feeder with no laterals or taps To calculate the distance d to the fault, we begin with a simple KVL loop around the positive, negative and zero sequence parts of Figure 2.10 to solve for sequence voltage at the fault: (1) = Vs(1) − DIf a ZL (2) = Vs(2) − DIf a ZL (0) = Vs(0) − DIf a ZL Vf Vf Vf (0) Vf (1) + Vf (2) + Vf (1) (1) (2.60) (2) (2) (2.61) (0) (0) (2.62) (0) (2.63) = 3If a Rf Summing equations 2.60, 2.61 and 2.62. (0) Vf (1) + Vf (2) + Vf h i (1) (1) (2) (2) (0) (0) = Vs(0) + Vs(1) + Vs(2) − D If a ZL + If a ZL + If a ZL (0) We can substitute: Vf (1) + Vf (2) + Vf (0) = Vf and Vs (1) + Vs (2) + Vs (1) (1) (2) (2) (0) (0) Vf = Vs − D If a ZL + If a ZL + If a ZL (2) (2.64) = Vs . (2.65) (1) The Girgis method assumes that ZL = ZL . h i (1) (1) (2) (0) (0) Vf = Vs − D ZL If a + If a +If a ZL 22 (2.66) Figure 2.10: Single line-to-ground fault sequence networks. Rearranging yeilds: (1) DZL Vf = Vs − (0) (1) (1) If a ! + (0) (0) ZL If a (1) ZL ! + (0) (0) ZL If a (1) ZL ! + (2) If a If a − (0) If a If a + (0) (1) −Z (0) Z If a L (1) L ZL (2.67) (2) Substituting If a − If a = If a + If a : Vf = Vs − (1) DZL Vf = Vs − (1) DZL (2.68) If we simplify: Solving for Vs : 23 (2.69) (1) DZL Vs = Vf + If a + (0) (1) −Z (0) Z If a L (1) L ZL ! (2.70) Substituting Equation 2.63: Vs = (0) Let k = (0) 3If a Rf + (1) DZL If a + (0) (1) (0) ZL − ZL If a (1) ZL ! (2.71) (1) ZL −ZL (1) ZL (0) (1) Vs = 3If a Rf + DZL (0) If a + If a k (2.72) (0) Equation 2.72 can be divided by If a + If a k which gives: (0) Vs If a + (0) If a k 3If a Rf = If a + (1) (0) If a k + DZL (2.73) The above equation can be used to calculate the positive sequence reactance to the fault. This is accomplished by taking the imaginary part of both sides of Equation 2.73. Assuming (0) (0) If and If a + If a k are in phase, the imaginary part of Im 3If a Rf (0) If a +If a k would equal 0. This yeilds: Vs If a + (0) If a k = DX (1) L (2.74) The above solution is called the positive sequence reactance method[9]. The obvious drawback (0) of this solution is the assumption that If and If a + If a k are in phase. The Girgis method offers a different solution which does not make this assumption. To begin, we define the apparent impedance seen at the measurement bus as Zapp = Vs (0) . If a +If a k (0) Zapp = 3If a Rf If a + (0) If a k (1) + DZL (2.75) (0) We then substitute Icomp = 3If a , where Icomp is the compensating current fed into the fault. Zapp = Icomp Rf If a + (0) If a k 24 (1) + DZL (2.76) (0) Next, the compensating current Icomp and the selected current If a + If a k are broken into real and imaginary parts: Icomp = Id + jIq (2.77) (0) If a + If a k = Is1 + jIs2 (2.78) (1) The positive sequence impedance of the line, ZL is broken into real and imaginary parts as well: (1) (1) (1) ZL = RL + jXL (2.79) Substituting 2.77,2.78, and 2.79 into 2.76: R (I + jI ) q f d (1) (1) Zapp = D RL + jXL + Is1 + jIs2 (2.80) In the above equation, the fault resistance and distance to the fault are unknown. To solve for the distance to the fault, the apparent impedance is broken in real and imaginary parts. This yields two equations and two unknowns. (1) Re (Zapp ) = DRL + Rf Id Is1 + Iq Is2 I2 + I2 | s1 {z s2 } (2.81) N (1) Im (Xapp ) = DXL + Rf Iq Is1 − Id Is2 I2 + I2 | s1 {z s2 } (2.82) M Substituting M and N for the terms above: (1) (2.83) (1) (2.84) Re (Zapp ) = DRL + N Rf Im (Xapp ) = DXL + M Rf Solving for D: D= Rapp M − Xapp N (1) (1) (2.85) RL M − XL N The above equation represent the direct determination of the distance to the fault from the measurement point. 25 2.3.3 Assessment of the Girgis Algorithm: Advantages and Disadvantages The Girgis algorithm is a very simple algorithm that can be easily implemented by a utility for basic fault locating. However, the method does have many negative attributes that make it an unacceptable choice for many modern utilities. The following conditions were not considered by the Girgis algorithm: non-homogenous lines, mutual coupling and system loading conditions. System Loading The Girgis algorithm considers the feeder to be unloaded at the time of the fault occurrence. This assumption causes large errors in heavily loaded feeders. In the event that the fault were to occur at the remote end of a long feeder, it is often the case that the current seen at the substation during the fault is not much greater than the load current. In this case, the load current presents a major issue resulting in degraded accuracy at the remote end of the network. Non-Homogeneous Lines and Mutual Coupling The direct determination of the distance to the fault assumes equal mutual coupling and self impedances of the line. In the event that the we have equal self impedance and unequal mutual impedance or visa-versa this results in coupling between sequence components1 . In practice, equal self impedance and mutual coupling terms are rarely the case. The Girgis algorithm also assumes the feeder conductors to be homogeneous. Many feeders are composed of many different types and sizes of conductor, resulting in a non-homogeneous system. This is a major disadvantage of this algorithm. Localization of Multiple Fault Possibilities The Girgis algorithm, much like many impedance based algorithms can return multiple fault possibilities. For example, if the fault is found to be 1 mile from the measurement point, there may be multiple locations that are 1 mile from the measurement point. The author does recognize this as a limitation and presents a excellent solution. When multiple fault locations are found, the operating characteristics of protective devices are used to eliminate possibilities. This will be discussed in a later chapter. 1 The 3-phase system is no longer decoupled. 26 2.4 Fault Locating using Digital Fault Recorder Data(Saha Algorithm) 2.4.1 Overview of Saha Method The algorithm proposed by Mourari Saha uses fundamental voltages and current available at the substation before and after the fault[1]. The algorithm proposed by Saha can be broken into two major steps: calculation of the fault loop impedance and calculation of impedance along the feeder. By comparing the measured impedance with the calculated feeder impedance, an indication of the fault location can be obtained[1]. 2.4.2 Fault Loop Impedance Determination The algorithm suggested by Saha requires that the positive sequence fault loop impedance be calculated from the available voltages and currents at the substation. This impedance is later used to determine the faulty node in the network. To begin our analysis we consider a Phaseto-Phase fault involving phases B and C at some node in the network. A phase-to-phase fault is shown in Figure 2.11 at any arbitrary point in the distribution network. The parameters If a , If b and If c are the fault currents measured at the substation. Assuming the system to be unloaded at the time of fault we can easily show that for a Bto-C fault that If c = −If b and If a = 0. We can now transform the fault currents flowing in the network into their respective symmetrical components using the transform in Equation 2.86. (0) If a 1 1 1 0 (1) 1 If a = 1 α α2 If b 3 (2) 1 α2 α −If b If a (2.86) Reducing Equation 2.86 results in the following: (1) (2) If a = −If a (2.87) The above equation forms the foundation of solving for the positive sequence fault loop impedance. Using Equation 2.87 we can form its circuit representation shown in Figure 2.12. If we preform a simple KVL loop on Figure 2.12, we obtain: (1) (1) (1) (1) (2) (2) (2) Vf a − If a Zkk − Zf If a + If a Zkk − Vf a = 0 (2.88) (1) Where the positive sequence measured voltage is Vf a and the negative sequence measured (2) voltage is Vf a . The thevanin positive and negative sequence impedances looking into the 27 (1) (2) system at some arbitrary bus k is defined as Zkk and Zkk . Figure 2.11: B-to-C Fault Figure 2.12: Sequence Network Diagram for a Phase-to-Phase Fault. Using Equation 2.87, we can eliminate all negative sequence currents: (1) (1) (1) (1) (1) (2) (2) Vf a − If a Zkk − Zf If a − If a Zkk − Vf a = 0 If we solve Equation 2.89 for the fault loop impedance we get: 28 (2.89) (1) (2) Vf a − Vf a (1) (2) = Zkk + Zf + Zkk (1) If a (2.90) We can break down Equation 2.90 in much simpler terms by analysing the numerator portion of the equation. The pre-fault measured voltages can be broken into their corresponding sequence components by using a equation similar to Equation 2.86: Vaf 1 1 1 (0) Vaf (1) Vbf = 1 α2 α Vaf (2) Vcf 1 α α2 Vaf (2.91) If we extract Vbf and Vcf we get the following equations: (0) (1) (0) (1) (2) Vbf = Vaf + Vaf α2 + Vaf α (2) Vcf = Vaf + Vaf α + Vaf α2 (2.92) (2.93) Subtracting Equation 2.92 from 2.93 yeilds: (1) Vbf − Vcf = Vaf (2) α2 − α + Vaf α − α2 (2.94) √ (2) √ − 3j) + Vaf 3j) (2.95) Substituting α = 16 120◦ : (1) Vbf − Vcf = Vaf (2) (1) We can now solve for Vaf − Vaf : (2) (1) Vaf − Vaf = Vbf − Vcf √ 3j (2.96) If we substitute 2.96 into 2.90 we get: Vbf −Vcf √ 3j (1) If a (1) (2) = Zkk + Zf + Zkk (2.97) Using a the symmetrical component transform similar to Equation 2.86, we can show that the positive sequence fault current yields: (1) If a = 1 αIf b − α2 If b 3 29 (2.98) Reducing yields: √ (1) If a = 3 jIf b 3 (2.99) Substituting Equation 2.99 into Equation 2.97: Vbf −Vcf √ 3j √ 3 3 jIf b (1) (2) = Zkk + Zf + Zkk (2.100) Reducing Equation 2.100 yields: Vbf − Vcf (1) (2) = Zkk + Zf + Zkk If b (2.101) (1) (2) If we assume that the positive and negative sequence impedances are equal Zkk = Zkk : Vbf − Vcf (1) = 2Zkk + Zf If b (2.102) During fault conditions 2If b = Ibf − Icf : Vbf − Vcf (1) = Zkk + Zf Ibf − Icf (2.103) Assuming the fault to be bolted Zf = 0: Vbf − Vcf (1) = Zkk Ibf − Icf (2.104) The above equation represents the positive sequence impedance to the fault. We can use the available voltages Vbf and Vcf and currents If b and If c to calculate the positive sequence fault loop impedance. However, with the fault resistance being unknown, we must assume that the fault is bolted Zf = 0. 2.4.3 Determination of the Faulty Node After the positive sequence fault loop impedance has been found, we then search for the faulty node. To begin our search for the faulty node we consider a simple substation with two feeders. Let us assume that the only available measurements are the bus voltage and supply current from the source: Ṽ and Ĩ. The pre-fault positive sequence impedance of the fault feeder is (1) (1) defined as Zk . The parallel connected feeder positive sequence impedance is defined as Zlk . 30 Figure 2.13: Simple Substation with Two Parallel Feeders during Pre-Fault Conditions. During the pre-fault conditions, we can define the pre-fault positive sequence impedance (1) seen by the fault locator as Zpre . This is represented in equation form as: (1) (1) Zpre (1) Zk Zlk = (1) (2.105) (1) Zk + Zlk During fault conditions, as shown in Figure 2.14, we represent the positive sequence impedance seen by the fault locator as: (1) (1) Zf (1) Zf k Zlk Vb − Vc = = (1) (1) Ib − Ic Zf k + Zlk (2.106) (1) Our objective is to calculate the positive sequence loop impedance of the faulty feeder Zf k . (1) Solving Equation 2.106 for Zf k we get: (1) (1) Zf k (1) Zf Zlk = (1) (1) (2.107) Zlk − Zf (1) If we solve Equation 2.105 for Zlk we get: (1) (1) Zlk = (1) Zpre Zk (1) (1) Zk − Zpre 31 (2.108) Figure 2.14: Simple Substation with Two Parallel Feeders during Fault conditions. Substituting Equation 2.108 into Equation 2.107: (1) (1) Zf k (1) Zk Zpre = (1) (1) Zpre − (1) Zk − Zpre (1) Zf ! (2.109) (1) Zk {z | kzk (1) } (1) Consequently, kzk can also be related to Zpre and Zlk : (1) kzk = Zpre (2.110) (1) Zlk Substituting: (1) (1) Zf k = (1) Zk Zpre (1) (1) Zpre (1) Zpre − Zf (1) (1) Zf k = (1) Zlk (1) Zk Zpre (1) (1) Zpre − Zf kzk We previously defined Zf as: 32 (2.111) (2.112) (1) Zf = Vφ−φ Va − Vb = Ia − Ib Iφ−φ (2.113) If we substitute Equation 2.113 into 2.117: Vφ−φ (1) Zf k = Iφ−φ − kzk (2.114) Vφ−φ (1) Zpre The above equation represents the positive sequence loop impedance of the faulty feeder during fault conditions. It is assumed that the impedance of the adjacent parallel feeders do not change during fault conditions(this may not always be the case). Now that the positive sequence loop impedance of the faulty feeder has been calculated, we can begin to search for the faulty line. The algorithm suggested by Saha sweeps the network for the faulty node until a specific set of criterion exists. One the criterion has been met, the faulty line section is found. Figure 2.15: Cascaded Line Sections of Distribution Feeder. We will begin our search for the faulty node at some node i−1 in the network. We will represent (1) the impedance of the cable between i − 1 and i by Zsi−1 . The load at the remote node i is (1) represented by Zpi . By using network reduction, we can develop a relationship between the (1) (1) impedance seen looking into the system at i − 1 and i(Which is Zf i and Zf i−1 respectively). (1) (1) Zf i−1 = (1) Zf i Zpi (1) Zf i + (1) Solving for Zf i we get: 33 (1) Zpi (1) + Zsi−1 (2.115) (1) (1) Zf i = Zpi (1) (1) Zf i−1 − Zsi−1 (1) (1) (2.116) (1) Zpi − Zf i−1 + Zsi−1 Let us assume the substation bus to be i − 1; assuming the load impedances to be known, we can now traverse each line section and calculate the impedance seen looking into the system (1) (1) from the remote bus. As expected |Zf i | < |Zf i−1 | as we approach the faulty line. If we were (1) traverse down the feeder and the value of Im(Zf i ) would be become less than zero, we would know the fault exists between i − 1 and i. To begin our search for our faulty line section, we always begin at the substation and work outwards. In this particaluar scenario, the substation may represent i − 1. As we move outward (1) (1) on the feeder, the value of Im(Zf i ) decreases. When the value of Im(Zf i ) becomes negative, the faulty line section has been found[32]. This part of the algorithm only identifies that the line section between i − 1 and i is faulty. The distance from i − 1 to the fault will be covered in the next section. 2.4.4 Distance to the Fault After we have identified the fault line section(i and i − 1) we must now determine the distance from node i − 1 to the fault(distance down the line to the fault). Using a change in notation, we will call the faulted line k and k + 1 in the following example(k = i − 1 and k + 1 = i). Figure 2.16: Faulted Distribution Feeder[1]. Using Figure 2.16, we will place a the fault between nodes k and k + 1. Our objective is to calculate the distance from node k to the fault. 34 (1) Let us begin by assuming that the positive sequence loop impedance from node 1 to k, Z1k is known from pre-calculated tabulated values. Also, we will assume that the impedance of the (1) shunt load at node 2 Zl2 is also known. Any impedance beyond node k is lumped together as (1) a shunt impedance called ∆Zf . The circuit representation of the faulty network seen by the fault locator is represented by Figure 2.17. Figure 2.17: Circuit Representation of Network for a Fault located between 1 and k. We will begin our derivation by assuming that the impedance seen by the fault locator is defined (1) as Z1f . (1) Z1f = Vφ−φ Iφ−φ (2.117) In the above figure, the variable m is used as a percentile over the total length of the cable from node 1 to node k. In this example the load is 1 − m distance from the measurement point and m from the origination terminal of the faulted line section(node k). The equation representation of impedance seen by the fault locator described by Figure 2.17: (1) Z1f (1) (1) mZ1k + ∆Zf (1) Zl2 Vφ−φ (1) = = + (1 − m) Z1k (1) (1) (1) Iφ−φ mZ1k + ∆Zf + Zl2 (1) If we solve for the unknown variable, ∆Zf we get: 35 (2.118) (1) ∆Zf = (1) Previously we defined ∆Zf (1) (1) (1) (1) 2 mZ1k + Zl2 − mZ1k (1) (1) (1) (1) mZ1k − Zl2 − Z1k − Z1f (1) Z1k − Z1f (2.119) as the lumped impedance representative of all elements beyond (1) k. In order to solve for the distance to the fault from k, we must define ∆Zf in much more detail. (1) We can represent ∆Zf as the circuit shown in Figure 2.18. All elements beyond node k are represented, including the fault resistance. In Figure 2.18, x represents the distance to the (1) fault from node k and ZL represents the positive sequence impedance of the line from node (1) k to k + 1. Also since a shunt load is present at node k, this is represented by Zlk . We also must represent all elements beyond node k + 1; this positive sequence thevanin impedance is (1) represented by Zk+1 . Figure 2.18: Circuit Representation of Network for a Fault located between k and k + 1. Using network reduction we can reduce Figure 2.18 to the following equation: (1) Zlk (1) ∆Zf (1) xZL + = (1) Zlk + (1) xZL ! (1) (1) Rf (1−x)ZL +Zk+1 + 36 (1) (1) Rf +(1−x)ZL +Zk+1 (1) (1) Rf (1−x)ZL +Zk+1 (1) (1) Rf +(1−x)ZL +Zk+1 (2.120) If we set Equation 2.119 and Equation 2.120 equal and solving for Rf : Rf = x2 A − xB + C (2.121) Where A,B and C are: (1) 2 (1) (1) Zlk − ∆Zf A= (1) (1) (1) (1) (1) (1) Zlk − ∆Zf ZL + Zk+1 − ∆Zf Zlk (1) B= ZL ZL (1) (1) (1) (1) (1) (1) (1) (1) Zlk − ∆Zf ZL + Zk+1 − ∆Zf Zlk + 2∆Zf Zlk (1) (1) (1) (1) (1) (1) Zlk − ∆Zf ZL + Zk+1 − ∆Zf Zlk (1) (1) (1) (1) ∆Zf Zlk ZL + Zk+1 C= (1) (1) (1) (1) (1) (1) Zlk − ∆Zf ZL + Zk+1 − ∆Zf Zlk (2.122) (2.123) (2.124) Taking the imaginary part of the quadratic function for the fault resistance Rf : Im (Rf ) = x2 Im(A) + xIm(−B) + Im(C) = 0 (2.125) Where the imaginary parts of A,B and C are: Im(A) = Ai Im(B) = Bi Im(C) = C (2.126) i The resultant roots α1 and α2 of Equation 2.125 are: Bi + q α1 = 2Ai Bi − x = α2 = Bi2 − 4Ai Ci q Bi2 − 4Ai Ci 2Ai 37 (2.127) (2.128) Since α1 is considered a invalid solution, the distance to the fault from k is x = α2 . 2.4.5 Assessment of the Saha Algorithm: Advantages and Disadvantages The algorithm suggested by Saha has many advantages and addresses many of the issues that other algorithms fail to consider. The algorithm compensates for system loading, fault resistance, non-homogeneous feeder conductors and measurement issues(only available current is the main transformer current). However, there are several key disadvantages of the Saha algorithm. One of which is that the positive sequence fault loop impedance is used to calculate the faulty line section assuming unloaded conditions and a bolted fault. The algorithm also presents a direct determination for distance to the fault, but this solution is highly dependent on topology of the system. Also, the author does not address localization of multiple fault possibilities if (1) there exists two possible paths on a feeder where Im(Zf i ) < 0. Problems with Determining the Faulty Line Section The Saha algorithm uses the positive sequence fault loop impedance to directly determine the faulty line section. To achieve this, the algorithm must assume the fault to be bolted and the system to unloaded at the time of fault. For systems that are lightly loaded, this is an acceptable way of calculating the faulty line section. However, for heavily loaded feeder, the load currents become a large portion of the fault currents making this assumption possibly invalid. Problems with Determining Distance to the Fault Once the faulty line section has been determined, when then calculate the distance to the fault from the origination node of the faulty line section(see Figure 2.18). However, the solution presented in Equation 2.128 is dependent on toplogy. To illustrate this, a tap load could be inserted between nodes 2 and k, as shown in Figure 2.19. Inserting a tapped load between nodes 2 and k complicates the direct determination of the positive sequence fault loop impedance shown in Equation 2.118. Therefore, we can conclude that the direct determination of the distance to the fault in Equation 2.128 is a rigid solution that is dependent on network topology. This issue was not addressed by the author. Localization of Multiple Fault Possibilities As with many impedance based algorithms, there are usually multiple possible locations of the fault. When using the positive sequence fault loop impedance it is often the case that (1) there is more than one location to satisfy the criterion for a faulty line section(Im(Zf i ) < 0). Localization or ranking of the possibilities was not considered by the author. 38 Figure 2.19: Tapped Load inserted between node 2 and node k. 2.5 Conclusion The algorithms covered in this section use fundamental voltages and currents available at the substation to calculate the location of the fault. Impedance based algorithms, like the ones presented here often have the same key disadvantages: localization of multiple fault possibilities and error introduced by system loading. It is often the case that some uncertainty exists when modelling load. Many impedance based algorithms rely on accurate load information throughout the network in order to calculate the location of the fault. However, the dynamic nature of system load is very difficult to predict and can introduce large errors in fault locating. If a reasonable amount of information is know about the system loading, this is usually sufficient for most algorithms to produce acceptable fault locating accuracies([8],[1]). One of the major flaws of the impedance based algorithm is localizing multiple fault possibilities. It is often the case that there exists multiple locations where the Thevanin impedances are very similar resulting in two or more solutions. In order to rank them, Girgis suggests using the characteristics of the protective devices that interrupted the fault to localize the fault to one solution. This is a simple and effective way of localizing multiple fault possibilities. 39 Chapter 3 Model Based Fault Locating 3.1 Introduction In this section we propose a model based FLA(Fault Locating Algorithm) that uses recorded fault data available at the substation bus. The FLA identifies all possibly fault nodes by comparing model derived short circuit data to the observed fault current. In the event that there are multiple possibilities, the FLA executes a localization sub-algorithm. The localization algorithm uses load flow data and protective device characteristics(operating time) to rank all possibilities. After all possibilities are ranked, the results are printed out in the MATLAB console for the user. Figure 3.1 shows a high level overview of the proposed FLA. The FLA can be broken into several key steps: • Simulation • Sampled Data Conditioning • ”Steady State” Fault Current Extraction • Fault Type Identification • Identify Possibly Faulted Nodes • Localization • Ranking • Printout 40 Figure 3.1: High-Level Overview of FLA. 3.2 Sampled Data Conditioning Many modern relays and IEDs have the capability to record pre-fault and post-fault voltage and current waveforms at very high resolutions. Most modern protective relays can capture resolutions up to 64 samples per cycle or higher [11](depending on the vendor). One of the excellent attributes of the proposed method is that it does not require high resolution sampling. Testing performed in MATLAB indicated that 16 samples per cycle provides sufficient resolution for the proposed method. Since most modern protective relays and DFRs have the capability of 64 samples per cycle or more, all testing done in this paper was performed at 64 samples per cycle. For example, the SEL(Schweitzer Engineering Labs) 451 series relay has the capability to sample up to 133 samples per cycle. Manufacturers of protective relays and DFRs have incorporated the ability to share raw sampled fault data in many of their software packages. An excellent example of this is the SEL-5601 software package that allows the user view captured 41 Figure 3.2: Handling of Raw Data Passed to the Fault Locator. oscillography from SEL relays. The method suggested here assumes that the data it receives is unfiltered fault data(provided by MATLAB Simulink). A DFT(Discrete Fourier Transform) is later used to analyse the fault data to extract the 60Hz fundamental component for analysis. The complete FLA process of conditioning the sampled data is shown in Figure 3.2. Figure 3.3: Sampling of Fault Current Recorded at 64 Samples Per Cycle Figure 3.4 is a excellent example of harmonic content present during a fault condition. The FLA method proposed uses fundamental frequency phasor quantities to perform all calculations. To remove these harmonics, we use the DFT algorithm built in MATLAB to extract 42 the magnitude and angle of the fundamental. Fourier analysis shows that periodic functions can be reproduced as a combination of complex exponentials whose frequencies are multiples of the fundamental frequency kf0 where f0 = 60Hz. We are particularly interested in the fundamental k = 1. The DFT transform used by MATLAB is shown in Equation 3.1 [12]. Figure 3.4: Bus Voltage During a Ground Fault. X (k) = N −1 X k x(n)e−2πj N n (3.1) n=0 The magnitude output of the DFT |X(k)| can be directly divided by the √ 2 to obtain the RMS value. XRM S = 3.3 |X (k) | √ 2 (3.2) Steady State Fault Current Extraction The FLA suggested here uses phasor quantities to preform calculations. During the occurrence of a fault, the current will go through a short transient period before reaching ”steady state” 43 value(Shown in Figure 3.5). The fault locator must ”wait” until the observed current reaches steady state. Once steady state has been reached, the RMS fault current value is captured for later use. Figure 3.5: RMS value of the 60Hz Fundamental during Line-to-Ground Fault. To calculate the steady state value of the observed current during a fault, a algorithm is used that was suggested in [13] . At the nth cycle, the relative change of the current between the nth + 1 cycle and the nth cycle is less than .1, then the second condition is checked. If the relative change between the nth + 2 cycle and the nth cycle is less than .1, then the current is considered to be in steady state in the nth cycle. The steady state current is considered to be the average of the nth + 1 and nth cycle. The full process of detecting the steady state of the observed fault current is shown in Figure 3.6. 3.4 Fault Tables The location of the fault in the network is determined using fault tables. Fault tables are the expected value of fault current for any given location of the fault in the network. The actual measured fault currents are compared to the expected(fault tables) to determine the location of the fault. The idea of the algorithm relies on the diversity of thevanin impedances throughout the network. Given that each point throughout the network yields a unique fault current value, the fault location is easily found. To illustrate the formation of a fault table, we consider a generic 6 node feeder shown in 44 Figure 3.6: Algorithm for detecting steady state fault current. Figure 3.7. To form the fault table, we apply a 3-Phase(Bolted) fault beginning at node A and concluding at node F. Each time the fault is moved throughout the feeder, the fault current at the substation is recorded. This forms the fault table shown in Table 3.1. This table represents the expected values of fault current if a 3-Phase fault did occur at Node A-Node F. To locate a fault, we simply compare our actual and expected values of fault current. For example, a 3-Phase fault occurs in our actual system and results in 7158 A of current flow. We would be able to rule out nodes A-C and nodes E-F due to their high/low expected values. The most likely location for the fault to have occurred is node D. Figure 3.7: Generic 6 Node Feeder. 45 Table 3.1: Fault Table for Figure 3.7 Node Node Node Node Node Node Node 3.4.1 Fault Current If A B C D E F 9553 8201 7542 7118 6346 5690 A A A A A A Sliding Fault Resolution In our previous 6 node network shown in Figure 3.7, we applied a fault at each node to form the fault table. Therefore, there can only be 6 possible places that the fault can occur(according to the table). It is a possibility that our 3-phase fault could occur between nodes A and B. Let us re-form the fault tables in Table 3.1 to include a fault between each node shown in Table 3.2. We now have a much higher resolution fault table. If we revisit our previous example of a fault occurrence resulting in 7158 A, we now have a much different problem. If the fault were to occur at node D, we should see 7118 A of expected current. It is evident that the most likely location is still node D, but other possibilities must be considered. With the higher resolution table, a fault location between node C and node D(7330 A expected value) or between node C and node E(6944 A expected value) are now likely possibilities. Although we have increased our resolution and accuracy, we have increased the number of possible fault locations. The lower resolution fault tables result in a larger current diversity, which yields less possibilities. In later sections we will introduce the concept of ”localization” techniques. Localization techniques allow us the ability to choose high resolution fault tables while being able to eliminate certain possibilities. This will be discussed on later sections. When choosing a fault table, it is important to consider the units of resolution. In Test Case 4, a sliding fault is placed at each distribution pole. This will achieve two objectives: accuracy and clarity. In a distribution system, poles are often located a short distance apart usually within line of sight. Line crews will be able to exactly locate the fault by the pole name or location(this achieves clarity of information). Using pole-to-pole sliding faults do not offer significant current diversity(between 50-100A), however this will allow the fault locator to select the exact pole that is faulted. For example, the output of the FLA will indicate that the fault is located at Pole 5567 ±3 poles with Pole 5567 being the most likely. 46 Table 3.2: Increased Resolution Fault Table for Figure 3.7 Node Node A Node B Between Between Node C Node D Between Between Node E Node F Between 3.4.2 Fault Current If Node A/B Node A/C Node C/D Node C/E Node E/F 9553 8201 8877 8547 7542 7118 7330 6944 6346 5690 6018 A A A A A A A A A A A Selecting Possible Fault Locations from Fault Tables In a ideal model, the expected and actual currents would be identical. However, measurement, modelling and other errors introduce differing values than expected. Therefore, a window of ±3% was included to account for all associated error. Selecting possible fault locations from the fault table is done by collection all values that are within ±3% of the actual value. Each fault table entry(Iexpected ) is compared to the actual value of the fault current to determine if the location is considered to be faulted. In our previous example, a 3-Phase fault produced a current of 7158 A measured at the substation. Using Table 3.2, each fault table entry is evaluated to determine if the associated location is faulted. According to the criterion all locations where the current is greater than 6943.26 A and less than 7332.74 A is considered a possible location. The ±3% window for selecting possible fault locations can be expanded or contracted depending on modelling confidence. If the window is expanded, this will result in much more possible fault locations when traversing the fault tables. However, this will allow for more measurement and modelling uncertainties. If the window is contracted, this opens the possibility that the fault location may not be found. 3.4.3 Fault Identification and Fault Table Selection When a fault occurs in the system, the fault locator must identify the type of fault to determine the correct choice of fault table. For example, if a line-to-line fault occurs in our network, we will select the fault table for line-to-line faults. For a line-to-ground fault, we would select our 47 line-to-ground table. When identifying the fault type, we must also record the affected phases. For example, if a phase-to-phase fault occurs, we would need to know that the fault involves phases B and C. Each type of fault(except 3-phase) will contain three fault tables: • Line-to-Ground Fault: A-G, B-G, C-G • Line-to-Line-Ground Fault: A-B-G, B-C-G, and C-A-G • Line-to-Line Fault: A-B, B-C, C-A • 3-Phase: A-B-C To classify the fault type, we set the fault locator to pickup similar to a standard overcurrent relay. A standard phase over-current relay is usually set to 1.5If ull−load . A standard ground over-current element is usually set above the maximum known 3I (0) residual imbalance. This philosophy was used as a threshold current or pick-up to detect the fault type and affected phases. The values IAT ,IBT ,ICT and IN T represent the user defined threshold values. Identification of Phase-to-Phase Faults Phase-to-Phase faults contain positive sequence I (1) and negative sequence I (2) currents only. With the absence of zero-sequence currents we can detect a Phase-to-Phase faults using the following criterion: A-B Fault:|If a | > IAT and |If b | > IBT and |If c | < ICT and |In | < IN T Identification of Phase-to-Phase-to-Ground Faults Phase-to-Phase-to-Ground faults contain positive sequence I (1) , negative sequence I (2) and zero sequence I (0) currents. Using this, we can detect Phase-to-Phase-to-Ground faults in a similar fashion as Phase-to-Phase Faults. A-B-G Fault:|If a | > IAT and |If b | > IBT and |If c | < ICT and |In | > IN T Identification of Phase-to-Ground Faults Phase-to-Ground faults contain positive sequence I (1) , negative sequence I (2) and zero sequence I (0) currents. Using this, we can detect Phase-to-Ground faults in a similar fashion as Phaseto-Phase Faults. A-G Fault:|If a | > IAT and |If b | < IBT and |If c | < ICT and |In | > IN T 48 Identification of 3-Phase Faults Three phase faults contain positive sequence I (1) currents only(assuming a balanced 3-Phase fault). The absence of negative and zero sequence currents indicate a three phase fault. A-B-C Fault:|If a | > IAT and |If b | > IBT and |If c | > ICT and |In | < IN T Evolving Faults Evolving faults begin as one type of fault and end as another. Faults can begin involving one phase and then flash-over to another phase. For example a fault may begin as a phase-to-phase fault involving B and C phases; however, after a short amount of time, the arcing between B and C may flash-over to A. This results in a fault beginning as a Phase-to-Phase fault and then ending as a 3-phase fault. The FLA here does not consider evolving faults. A simple MATLAB script can be included in the FLA to detect an evolving fault. If a evolving fault does occur, this does not imply that the fault locator cannot calculate the fault location. Figure 3.8 shows a Phase-to-Phase fault involving Phases B and C and then transitioning into a 3-Phase fault. Since the final fault is 3-Phase, the fault locator can ignore the Phase-to-Phase sampled data, and consider the fault to be 3-Phase. If the current has reached steady state before the downstream protective device interrupts, the fault can assumed to be 3-phase. 3.4.4 Calculation of Fault Currents in the Fault Table: Fault Resistance The calculation of the fault currents in the fault table are done via the process outlined in Section 3.4. The system is considered to be under loaded conditions during the fault, and all load currents are considered in the solution. However, the arcing resistance of the fault is a unknown when calculating the fault current. According to EPRI studies, a bolted fault assumption is an acceptable assumption for fault locating purposes([17],[7],[15]). In this paper, all studies are done with a bolted fault assumption Rf = 0. Detailed distribution fault analysis under loaded conditions is provided in Appendix C. 3.5 Localization Techniques In large distribution networks, there likely exists multiple locations where if a fault were to be applied would result in the same fault current observed at the substation. If we were to form the thevanin equivalent for all of these locations we would find that there impedances are very similar. The FLA suggested here relies on diversity of impedances throughout the network(mutual coupling and non-homogeneous conductor sizing) to lessen the chance of two nodes being chosen as possibilities. In the case that there exists more than one possibility of 49 Figure 3.8: Phase-to-Phase evolving into a 3-Phase fault[13]. the location of the fault, we can use localization techniques to rank the possibilities from best match to worst match. 3.5.1 Localization Using Protective Devices When a fault occurs in distribution system, a protective device such as a fuse, breaker or recloser will interrupt the fault before damage can occur. The amount of time before the protective device operates and interrupts fault current is unique to each device. The operating time of each device is determined by its operating characteristic. Protective devices such as fuses can be selected with many different types of operating characteristics: ”T” speed, ”K” speed, ect. Breakers and reclosers can also be set using time over-current curves to achieve the desired operating characteristic. Generally speaking, most protective devices used in distribution networks have a operating time that is inversely proportional to current. Localizing using protective devices narrows the possibilities to a specific zone of protection. If a recloser operated during the fault, then possibilities that are with a fuse’s zone of protection are much less likely(assuming fuse blowing coordination). Therefore, the concept of localization using protective devices pinpoints a zone of protection that a fault occured in. Once a zone of protection has been identified, all other possibility can be ranked as less likely. If the fault locator knows the operating characteristics of the protective devices in the 50 network, the fault can be localized. To illustrate this, we will refer back to our feeder in Figure 3.7 with a few changes as shown in Figure 3.9 . Let us consider that a fault occurs in our network with resulting in a magnitude of 8620 A. Using Table 3.2 there are only two possibilities between nodes A/B and nodes A/C. Since we have two possible fault locations we must localize and rank the possibilities. Figure 3.9: Generic 6 Node Feeder with Fuses and Overcurrent Relay. The time-current characteristics for the overcurrent relay and fuses used in the feeder are shown in Figure 3.10. Using Figure 3.9 we can see that the two fault possibilities lie in differing zones of protection. If the fault were to occur between nodes A and C, this would be interrupted by the circuit breaker. If the fault were to occur between A and B, this would be interrupted by the fuse. Using the time-current characteristics in Figure 3.10, we can see that the fuse operates much faster than the overcurrent relay controlling the circuit breaker. If we see a fast clearing of the fault, we know that the fault must have occurred in the fuses zone of protection. If we see a slower clearing than the fuse, then the fault must have occurred in the overcurrent relays zone of protection. Therefore, the concept of localization using protective devices pinpoints a zone of protection that a fault occurred in. If we draw a vertical line on Figure 3.10, we can graphically determine the operating time of each device. For a fault of 8620 A the fuse operates in .1 seconds(total clearing time) and the overcurrent relay operates in .2 seconds. Let us assume that Figure 3.11 is the observed waveform that results in a steady state RMS fault current of 8620 A. Using this observed current, we can see that the fault occurrence occurs at .1 seconds and the fault is cleared by the protective device at approximately .2 seconds. This data implies that the protective device observing the fault current operated in approximately .1 seconds. This operation is much too fast for it to have occurred in the overcurrent relay’s zone of protection, so the possibility of the fault being between nodes B and C is eliminated or de-ranked. Therefore, the fault must have been interrupted by the fuse and occurred in the 51 Figure 3.10: Operating Times for a 8620 A Fault Through Current. fuses zone of protection. This leaves the possible location of the fault being between nodes A and B as the most probable location. 3.5.2 Zones of Protection As we previously discussed, the fault locator uses protective devices to pinpoint a zone of protection that a fault occurred in. By pinpointing the exact zone of protection, we can derank all other possibilities outside that zone. To identify the zone of protection, we use the operating time observed to determine which device in the system has operated. Without zones of protection, the fault locator would have no way of knowing each fault possibility’s upstream protective device. The main protection for a specific zone of protection is called primary protection. The FLA requires that each possible fault location in the fault tables have an associated primary protective device. Having an associated protective device allows the FLA to compare the observed operating times with the expected operating times for each fault possibility. This allows each fault possibility to have a associated time mismatch between observed and expected operating times. To illustrate the primary zones of protection for a feeder, we begin with the network shown in Figure 3.9. To find the associated protective device, we pick a possible fault location and traverse upstream until we arrive at the first protective device. Figure 3.12 shows the primary zones of protection for each protective device in the network. There are a total of four zones: three fuse zones(shown in blue) and one breaker zone(shown in red). The breakers zone of 52 Figure 3.11: Observed Current during Fault Conditions for Figure 3.9. protection stretches from the terminals of the breaker to the line side of each fuse. The fuses zone of protection stretches from the load side of the fuse to each remote node. In addition to specifying the primary protective device for each entry in the fault table, the user must also specify the type of protective device and subclass. For example, the user would program a ”fuse” as the protective device and ”100KS” as the subclass(100KS Fuse). 3.5.3 Localization using Fuse Characteristics A fuse is a simple protective element with a metallic link that operates under fault conditions. During fault conditions, excessive current causes the metallic link in the fuse to heat and begin to melt. Once the metallic link begins to melt, the element will begin to separate into two parts forming an open circuit. The amount of time required for the fuse to begin melting is referred to as the melting time. Fuse characteristics provided by the manufacturer have an associated minimum melting curve. The minimum melt time for a fuse indicates that fault current has caused the metallic link to melt and begin arcing within the fuse. When the metallic link has melted, an arc is formed across the severed link. As a result, the arc provides a path for current to flow. In most conventional fuses it is necessary to wait until zero-crossing until the arc is extinguished. As a result, the time-current characteristics for fuses include a minimum melt tmelt and a arcing 53 Figure 3.12: Zones of Protection for Figure 3.9. time tarc . After the arc has been extinguished, the total clearing time has been achieved. The total clearing time of a fuse is the sum of the minimum melt and arcing time. For fault locating purposes, the total clearing time time-current characteristic is used to predict operating times of fuses. ttct = tarc + tmelt (3.3) Fuse manufacturers, such as SandC, provide time-current characteristics for coordinating purposes. This characteristic is usually provided in spreadsheet form, which can be plugged into the FLA. The fuse time-current characteristics allow the FLA to calculate the estimated operating time ttct . For more information on how the esitmated fuse observed fault current is calculated see Section 3.5.4. Figure 3.13: FLA Fuse Localization Algorithm. To determine which fuse has operated in a network, the FLA compares our observed op- 54 erating time(measured by the fault locator) to the expected operating time(calculated by the fault locator). The observed operating time of the device is determined by recording the point in time at which the current magnitude crosses the 1.5If ull−load value. When the current is increasing and passes the 1.5If ull−load threshold, this is considered the beginning of the fault. When the protective device operates and the current drops below the threshold of 1.5If ull−load , this time is recorded as the end of the fault. Subtracting the yields the total fault duration and operating time top . For each fault possibility’s upstream protective device, we calculate the time mismatch between the operating time observed top and the calculated operating time ttct : ∆te = ttct − top (3.4) The time mismatch equation allows the fault locator to calculate the difference between the expected and observed value. This quantifies how closely each fault possibility’s upstream protective device matches the actual observed conditions. If the time mismatch between expected and observed is large, then the associated device is not likely to have interrupted the fault. If the time mismatch is small, then the protective device associated with the fault possibility is the most likely to have interrupted the fault. A high level overview of the FLA fuse localization algorithm is given in Figure 3.13. Ranking the Best Matched Fuse After the FLA has calculated the mismatch ∆te for all applicable fuses, it must choose the best matched fuse. This will indicate the most likely zone of protection the fault occurred in. To choose the best matched fuse, the FLA uses unity based min-max normalization. When the vector of mismatches is normalized, all time mismatch values will take on a value between 0 and 1. After being normalized, the minimum time mismatch is normalized to 0, representing the most likely candidate. The largest mismatch is normalized to 1.0, representing the most unlikely candidate. All other values are appropriately scaled between 0 and 1. To illustrate this, a test was run on a feeder with two fuses with different operating characteristics. The time mismatch was calculated as the following: ∆te = 0.6557 ! 0.0357 (3.5) To normalize the mismatch vector ∆te we use the following relation: de = ∆t xi − min(∆te ) max(∆te ) − min(∆te ) 55 (3.6) de represents the normalized time mismatch vector. Each data point within The variable ∆t ∆te vector is represented using xi and the min and max of the ∆te vector is represented by min(∆te ) and max(∆te ) respectively. After normalization, the normalized time mismatch de is the following: vector ∆t de = ∆t 1 ! 0 (3.7) The first element in the vector was normalized to 1.0 is the most unlikely candidate with largest time mismatch. The last element in the vector was normalized to 0.0 which represents smallest time mismatch and most likely candidate. 3.5.4 Estimating Fault Current Through the Fuse During the fault, the only available measurements are at the substation. Due to loading, the fault current observed at the substation and the fault current observed by the fuse are not equivalent. Urban load can be generally classified as approximately 50% constant impedance and 50% constant power, which behaves as a constant current load [16]. Modelling all loads as constant current loads is considered a good approximation for most networks [17],[18]. If we assume constant current loads and the load currents do not change during fault conditions([6]),[22]), the load observed at the substation is a superposition of the current flowing due to the fault itself If and the steady state load currents Iload . These superimposed currents are shown in Figure 3.14. A detailed explanation of fault analysis under loaded conditions is covered in Appendix C. Load models presented in Appendix C describe load behaviour under normal conditions. A piecewise load model is used to describe load behaviour under faulted conditions. Figure 3.14: Superimposed Currents Through Faulted Fuse. 56 Isub = If + Iload (3.8) The currents observed by the fuse also comprise a superposition of currents. The fault current observed by the fuse is comprised of the fault current due to the fault itself and the steady state load currents beyond the fuse Iload−0 . If we consider only the current flowing due to the fault itself, the fault locator at the substation and the downstream fuse are observing the same current If . However, when the load currents are superimposed, the fault locator will observe a larger fault current than the fuse. Therfore, the FLA estimates the fault current observed by the fuse to be a superposition of the current flowing due to the fault itself If and the steady state load currents beyond its terminals Iload−0 . If use = If + Iload−0 (3.9) To estimate the operating time of the downstream fuse, we are first required to approximate the observed current during fault conditions. Since the downstream fuse and fault locator are observing the same current flowing due to the fault itself, we begin with Equation 3.8. The load current flowing just before the fault at t = 0− is defined as Iload and is subtracted from the steady state observed substation fault current: If = − If + Iload | {z } Iload |{z} (3.10) Observed Pre-Fault Current Observed Fault Current Since the load current at the fuse just before the occurrence of the fault is not know, it must be estimated from stored load flow data. We will utilize the calculated fault current computed above(Equation 3.10) due to the fault itself to estimate the current observed by the fuse during fault conditions. Using the database load current value, we can estimate the observed fault current by summing the phasor quantities of the fault current due to the fault itself If and the expected database load Iload−0 1 : If use = If |{z} + Iload−0 | {z } (3.11) Expected Pre-Fault Current Fault Current The variable Iload−0−d can be generalized in a summation of all n loads tapped beyond the terminals of the fuse: If use = If + n X Iload−0−d (3.12) d=1 In Equation 3.13, the load connected to the applicable phase beyond the fuse is represented 1 It likely that the actual fuse load current just before the fault occurrence and the expected current flow Iload−0 are different. The effects of Load Perturbations is explored in Chapter 4.8.1. 57 a b c as a summation of individual tapped loads Iload−0−d , Iload−0−d , and Iload−0−d . The fault currents due to the fault itself on each phase is represented by If −a ,If −b and If −c . For example, for a Line-to-Ground fault involving Phase B, the currents flowing through the fuse calculated by the FLA would be: 0 Pn If use = If −b + 0 a Iload−0−d Pd=1 n b Iload−0−d Pd=1 n c d=1 Iload−0−d = Pn a d=1 Iload−0−d Pn b If −b + d=1 Iload−0−d Pn c d=1 Iload−0−d (3.13) The full process of estimating the fault current through the fuse is shown in Figure 3.15. Figure 3.15: Fault Current Estimation Algorithm in FLA. 3.6 Localization using Load-Flow Rejection When a distribution feeder lacks protective device diversity, load-flow characteristics must be used to localize the fault. Load flow rejection allows the FLA to identify the protective device that operated even if they are identical. For example, if there are two fault possibilities and both are in the zone of 80KS fuses, their operating times cannot be used to determine which fuse has operated. This scenario is not limited to fuses. If there exists two or more reclosers in the feeder that are set identically, it is not possible to localize using operating times. To alleviate this particular problem, load-flow rejection is used to localize two protective devices that have identical operating times. When a fuse operates for a fault in its zone, the loads connected to that fuse are open circuited. The load that was previously connected to the feeder is no longer present and results 58 in a load loss(rejection) observed at the substation. If a load-flow data table is formed, the observed load loss at the substation can be compared to the table to determine which device has operated. 3.6.1 Calculating Best Matched Device from Load Flow Rejection To begin localizing using Load Flow Rejection, the FLA will calculate the observed load rejection at the substation(Equation 3.14). This calculation is done in the fault locator by observing several cycles before the current first exceeds 1.5If ull−load and several cycles after the last drop below 1.5If ull−load . Several cycles before the first current exceeds 1.5If ull−load is defined as the pre-fault current Ipre . Several cycles after the last drop below 1.5If ull−load is defined as the post fault load Ipost . As mentioned the FLA saves all times where the current crosses 1.5If ull−load . Pre-fault(Ipre ) and Post-Fault(Ipost ) values are shown in Figure 3.16. Iob = Ipre − Ipost (3.14) Figure 3.16: Current Rejection after Recloser Lockout. Since the observed load rejection is now known, the FLA will calculate the current mismatch 59 for each possibilities’s upstream device. The mismatch is defined as the difference between the expected load rejection for each device and the observed load rejection. The expected load rejection for each device comes from the load flow data table stored within the fault locator. To calculate the current mismatch of each protective device ∆Ie , we use the following relation: ∆Ie = Iob − Iexp (3.15) An overview of the process of load flow rejection localization is shown in Figure 3.17. Figure 3.17: Load Flow Rejection Algorithm in the FLA. Ranking the Best Matched Fuse In the previous sections, the time mismatch vector was normalized in order to rank the protective device’s match to the observed operating time. The same process is performed here with load mismatch instead of time mismatch. To choose the best matched fuse, the FLA uses unity based min-max normalization. When the vector of mismatches is normalized, all load mismatch values will take on a value between 0 and 1. After being normalized the minimum load mismatch is normalized to 0, representing the most likely candidate. The largest mismatch is normalized to 1.0, representing the most unlikely candidate. All other values are appropriately scaled between 0 and 1. To illustrate this, a test was run on a feeder with six fuses of different load values. The load mismatches for each of the six fuses are as follows: 60 ∆Ie−f use = 3.1167 3.7360 0.5196 2.2753 1.8776 0.0476 (3.16) To normalize the mismatch vector ∆Ie−f use we use the following relation: ∆Id e−f use = xi − min(∆Ie−f use ) max(∆Ie−f use ) − min(∆Ie−f use ) (3.17) The variable ∆Id e−f use represents the normalized load mismatch vector. Each data point within ∆Ie−f use vector is represented using xi and the min and max of the ∆Ie−f use vector is represented by min(∆Ie−f use ) and max(∆Ie−f use ), respectively. After normalization, the normalized load mismatch vector ∆Id e−f use is the following: ∆Id e−f use = 0.8321 1.0000 0.1280 0.6040 0.4961 0 (3.18) What we see in ∆Id e−f use is a clear representation of the most likely fuse to have operated. The third element in the vector was normalized to 0.1280, representing a likely candidate. The second element in the vector was normalized to 1.0, representing the most unlikely candidate. The last element in the vector was normalized to 0.0 which represents smallest load mismatch and most likely candidate. 3.7 Combining Localization Data for Best Match In previous sections, we were able to localize and rank a fault possibility from load flow rejection and protective device characteristics. To provide the most accurate localization information, the data from both the load flow rejection and protective device characteristics are combined. The consideration of all localization data creates a final ranking vector in the FLA, which is used to determine the best matched node. 61 3.7.1 Final Ranking of Each Possibility To begin final ranking of a fault possibility, we again consider if the fault possibility’s protective device is a recloser, breaker, or fuse. If the device is a recloser we must consider the load flow rejection, short-time mismatch, long-time mismatch and open interval timing. If the device is a fuse we must consider the load flow rejection and operating time mismatch. Each possible fault location has a mismatch from the observed fault current which also must be considered. The expected fault current If −exp for each fault possibility is pulled from the fault tables and compare to the observed fault current If −ob . The current mismatch is defined as: ∆If = |If −ob − If −exp | (3.19) The fault current mismatch is normalized using the following formulation: df = ∆I xi − min(∆If ) max(∆If ) − min(∆If ) (3.20) df represents the normalized fault current mismatch vector. Each data point The variable ∆I within ∆If vector is represented using xi and the min and max of the ∆If vector is represented by min(∆If ) and max(∆If ) respectively. Each fault possibilities fault current mismatch and associated upstream protective device mismatches are combined to calculate the final ranking vector n. For a fault possibility with a upstream fuse: nf use,k = de ∆t |{z} + Normalized Time Mismatch ∆Id e−f use | {z } + Normalized Load Rejection Mismatch df ∆I |{z} Normalized Fault Current Mismatch (3.21) For a fault possibility with a upstream recloser: nrecloser,k = be |{z} Normalized Time Mismatch + d ∆Ie−recloser | {z } Normalized Load Rejection Mismatch + df ∆I |{z} Normalized Fault Current Mismatch (3.22) A master ranking vector η is formed that contains all fault possibilities nr,1 , nr,2 , all the way to k th and final fault possibility nr,k . The sub-script variable r is used to identify the protective device type where r = f use or r = recloser. 62 nr,1 nr,2 η= .. . nr,k (3.23) The η matrix is then normalized using the following relation: ηb = xi − min(η) max(η) − min(η) (3.24) The variable ηb represents the final normalized ranking vector. Each data point within η vector is represented using xi (nr,1 · · · nr,k ) and the min and max of the η vector is represented by min(η) and max(η) respectively. The final normalized ranking vector is used by the FLA to rank all the possibilities from most likely to least likely. The normalized vector also allow the fault locator to quantify how the intermediate possibilities are ranked relative to the best match. 63 3.8 Localization Flow Chart To clarify the exact procedure used to localize the fault, a localization flow chart is shown in Figure 3.18. Figure 3.18: FLA Localization Algorithm Flow Chart. 64 Chapter 4 Fault Locator Test Results 4.1 Introduction to the Notional Feeder, Stewart Street Feeder and Test Cases To test the proposed FLA, a MATLAB Simulink model of a Progress Energy 12kV feeder was used. Model parameters such as line impedances, transformer ratings and load data were provided by Progress Energy. In this paper, we refer to this feeder as the Notional Feeder(NF). MATLAB Simulink was chosen to simulate the NF because of its ability to perform discrete time simulations and data capture. Current waveforms captured after simulation can be recorded in Simulink and passed to the FLA for execution(Figure 4.1). A one-line of the NF is shown in Figure 4.2. This chapter is comprised of three different test cases using the NF model. Test Case 1 is performed using the FLA with no localization algorithm. No protective devices are present in the feeder model while testing. As a result, the FLA ranks multiple fault possibilities using the observed fault current only. During Test Case 2 and Test Case 3, fuse and recloser models are inserted into the NF. With the addition of protective devices, the localization algorithm is used to rank possibilities. During Test Case 3, the FLA is tested using both Fuse Saving and Fuse Blowing coordination schemes. During Test Case 4, the Stewart Street 12.47kV feeder is tested using DEW models provided by Allegheny Power. The Stewart Street feeder is much larger than the NF, and contains hundreds of nodes and tapped loads. Short circuit and load flow analysis is performed in DEW and passed to the FLA localization algorithm. A detailed overview of the Stewart Street feeder is given in Section 4.7. 65 4.2 Notional Feeder Fault Tables and Short Circuit Data The fault tables needed by the FLA are gathered by applying a bolted fault(Rf = 0) at each node in the NF. After a sufficient time has passed, the RMS current reaches a ”steady state” and it is recorded in Microsoft Excel spreadsheet format. The spreadsheet is automatically imported into the FLA upon execution of the algorithm. The fault table used during Phase A to ground faults is provided in Table 4.1. Table 4.1: Notional Feeder Fault Table for SLG Faults on A Phase. Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 RMS Current Fault Type 6950 5145 3196 3440 4422 4844 4989 4088 2585 2827 3325 2186 1886 4260 3080 3020 2819 8800 A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G A-G 66 4.3 4.3.1 Test Case 1: Notional Feeder Testing With No Localization Introduction: Test Conditions and Procedure The first test case performed with the FLA is done with no localization on the Notional Feeder. Simple fault tables are used to rank faults from best to worst match. Fault current data is captured at the substation bus of the NF using the ”Goto Workspace” block set in Simulink. After the data is recorded in the MATLAB workspace, the FLA algorithm(written in MATLAB code) is executed. After execution and the results are captured using a screen shot of the MATLAB console. A high level overview of the test procedure is shown in Figure 4.1. Figure 4.1: Simulation Testing Procedure using MATLAB Simulink. Before simulating a system fault all initial states are started at steady-state conditions. According to [7], most line-to-ground faults last 8.35 cycles before being cleared by protective devices. As a result, all line-to-ground fault durations during Test Case 1 simulations last for 8.35 cycles being removed. During fault conditions, the fault is assumed to be bolted Rf = 0. Since single line-to-ground faults are the most common, the most attention is given to this fault type. 4.3.2 FLA Testing for Line-to-Ground Faults In this section, we consider several line-to-ground faults at various nodes in the network. After the fault is applied, the FLA executed and the MATLAB console printout is recorded. A lineto-ground fault was tested at the following nodes: Node 4, Node 11, Node 15, Node 17. For the location of the faulted nodes, refer to the system one-line Figure 4.2. After the FLA is executed, the calculated fault current mismatch percentage is recorded for ranking purposes. The percent mismatch is the difference between the observed and expected fault current, relative to the observed current, for each node. The node with the lowest mismatch is considered the best 67 Figure 4.2: Test Case 1 Notional Feeder One-Line Model. match. A summary of the line-to-ground test results are in Section 4.3.4. 4.3.3 FLA Testing for Line-to-Line Faults In this section, we also consider line-to-line faults at various nodes in the network. After the fault is applied, the FLA executed and the MATLAB console printout is recorded. A line-toline fault was tested at the following nodes: Node 15 and Node 17. For the location of the faulted nodes, refer to the system one-line Figure 4.2. After the FLA is executed, the fault current mismatch percentage is recorded for ranking purposes. The percent mismatch is the difference between the observed and expected fault current, relative to the observed current, for each node. The node with the lowest mismatch is considered the best match. A summary of the line-to-line test results are in Section 4.3.4. 68 4.3.4 Test Case 1 Results: During Test Case 1, a total of 6 cases involving phase-to-phase and line-to-ground faults were tested at various nodes in the network. In all test cases the faulted node was correctly identified. A summary of the test results are in Tables 4.2 and 4.3. Table 4.2: Line-to-Ground Simulation Results for Test Case 1 Simulation Number A-G Fault at Node Possibilities 1 2 3 Node 4 Node 11 Node 15 4 Node 17 Node 4 Node 11 Node 15(Best Match) Node 16(Worst Match) Node 17(Best Match) Node 10(Worst Match) Mismatch % 0.0347% 0.0343% 0.1499% 2.0951% 0.0456 % 0.2381% Table 4.3: Phase-to-Phase Fault Simulation Results for Test Case 1 Simulation Number A-G Fault at Node Possibilities 5 Node 15 6 Node 17 Node 15(Best Match) Node 16(Worst Match) Node 17(Best Match) Node 10(Worst Match) 69 Mismatch % 0.0493% 3.5486% 0.1266 % 2.702% 4.4 Test Case 2: Localization using Load Flow and Protective Devices During Test Case 1, the FLA only utilized fault current as a means of determining the fault location and ranking(no protective devices were modelled). In Test Case 2, two substation breakers and two reclosers are added to the NF model as recommended by Progress Energy. With protective devices now present, load flow and protective device data is passed to the localization sub-algorithm to aid in the ranking process. The load flow data is captured using the MATLAB load flow tool and imported into the fault locator using Microsoft Excel spreadsheets. The fault locator also requires time-current characteristics on all reclosers and breakers present in the feeder as well as their respective locations ([19],[20]). Locations of each device and their time-current characteristics are imported into MATLAB using Microsoft Excel. Fault current data is captured at the substation bus of the NF using the ”Goto Workspace” block set in Simulink. After the data is recorded in the MATLAB workspace, the FLA algorithm(written in MATLAB code) is executed. An overview of the test procedure is shown in Figure 4.3. Figure 4.3: Test Case 2 Testing Procedure. Although all nodes were identified correctly in Test Case 1, many fault possibilities were nearly indistinguishable in percentage mismatch. For example, the results for a line-to-ground fault at Node 17 in Test Case 1 yielded a 0.045% mismatch and a 0.23% mismatch for Node 10. These two nodes are nearly indistinguishable and are only separated by a 0.185% margin. During the proper system conditions, the FLA Algorithm could incorrectly choose Node 10 as the best matched since both node have very similar fault currents(this is investigated more in Section 4.8.1). Given that Node 10 and Node 17 are located in two different branches of the feeder, they are protected by different devices. If the fault were to have occurred at Node 17, Recloser A would have operated for the fault. If the fault were to have occurred at Node 70 10, Substation Breaker A would have interrupted the fault. Since Recloser A and Substation Breaker A have different protective device settings, the fault location can be localized. Also, Substation Breaker A and Recloser A both carry measurably different load levels, allowing yet another parameter to localize with. After the recloser or breaker goes to the lockout state, the load rejection is calculated by the fault locator and used to localize the fault. Using both load flow and protective device characteristics allows the fault locator to localize two faults that were nearly indistinguishable in Test Case 1. Some of the same cases in Test Case 1 are run again to illustrate the effectiveness of the added localization techniques. The addition of localization will show that many indistinguishable cases in Test Case 1(i.e Node 17 fault test) are now resolved into much more confident choices. Most of the attention in this section will be given to line-to-ground faults since they are the most common. 4.4.1 Introduction: Test Conditions and Procedures During Test Case 1, no protective devices were present in the feeder and the fault was applied to the network for a allotted amount of time. During Test Case 2, protective devices are modelled and placed at designated points as recommended by Progress Energy Carolinas(as shown in Figure 4.4). Each recloser and substation breaker is set to 1 shot of fast reclosing and 3 shots of slow reclosing. Each recloser and substation breaker has two phase(fast and slow) and two ground relays(fast and slow). After the final shot of reclosing, the breaker or recloser opens and enters the lockout state. Progress Energy recommended breaker and recloser settings can be found in Appendix A.7. Given the computational intensity of these simulation and the length of time they take to complete, only 1 shot of fast and 1 shot of slow was performed before lockout of the substation breaker or recloser. Reducing the number of shots of each device did not effect the accuracy of the fault locator since all devices are set to a total of four shots. 4.4.2 FLA Testing for Line-to-Ground Faults In this section, we will consider line-to-ground faults at various nodes in the network. After the fault is applied, the FLA executed and the MATLAB console printout is recorded. A line-toground fault was tested at the following nodes: Node 17, Node 7 and Node 16. For the location of the faulted nodes, refer to the system one-line Figure 4.4. After the test simulation is run, the protective device mismatch and load rejection mismatch percentage is recorded for ranking purposes. 71 Figure 4.4: Notional Feeder One-Line Model with added Reclosers and Breakers. 4.4.3 A-Ground Fault at Node 17 A line-to-ground fault was place at Node 17 on Phase A as done in Test Case 1 resulting in two possible nodes. The two possibilities, Node 17 and Node 10 are nearly indistinguishable and are only separated by a few percent mismatch. In this section, we show that Node 10 can easily be eliminated as a possibility with the addition of the localization algorithm. After the ground fault was place at Node 17, the ground relay in Recloser A picked up and operated two times(shown in Figure 4.5). The first shot was a fast(short time) trip, followed by a open interval period of several cycles. The recloser then de-activates the fast ground curve then switch to slow for the second trip. After the fault does not clear on the second shot, the recloser goes into the lockout state and does not reclose. When the FLA has detected that the fault has cleared, it begins searching for all possible fault locations. The FLA has been coded 72 Figure 4.5: Test Case 2: Substation Phase A RMS current during a fault at Node 17. to use both fast and slow curves for localization. After Recloser A proceeds to the lockout state, the observed current at the substation bus decreases due to the disconnecting of load. The fault locator also uses this information to determine the most likely device that has operated in the network in addition to the protective device information. In Figure 4.5, the magnitude of the load rejection in shown. Test Results Data provided to the user of the FLA ranks the fault possibilities from best match to worst match. For each fault location possibility, the FLA must determine the correct upstream protective device. Both Node 10 and 17’s upstream protective devices were identified as Substation Breaker A and Recloser A, respectively. Once a protective device is associated with a node, the algorithm begins to localize using the observed operating times. The protective device localizing data shows that the fault could not have occurred a Node 10. The percent error from the observed and estimated operating times for Node 10 is 243.5%, indicating that for a fault at Node 10, the interrupting time would have been much slower. 73 The percent error from the observed and estimated operating times for Node 17 is only 30.4%, indicating that the fault must have occurred within the zone of Recloser A(Node 17). A summary of this data is shown in Table 4.4. Table 4.4: Percent Mismatch Table for Protective Device Localization. Protective Device Percent Mismatch Substation Breaker A(Node 10) Recloser A(Node 17) 243.5% 30.4% Load flow rejection provides a additional layer of security for localization. After the recloser or breaker enters the lockout state, there is an expected current rejection at the substation for each phase. Observed current rejections poorly matched a load rejection of Substation Breaker A and is reflected in the mismatch calculated by the fault locator. For Node 10, the rejection mismatch for Phase A, B and C are 458%, 175% and 455% respectively. This poor match indicates that if the fault had occurred at Node 10, there would have been a much larger load rejection. Node 17 is the preferred choice with a Phase A, B and C mismatch of 6.3%, 8.2% and 6.84% respectively. This data is summarized in Table 4.5. Table 4.5: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Substation Breaker A(Node 10) Substation Breaker A(Node 10) Substation Breaker A(Node 10) Recloser A(Node 17) Recloser A(Node 17) Recloser A(Node 17) Phase A: 458% Phase B: 175% Phase C: 455% Phase A: 6.3% Phase B: 12.9% Phase C: 5.54% Using localization it is easy to distinguish that the fault cannot be at Node 10. In Test Case 1, the fault locator was able to still select Node 17 as the correct faulty node, however, there were no measures of certainty. With the addition of localization data, Node 10 can be thrown 74 out as a possibility. 4.4.4 A-Ground Fault at Node 7 For this test a line-to-ground fault is applied to Node 7 in Substation Breakers B zone of protection. Using the fault tables for line-to-ground faults, only two possibilities can be established: Node 6 and Node 7. Both of these nodes are nearly identical in fault current magnitude, making them indistinguishable if localization is not used. Since Node 6 is in Relcoser B’s zone of protection, the localization algorithm can easily distinguish between the two locations using load rejection and observed protective device operation. Figure 4.6: Test Case 2: Substation Phase A RMS current during a fault at Node 7. After the ground fault was place at Node 7(shown in Figure 4.4), the ground relay in Substation Breaker B picked up and operated two times. The first shot was a fast(short time) trip, followed by a open interval period of several cycles. The recloser then de-activates the fast ground curve then switch to slow for the second trip(Shown in Figure 4.6) . After the fault does not clear on the second shot, the recloser goes into the lockout state and does not reclose. When the FLA has detected that the fault has cleared, it begins searching for all possible fault locations. 75 Test Results For a fault in the zone of protection of Substation Breaker B(Node 7), the interruption time is much slower than Recloser B. Had the fault actually occurred in the zone of the recloser(Node 6) the fault locator would have observed a much faster ground relay operation, thereby indicating a fault at Node 6. Since the ground relay operation was much slower, the best matched device is either Substation Breaker B or Substation Breaker A. However, since all faults in the Substation Breaker A’s zone do not match the fault current magnitude of the observed fault, they can be eliminated. This essentially eliminates Node 6 as a potential fault location and is therefore ranked as worst match. The protective device localizing data shows that the fault could not have occurred a Node 6. The percent error from the observed and estimated operating times for Node 6 is 138.5%, indicating that for a fault at Node 6, the interrupting time would have been much faster. The percent error from the observed and estimated operating times for Node 7 is only 18.24%, indicating that the fault must have occurred within the zone of Substation Breaker B(Node 7). A summary of this data is shown in Table 4.6. Table 4.6: Percent Mismatch Table for Protective Device Localization Protective Device Percent Mismatch Substation Breaker B(Node 7) Recloser B(Node 6) 18.24% 138.5% Load flow rejection provides a additional layer of security for localization. After the recloser or breaker enters the lockout state, there is an expected current rejection at the substation for each phase. Observed current rejections poorly matched a load rejection of Recloser B and is reflected in the mismatched calculated by the fault locator. For Node 6, the rejection mismatch for Phase A, B and C are 48.9%, 50.1% and 50.1% respectively. This poor match indicates that if the fault had occurred at Node 6, there would have been a much smaller load rejection. Node 7 is the preferred choice with a Phase A, B and C mismatch of 4.22%, 1.20% and 1.87% respectively. A summary of this data is in Table 4.7. Using localization it is easy to distinguish that the fault cannot be at Node 6. With the above data, Node 6 can be thrown out as a possibility. 76 Table 4.7: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Substation Breaker B(Node 7) Substation Breaker B(Node 7) Substation Breaker B(Node 7) Recloser B(Node 6) Recloser B(Node 6) Recloser B(Node 6) 4.4.5 Phase Phase Phase Phase Phase Phase A: B: C: A: B: C: 4.22% 1.20% 1.87% 48.9% 50.1% 50.2% Limitations of the Localization Algorithm: A-Ground Fault at Node 16 In certain cases, the proposed localization algorithm built into the FLA will not be able to provide any additional information on the true fault location. This phenomena occurs when two possibilities exist in the same zone of protection for a given device. When a fault occurs in the zone of protection for any given device, such as a fuse, the fuse will operate and result in a load rejection at the substation. If two possibilities exist in the zone of the device that operated, it will result in a identical load and protective mismatch vector for both possibilities. Therefore, it can be said that if two possibilities exist within the same zone of protection, they cannot be localized. An excellent example of this in the NF is nodes 15 and 16. Both of these locations are separated by a short line segment approximately .356 km long, offering minimal short circuit difference between the nodes. This results in mutual possibilities when a fault occurs at either of the nodes. If a fault occurs at Node 15, then a Node 16 will be a mutual possibility. To test this, a line-to-ground fault was placed at Node 16, resulting in two ground relay operations(one fast and one slow) of Recloser A. After two shots of reclosing, Recloser A enters the lockout state and remains in the open position. Since both nodes are in the same zone of protection, they will have the same protective device mismatch and load rejection mismatch. The fault locator is forced to use only fault current to localize the fault. When this occurs, the fault locator will print a warning to the user that the localization algorithm detected two fault possibilities within the same zone of protection. This is shown in Figure 4.7. In this particular test, Node 16 was still identified as the correct faulted node. This was achieved by using fault tables only(Test Case 1). We can conclude that the proposed localization algorithm is effective if all possibilities do 77 Figure 4.7: Fault Locator Ranking of Fault at Node 16. not exist within the same zone of protection for a given device. If this is the case, only fault tables can be used to localize. As of late, the popularity of fuse blowing schemes requires that fault locating algorithms adapt to this protective scheme. A properly coordinated fuse blowing scheme allows the fuse to interrupt the fault before any upstream device(such as a recloser) is allowed to trip. 78 4.5 Test Case 3: Fault Locating on Fuse Saving or Fuse Blowing Schemes 4.5.1 Introduction: Notional Feeder with Fuse Blowing Coordination During Test Case 2, the NF was protected by both reclosers and reclosing substation breakers without the presence of fuses. Given the popularity of fuse blowing schemes, a new case was introduced to test this protection scheme. A properly coordinated fuse blowing scheme allows the fuse to interrupt the fault before the upstream breaker can trip. The FLA presented here is easily adaptable to fuse blowing schemes, however, the fault locator must be told that the feeder is being protected by a fuse blowing scheme. Figure 4.8: Fuse Blowing Scheme on Notional Feeder. 79 4.5.2 Introduction: Fuse Blowing Scheme Test Conditions To implement a common fuse blowing scheme, the NF protection system was reconfigured to contain 26 SandC T Speed Fuses and a main reclosing substation breaker. Pickups and time-dial settings were changed in the substation breaker to allow fuse blowing coordination between all downstream fuses. Each fuse is named in the feeder and is shown along with the characteristic in Figure 4.8. The reclosing substation feeder breaker fast curve was disabled, thereby allowing the fuse to blow. The reconfigured protection system is shown in Figure 4.8. Each fuse link was modelled in MATLAB Simulink using test data provided by SandC [21]. To ensure adequate coordination, ASPEN One-Liner coordination tool was used to ensure proper fuse-fuse and fuse-breaker coordination per IEEE standards and recommendations[17]. All fuse and breaker information was imported into the FLA for fault localization. 4.5.3 FLA Testing for Line-to-Ground Faults: Fuse Blowing In this section, we will consider line-to-ground faults at various nodes in the network. After the fault is applied, the FLA executed and the MATLAB console printout is recorded. A line-toground fault was tested at the following nodes: Node 6, Node 10 and Node 17. For the location of the faulted nodes, refer to the system one-line Figure 4.8. After the test simulation is run, the protective device mismatch and load rejection mismatch percentage is recorded for ranking purposes. 4.5.4 Line-to-Ground Fault at Node 17 The first fuse blowing scheme test was performed with a line-to-ground fault at Node 17. For a fault at this node, the fault locator will produce two possible fault locations: Node 10 and Node 17. Node 10 can be easily eliminated using the localization algorithm due to the slower speed 200T fuse protecting this node. As a result, the fault locator will observe a faster fuse operation, indicating that the fault is in the zone of a 140T or faster fuse. Since the only other fault possibility is Node 17, which is in the zone of a 140T fuse, it is ranked as best match. During the fault, the fault locator records the observed fuse operating time which is used for localization. During this part of the algorithm, the fault locator will notify the user that it is localizing using a fuse blowing scheme. During testing, the fault locator has correctly identified that the fault must be in the zone of a fuse, since no reclosing was observed. This data indicates that the fault could not have occured on the main feeder, as it is protected only by the substation breaker. As indicated in the Figure 4.9, the observed fuse operating time is .353 seconds. 80 Figure 4.9: Fault Locator Observed Fault Current for Fault at Node 17. Test Results Data provided to the user of the FLA ranks the fault possibilities from best match to worst match. For each fault location possibility, the FLA must determine the correct upstream protective device. Both Node 10 and 17’s upstream protective devices were identified as Fuse N142 and Fuse N14, respectively. Once a protective device is associated with a node, the algorithm begins to localize using the observed operating times. The protective device localizing data shows that the fault could not have occurred a Node 10. The percent error from the observed and estimated operating times for Node 10 is 168.3%, indicating that for a fault at Node 10, the interrupting time would have been much slower. The percent error from the observed and estimated operating times for Node 17 is only 14.5%, indicating that the fault must have occurred within the zone of Fuse N14. A summary of this data is shown in Table 4.8. Load flow rejection provides a additional layer of security for localization. After the fuse blows, there is an expected current rejection at the substation for the applicable phase. Observed current rejections poorly matched a load rejection of Fuse N142 and is reflected in the mismatched calculated by the fault locator. For Node 10, the rejection mismatch for Phase 81 Table 4.8: Percent Mismatch Table for Protective Device Localization Protective Device Percent Mismatch Fuse N14(Node 17) Fuse N142(Node 10) 14.5% 168.3% A is 377.0%. This matching indicates that if the fault had occurred at Node 10, there would have been a larger load rejection. Node 17 is the preferred choice with a Phase A load rejection mismatch of 14.7%. A summary of this data is in Table 4.9. Table 4.9: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Fuse N14(Node 17) Fuse N142(Node 10) Phase A: 14.7% Phase A: 377.0% Using localization it is easy to distinguish that the fault cannot be at Node 10. With the above data, Node 10 can be thrown out as a possibility. 82 4.5.5 Line-to-Ground Fault at Node 6 The second fuse blowing scheme test was performed with a line-to-ground fault at Node 6. For a fault at this node, the fault locator will produce two possible fault locations: Node 6 and Node 7. Node 7 can be easily eliminated using the localization algorithm due to the faster speed 50T fuse protecting this node. As a result, the fault locator will observe a slower fuse operation, indicating that the fault is in the zone of a slower speed fuse. Since the only other fault possibility is Node 6, which is in the zone of a 200T fuse, it is ranked as best match. Figure 4.10: Fault Locator Observed Fault Current for a fault at Node 6. During the fault, the fault locator records the observed fuse operating time which is used for localization. During this part of the algorithm, the fault locator will notify the user that it is localizing using a fuse blowing scheme. Also, the fault locator correctly identified that the fault must be in the zone of a fuse, since no reclosing was observed. This data indicates that the fault could not have occurred on the main feeder, as it is protected only by the substation breaker. As indicated by Figure 4.10, the observed fuse operating time is .229 seconds. 83 Test Results Data provided to the user of the FLA ranks the fault possibilities from best match to worst match. For each fault location possibility, the FLA must determine the correct upstream protective device. Both Node 6 and 7’s upstream protective devices were identified as Fuse N1 and Fuse N23, respectively. Once a protective device is associated with a node, the algorithm begins to localize using the observed operating times. Table 4.10: Percent Mismatch Table for Protective Device Localization Protective Device Percent Mismatch Fuse N1(Node 6) Fuse N23(Node 7) 32.31% 89.6% The protective device localizing data shows that the fault could not have occurred a Node 7. The percent error from the observed and estimated operating times for Node 7 is 89.6%, indicating that for a fault at Node 7, the interrupting time would have been much faster. The percent error from the observed and estimated operating times for Node 6 is only 32.31%, indicating that the fault must have occurred within the zone of Fuse N1. A summary of this data is shown in Table 4.10. Load flow rejection provides a additional layer of security for localization. After the fuse blows, there is an expected current rejection at the substation for the applicable phase. Observed current rejections poorly matched a load rejection of Fuse N23 and is reflected in the mismatched calculated by the fault locator. For Node 7, the rejection mismatch for Phase A is 70.7%. This poor match indicates that if the fault had occurred at Node 7, there would have been a much smaller load rejection. Node 6 is the preferred choice with a Phase A load rejection mismatch of 8.27%. A summary of this data is in Table 4.11. Table 4.11: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Fuse N1(Node 6) Fuse N23(Node 7) Phase A: 8.27% Phase A: 70.7% 84 Using localization it is easy to distinguish that the fault cannot be at Node 7. With the above data, Node 7 can be thrown out as a possibility. 4.5.6 Introduction: Notional Feeder with Fuse Saving Coordination Although fuse saving is falling out of favor with many utilities, it is still in mainstream use. A properly coordinated fuse saving scheme allows the upstream recloser instantaneous overcurrent element to trip before the fuse is allowed to blow. Reclosing before the fuse is allowed to blow allows a temporary fault to be cleared by recloser rather than by the fuse. This reduces outages and the amount of line crew dispatches into the field. The FLA presented here is easily adaptable to fuse saving schemes, however, the fault locator must be told that the feeder is being protected by a fuse saving scheme. In the event that the feeder is set to a hybrid scheme(fuse saving and fuse blowing), the fault locator must be set to fuse saving mode. 4.5.7 Introduction: Fuse Saving Scheme Test Conditions To implement a common fuse saving scheme, the Notional Feeder protection system was reconfigured to contain 26 SandC T Speed Fuses and a main reclosing substation breaker. Pickups and time-dial settings were changed in the substation breaker to allow fuse saving coordination between all downstream fuses. The reclosing substation feeder breaker was set to one shot of fast before switching to the slow curve and allowing the fuse to blow. The reconfigured protection system is shown in Figure 4.8. Each fuse link was modelled in MATLAB Simulink using test data provided by SandC [21]. To ensure adequate coordination, ASPEN One-Liner coordination tool was used to ensure proper fuse-fuse and fuse-breaker coordination per IEEE standards and recommendations. All fuse and breaker information was imported into the FLA for fault localization. 4.5.8 FLA Testing for Line-to-Ground Faults: Fuse Saving In this section, we will consider line-to-ground faults at various nodes in the network. After the fault is applied, the FLA executed and the MATLAB console printout is recorded. A lineto-ground fault was tested at the following nodes: Node 10 and Node 6. For the location of the faulted nodes, refer to the system one-line Figure 4.8. After the test simulation is run, the protective device mismatch and load rejection mismatch percentage is recorded for ranking purposes. 85 4.5.9 Line-to-Ground Fault at Node 10 The first fuse saving scheme test was performed with a line-to-ground fault at Node 10. For a fault at this node, the fault locator will produce two possible fault locations: Node 10 and Node 17. Node 17 can be easily eliminated using the localization algorithm due to the faster speed 140T fuse protecting this node. As a result, the fault locator will observe a slower fuse operation, indicating that the fault is in the zone of a 200T or slower fuse. Since the only other fault possibility is Node 10, which is in the zone of a 200T fuse, it is ranked as best match. As shown in Figure 4.11, the substation breaker instantaneous ground element interrupts the fault before the fuse is allowed to operate. After a open interval time, the breaker recloses with the instantaneous ground element disabled. The ground time-overcurrent element remains enabled and allows the fuse to blow. After the fuse blows, the ground fault is cleared. Figure 4.11: Fault Locator Observed Fault Current for a Fault at Node 10. Test Results Data provided to the user of the FLA ranks the fault possibilities from best match to worst match. For each fault location possibility, the FLA must determine the correct upstream 86 protective device. Both Node 10 and 17’s upstream protective devices were identified as Fuse N142 and Fuse N14, respectively. Once a protective device is associated with a node, the algorithm begins to localize using the observed operating times. The protective device localizing data shows that the fault could not have occurred a Node 17. The percent error from the observed and estimated operating times for Node 17 is 53.2%, indicating that for a fault at Node 17, the interrupting time would have been much faster. The percent error from the observed and estimated operating times for Node 10 is only 9.71%, indicating that the fault must have occurred within the zone of Fuse N142. A summary of this data is shown in Table 4.12. Table 4.12: Percent Mismatch Table for Protective Device Localization Protective Device Percent Mismatch Fuse N14(Node 17) Fuse N142(Node 10) 53.2% 9.71% Load flow rejection provides a additional layer of security for localization. After the fuse blows, there is an expected current rejection at the substation for applicable phase. Observed current rejections poorly matched a load rejection of Fuse N14 and is reflected in the mismatched calculated by the fault locator. For Node 17, the rejection mismatch for Phase A is 75.1%. This poor match indicates that if the fault had occurred at Node 10, there would have been a much smaller load rejection. Node 10 is the obvious choice with a Phase A load rejection mismatch of 3.26%. A summary of this data is in Table 4.13. Table 4.13: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Fuse N14(Node 17) Fuse N142(Node 10) Phase A: 75.1% Phase A: 3.26% Using localization it is easy to distinguish that the fault cannot be at Node 17. With the above data, Node 17 can be thrown out as a possibility. 87 4.5.10 Line-to-Ground Fault at Node 6 The second fuse saving scheme test was performed with a line-to-ground fault at Node 6. For a fault at this node, the fault locator will produce two possible fault locations: Node 6 and Node 7. Node 7 can be easily eliminated using the localization algorithm due to the faster speed 50T fuse protecting this node. As a result, the fault locator will observe a slower fuse operation, indicating that the fault is in the zone of a slower speed fuse. Since the only other fault possibility is Node 6, which is in the zone of a 200T fuse, it is ranked as best match. As shown in Figure 4.12, the substation breaker instantaneous ground element interrupts the fault before the fuse is allowed to operate. After a open interval time, the breaker recloses with the instantaneous ground element disabled. The ground time-overcurrent element remains enabled and allows the fuse to blow. After the fuse blows, the ground fault is cleared. Figure 4.12: Fault Locator Observed Fault Current for a Fault at Node 6. Test Results Data provided to the user of the FLA ranks the fault possibilities from best match to worst match. For each fault location possibility, the FLA must determine the correct upstream pro- 88 tective device. Both Node 6 and 7’s upstream protective devices were identified as Fuse N1 and Fuse N23, respectively. Once a protective device is associated with a node, the algorithm begins to localize using the observed operating times. The protective device localizing data shows that the fault could not have occurred a Node 7. The percent error from the observed and estimated operating times for Node 7 is 89.6%, indicating that for a fault at Node 7, the interrupting time would have been much faster. The percent error from the observed and estimated operating times for Node 6 is only 32.3%, indicating that the fault must have occurred within the zone of Fuse N1. A summary of this data is shown in Table 4.14. Table 4.14: Percent Mismatch Table for Protective Device Localization Protective Device Percent Mismatch Fuse N1(Node 6) Fuse N23(Node 7) 32.3% 89.6% Load flow rejection provides a additional layer of security for localization. After the fuse blows, there is an expected current rejection at the substation for the applicable phase. Observed current rejections poorly matched a load rejection of Fuse N23 and is reflected in the mismatched calculated by the fault locator. For Node 7, the rejection mismatch for Phase A is 70.7%. This poor match indicates that if the fault had occurred at Node 7, there would have been a much smaller load rejection. Node 6 is the preferred choice with a Phase A load rejection mismatch of 8.27%. A summary of this data is in Table 4.15. Table 4.15: Percent Mismatch Table for Load Rejection Localization Protective Device Percent Mismatch Fuse N1(Node 6) Fuse N23(Node 7) Phase A: 8.27% Phase A: 70.7% Using localization it is easy to distinguish that the fault cannot be at Node 7. With the 89 above data, Node 7 can be thrown out as a possibility. 4.5.11 Limitations of the FLA on Fuse Blowing or Fuse Saving Coordinated Feeders One of the inherent drawbacks of the FLA is that the fault current must reach steady state for the fault location to be determined. In fuse blowing and fuse saving schemes, high speed fuses(N, QR and K) can melt before the current reaches a steady state value. This phenomena was observed in the Notional Feeder at Node 8, which is protected by a 50T fuse. The available fault current at this node makes the clearing time of this fuse very quick, and subsequently the fault current does not reach steady state. As a result, the fault locator failed to determine the location of the fault. Figure 4.13 shows the observed fault current by the fault locator for a fault at Node 8, notice that the current never reaches steady state. Figure 4.13: Fault Locator Observed Fault Current for Node 8 Fault(Fuse Blowing Coordination). 90 4.6 Notional Feeder Test Results Summary The following sections give a brief summary of the test results obtained during each test case using the Notional Feeder(NF). 4.6.1 Test Case 1 Summary During Test Case 1, the proposed FLA was tested on the NF containing no protective devices with no localization. Phase-to-Ground faults were applied at Node 4, Node 11, Node 15 and Node 17. The FLA was also tested with Phase-to-Phase faults at Node 15 and Node 17. During all Phase-to-Phase and Phase-to-Ground tests, the FLA correctly identified the faulty node. 4.6.2 Test Case 2 Summary During Test Cases 2, substation breakers and reclosers were added to the NF as recommended by Progress Energy. Phase-to-ground faults were placed in the system at Node 17, Node 7 and Node 16. During all Phase-to-Ground tests, the FLA correctly identified the faulty node. Detailed test data for Node 17 and Node 7 showed that the localization algorithm can effectively resolve multiple possibilities into one certain fault location. However, the FLA localization does have limitations. During a ground fault at Node 16, the localization algorithm was unable to localize multiple possibilities. This was due to multiple possibilities existing in the same zone of protection. 4.6.3 Test Case 3 Summary During Test Case 3, the NF was reconfigured to accommodate fuse saving and fuse blowing schemes. Fuses were added at specific points in the NF using SandC T Speed fuse characteristics. With fuse blowing coordination, the FLA was tested by applying phase-to-ground faults at Node 17, Node 6 and Node 8 in the feeder model. The FLA correctly identified the faulty nodes for all tests, except Node 8. Detailed test data for Node 17 and Node 6 showed that the localization algorithm can effectively resolve multiple possibilities into one certain fault location for fuse blowing coordinated feeders. During a ground fault at Node 8, it was noticed that the FLA failed to locate the fault. One of the inherent drawbacks of the FLA is that the fault current must reach ”steady state” for the fault location to be determined. The available fault current at this node made the clearing time of the fuse very quick, and subsequently the fault current does not reach steady state. As a result, the FLA was unable to identify the faulty node for a line-to-ground fault at Node 8. 91 The final testing during Test Case 3 required re-coordinating the NF for fuse saving. With fuse saving coordination, the FLA was tested by applying phase-to-ground faults at Node 10 and Node 6 in the feeder model. The FLA correctly identified the fault nodes for all tests. Test results for Node 10 and Node 6 showed that the localization algorithm can effectively resolve multiple possibilities into one certain fault location for fuse saving coordinated feeders. 92 4.7 4.7.1 Test Case 4: Fault Locating on Large Scale Feeders Introduction: Stewart Street 12.47kV Feeder During Test Cases 1, 2 and 3, the Notional Feeder system model only consisted of 18 nodes, which is much smaller than most conventional feeders. Although it showed promising results, the algorithm must be tested on a much larger feeder to determine its accuracy and performance. To test the proposed FLA, a feeder was model was built in DEW by Allegheny Energy for short circuit analysis and load flow studies. The model consists of 405 power poles, 233 Single Phase Transformers, 211 3-Phase Line Sections, 51 2-Phase Lines and 480 Single Phase Lines. The protective equipment in the network consists of one recloser, and 69 T Speed Fuse Cutouts with fuse blowing coordination. A picture of the Stewart Street feeder is shown in Figure 4.14. Figure 4.14: Stewart Street 12.47kV Feeder Modelled in DEW. 93 4.7.2 Introduction: Test Conditions and Procedures The FLA proposed in this paper uses sampled waveform data to calculate the location of the fault. As of present, DEW does not offer a time domain based solution when calculating faults. As a result, a MATLAB Simulink equivalent model has been proposed to act as a interface between DEW and the FLA. Short circuit information and power flow data are passed to the MATLAB model to form the equivalent model. Details about the equivalent model are covered in Section 4.7.5. To obtain the short circuit data, the DEW Fault Analysis tool is used. This tool allows the user to calculate the reflected fault current at the substation bus under loaded conditions. When calculating the fault current under loaded conditions, DEW assumes that the load currents do not change after the fault is applied(constant current load). In the background of DEW, the power-flow algorithm is run on the feeder to obtain all pre-fault quantities. More detailed information about the formation of the FLA fault tables is discussed in Section 4.7.3. Figure 4.15: Test Procedure for Stewart Street Feeder using DEW. To test the FLA, a bolted line-to-ground fault is placed at various places in the Stewart Street Feeder. Faults are placed at a chosen power pole such as P4622(PXXX Format). The short circuit data(fault current magnitude and angle) is passed to the MATLAB Simulink equivalent model in addition to pre-fault load data. The pre-fault load current(magnitude and angle) are obtained via the Power Flow Tool in DEW. After passing the short circuit and prefault data to MATLAB, the Simulink model is executed along with the FLA. The results of the FLA are recorded in the proceeding sections. A high level overview of the testing procedure is shown in Figure 4.15. 94 4.7.3 Fault Tables for the Stewart Street Feeder As previously mentioned, the FLA determines the location of the fault from the observed fault current at the substation bus. To obtain the fault current magnitude at the substation bus under loaded conditions, DEW assumes that the load currents do not change during fault conditions(constant current load model)[22]. The resultant fault current is the sum of the currents before the fault occurred(pre-fault) and the currents due to the fault itself. The DEW network fault analysis tool uses the pre-fault load flow solution and sums this with the fault current due to the fault itself. Using the display toolbox in DEW, the reflected fault current at the substation bus is calculated for a phase-to-ground fault under loaded conditions and is shown in Figure 4.16. Figure 4.16: Reflected Fault Current at the Substation Bus for a Fault at Pole P4622. Since single line-to-ground are the most common fault type, focus was given to this fault type. Each line section in the Stewart Street feeder was faulted with a bolted line to ground fault and the resultant reflected fault current observed at the substation bus was recorded to form the FLA’s fault tables. 4.7.4 Load Flow Analysis on the Stewart Street 12.47kV Feeder To obtain the fault current magnitude under loaded conditions, DEW assumes that the load currents do not change during fault conditions(constant current load model)[22]. The load flow solution at the substation is needed later when building the MATLAB equivalent model in MATLAB. After executing the DEW power flow tool, the resultant power flow solution is given in Table 4.16. 95 Table 4.16: Substation Bus Load Flow Solution for Stewart Street Feeder. 4.7.5 Bus Current Phase A Current Phase B Current Phase C Substation Bus Total Load Total Load 421.90 6 -30.95◦ 2703.51 kW 1620.84 kVAR 310.96 6 -148.86◦ 2029.53 kW 1118.56 kVAR 397.01 6 90.34 2577.58 kW 1467.84 kVAR ◦ MATLAB Fault Modelling of the Stewart Street 12.47kV Feeder DEW software package does not offer time domain waveform fault data that was previously available in other test cases using MATLAB. Currently, DEW only provides fault current in phasor form. The FLA designed here only accepts raw time domain data and will not accept a phasor quantity. Therefore, to test the FLA on the Stewart Street feeder, a MATLAB interface model was developed using current sources and T Speed fuse models. To begin developing the interface model, we can say that the fault locator at the substation bus will observe a sum of the currents before the fault occurred I 0 and the currents due to the fault itself If . If −sub = I 0 + If (4.1) Using the thevanin impedances and pre-fault voltages, we can easily calculate the current flow due to the fault itself indicated by the equation below(Equation 4.2). Using the impedance tool in DEW, the thevanin impedance looking into the fault point Zth can be calculated. The pre-fault voltage V 0 is available via the DEW power flow tool. This allows the user to easily calculate the current flowing due to the fault itself. If = V0 Zth (4.2) We can also say the the fuse protecting the faulted line segment will also observe a sum of the currents before the fault occurred If0use and the currents due to the fault itself If . If −f use = If0use + If (4.3) Also, we must take into account that the fault locator must observe the full load current during the fault. Therefore a current source is placed in the circuit with a magnitude of the full load current with the fuse load current subtracted(Equation 4.4). This allows the fault locator 96 to no only see the full load current during the fault but the correct load rejection after the fuse operates. Irej = I 0 − If0use (4.4) During the pre-fault state, the If0use current source switch is closed which allows the fault locator at the substation bus to observe full load current and the fuse to observe its full load current. The pre-fault model is shown in Figure 4.17. In the faulted model shown in Figure 4.18, the If −f use current source switch is closed which allows the fault locator at the substation bus to observe the current due to the fault itself in addition to the full load. Also, the fuse is observing the current due to the fault itself in addition to its connected load. As shown in the post-fault model in Figure 4.19, the correct observed current by the fault locator is I 0 − If0use . This requires neither of the two current sources and both are disconnected. Figure 4.17: Pre-Fault Short Circuit Model. Figure 4.18: Faulty Short Circuit Model. 97 Figure 4.19: Post-Fault Short Circuit Model. 4.7.6 Fault at Pole P4622 on the Stewart Street 12.47kV Feeder FLA Testing Introduction The first test using the Stewart Street Feeder was performed using a single line-to-ground fault at distribution Pole P4622. This node is located on a remote portion of a lateral tap approximately midway down the feeder as shown in Figure 4.20. Node P4622 is protected by a 65T T-Link Fuse that is named FUSE654421506 by DEW(UID-Unique Identifier). MATLAB Equivalent Model: Load Flow and Fault Analysis Data To begin, several parameters were collected from the DEW load flow and fault analysis tools. First, the load flow analysis tool was used to obtain the current flow through the fuse during normal load conditions. By selecting the fuse after load flow is performed, we obtain the prefault voltage and current solution. The pre-fault values obtained via load flow is listed in Table 4.17. Table 4.17: Pre-Fault Load Flow Values Quantity Value Pre-Fault Voltage V 0 Pre-Fault Current If0use 6.9616 − 4.19◦ kV 27.576 − 31.63◦ A One of the quantities needed in the MATLAB interface model is the current due to the fault itself, If . To calculate this quantity, the thevanin impedance is needed Zth (Refer to Equation 4.2). The thevanin impedance can be obtained by using the Fault Analysis tool in DEW and 98 Figure 4.20: P4622 Node Location in Stewart Street 12.47kV Feeder Modelled in DEW. is given in Table 4.18 . Using the pre-fault voltage and thevanin impedance, we can calculate the reflected fault current observed at the substation due to the fault itself : If = V0 Zth . This leads to the following equation: If = 6.9616 − 4.19◦ kV = 1400.866 − 71.52◦ 4.9696 67.33◦ (4.5) Using the DEW fault analysis tool, we can easily check this calculation to ensure that it is valid. Referring to Figure 4.21, we can see that DEW obtains a solution of 1400.51 A observed at the substation recloser. Again, this solution is the fault current due to the fault itself, and load currents have not been considered. 99 Table 4.18: Fault Analysis Calculated Parameters Quantity Value Thevanin Impedance Zth Fault Current If 4.969096 67.33◦ Ohms 1400.866 − 71.52◦ A Figure 4.21: Reflected Fault Current at the Substation due to the fault itself. As we previously indicated, during a fault the upstream fuse will observe If −f use = If0use +If where If = 1400.866 − 71.52◦ and the pre-fault load flow through the fuse is If0use = 27.576 − 31.63◦ . If we sum these values, we will obtain the observed fault current under loaded conditions for the fuse. If −f use = If0use + If = 1400.866 − 71.52◦ + 27.576 − 31.63 = 1422.126 − 70.80◦ (4.6) We can quickly check this result in DEW by applying a fault at Node P4622 under loaded conditions. DEW obtains a loaded fault solution of If −f use = 14206 − 70.8◦ as shown in Figure 4.22. Using load flow data for the substation bus in Table 4.16 at the beginning of the chapter, we can calculate the observed fault current at the substation under loaded conditions. To calculate the observed fault current we sum the current due to the fault itself and the pre-fault load flow: If −sub = I 0 + If . The pre-fault load flow I 0 = 421.96 − 30.95◦ and the fault current due to the fault itself is If = 1400.866 − 71.52. 100 Figure 4.22: Observed Fault Current at FUSE654421506 during loaded conditions. If −sub = If0use + If = 421.96 − 30.95◦ + 1400.866 − 71.52◦ = 1743.076 − 62.46◦ (4.7) We can quickly verify this result in DEW by applying a fault at P4622 and clicking the substation recloser to obtain the reflected fault current at the substation. DEW calculates If −sub = 1741.526 − 62.46◦ for the observed fault current at the substation during loaded conditions. Figure 4.23: Observed Fault Current at Substation during loaded conditions. 101 The final value that is needed for the switching model is the bus current Irej . This current is calcuated as: Irej = I 0 − If0use = 421.96 − 30.95 − 27.576 − 31.63◦ = 394.446 − 30.90◦ A summary of the derived MATLAB interface model values is given in Table 4.19. Table 4.19: MATLAB Model Parameters Quantity Fuse Pre-Fault Load If0use Fuse Loaded Fault Current If −f use Load Rejection Irej 102 Value − 31.63◦ A 1422.126 − 70.80◦ A 394.446 − 30.90◦ A 27.576 (4.8) 4.7.7 FLA Test Results for P4622 Fault The FLA calculates 30 possible fault locations throughout the feeder. In Figure 4.24, the fault possibilities are shown plotted on the feeder map, each represented by a red circle. Figure 4.24: Possible Fault Locations in Stewart Street 12.47kV Feeder for a fault at P4622. The FLA identifies Node P4622 as the best matched possibility for the fault location. A screen-shot of the MATLAB is console is taken after the FLA is run and is shown in Figure 4.25. The FLA also lists Node P4619 as a best match because P4619 and P4622 are only 1 power pole span apart. Since both nodes are protected by the same fuse, and the two nodes are nearly electrically identical in short circuit current, the fault locator cannot localize any farther. The worst matches occurred at nodes P4238, P4236, P4235, N7970, N7955, N7972, N7973, P4240, P4247, and L1254805 which occurred in the zone of the recloser. The recloser phase and 103 Figure 4.25: Best Matched Locations for a fault at P4622 as calculated by the FLA. ground curves operate much slower than the 65T fuse characteristic that protects P4622. Since the recloser also carries more than 400A of load current, the fault locator ranks these nodes as the worst matched. Several other nodes were listed a likely possibilities: P4498, P4509, P4513, P4515, P4520, P4522, L1279017, N7974, 1L5936, N7976, N7977, P4241, L1254804, L1254806, L1254807, L1254808, L1254809, and P4268. These possibilities along with their total respective rank is shown in Appendix D, Table D.1. 104 4.7.8 Fault at Pole P4266 on the Stewart Street 12.47kV Feeder The second test using the Stewart Street Feeder was performed using a single line-to-ground fault at distribution pole P4266. This node is located on a remote portion of a lateral tap at the end of the feeder as shown in Figure 4.26. Node P4266 is protected by a 200T T Speed Fuse that is named FUSE1052482746 by DEW(UID-Unique Identifier). Figure 4.26: P4266 Node Location in Stewart Street 12.47kV Feeder Modelled in DEW. MATLAB Equivalent Model: Load Flow and Fault Analysis Data To begin, several parameters were collected from the DEW load flow and fault analysis tools. To begin, the load flow analysis tool was used to obtain the current flow through the fuse during normal load conditions. By selecting the fuse after load flow is performed, we get the current solution shown in Figure 4.27. This indicates that our pre-fault load flow through the fuse is If0use = 9.036 − 32.34◦ . 105 Figure 4.27: Upstream Fuse(FUSE1052482746) Load Flow Solution. The next element we must fetch from the load flow tool is the pre-fault voltage at the fault point, V 0 . To retrieve this value, the load flow tool is executed and pole P4266 is selected. As shown in Figure 4.28, V 0 = 6.9476 − 4.45◦ kV. A summary of the pre-fault values are given in Table 4.20. Figure 4.28: Pre-Fault Voltage at P4266. 106 Table 4.20: Pre-Fault DEW Load Flow Values Pre-Fault Voltage V 0 Pre-Fault Current If0use 6.9476 − 4.45◦ kV 9.036 − 32.34◦ A Another associated element that is needed is the thevanin impedance, Zth . This impedance can be obtained by using the Fault Analysis tool in DEW. The tool indicated that the thevanin impedance for a fault at Node P4266 is Zth = 4.72666 77.40◦ Ohms. If we use the pre-fault voltage and thevanin impedance, we can calculate the current due to the fault itself : If = V0 Zth . This leads to the following equation: If = 6.9476 − 4.45◦ kV = 1469.756 − 81.85◦ 4.72666 77.40◦ (4.9) Using the DEW fault analysis tool, we can easily check this calculation to ensure that it is valid. Referring to Figure 4.29, we can see that DEW obtains a solution of 1469.24 A observed at the substation recloser. Again, this solution is the fault current due to the fault itself, and load currents have not been considered. Figure 4.29: Reflected Fault Current at the Substation due to the fault itself. As we previously indicated, during a fault the upstream fuse will observe If −f use = If0use +If where If = 1469.756 − 81.85◦ and the pre-fault load flow through the fuse is If0use = 9.036 − 32.34◦ . If we sum these values, we will obtain the observed fault current under loaded conditions 107 for the fuse. If −f use = If0use + If = 1469.756 − 81.85 + 9.036 − 32.24◦ = 1475.636 − 81.59◦ (4.10) We can quickly check this result in DEW by applying a fault at Node P4266 under loaded conditions and select the upstream fuse(FUSE1052482746). DEW obtains a loaded fault solution of If −f use = 1473.26 − 81.54◦ , as shown in Figure 4.30. Figure 4.30: Observed Fault Current at upstream fuse(FUSE1052482746) during loaded conditions. Using load flow data previously given in the table at the beginning of the chapter(Table 4.16), we can calculate the observed fault current at the substation under loaded conditions. To calculate the observed fault current we sum the current due to the fault itself and the pre-fault load flow: If −sub = I 0 + If . The pre-fault load flow I 0 = 421.96 − 30.95◦ and the fault current due to the fault itself is If = 1469.756 − 81.85◦ . If −sub = I 0 + If = 421.96 − 30.95◦ + 1469.756 − 81.85◦ = 1766.46 − 71.17◦ (4.11) We can quickly verify this result in DEW by applying a fault at P4266 and clicking the substation recloser to obtain the reflected fault current at the substation. DEW calculates If −sub = 1764.246 − 71.24◦ for the observed fault current at the substation during loaded conditions. The final value that is needed for the switching model is the bus current Irej . This current 108 is calculated as: Irej = I 0 − If0use = 421.96 − 30.95 − 9.036 − 32.34◦ = 412.876 − 30.91◦ 4.7.9 (4.12) FLA Test Results for P4266 Fault The fault locator calculates 35 possible fault locations throughout the feeder. In Figure 4.31, the fault possibilities are shown plotted on the feeder map, each represented by a red circle. Figure 4.31: Possible Fault Location in Stewart Street 12.47kV Feeder for a fault at P4266. The FLA identifies Node P4266 as the best matched possibility for the fault location(Figure 4.32). The fault locator also lists Node L1254804(second) and Node P4268(third) as favourable matches because P4266, L1254804 and P4268 are only 3 power pole spans apart. Since both nodes are protected by the same fuse, and the three nodes are nearly electrically identical in short circuit current, the FLA cannot localize any farther. Figure 4.32 shows the best matched nodes as calculated by the FLA. 109 Figure 4.32: Best Matched Locations for a fault at P4266 as calculated by the FLA. The worst matches occurred at nodes P4380, P4378, P4375, P4238, P4236, P4235, N7970, N7955, N7972, N7973, P4240, P4247, and L1254805 which occurred in the zone of the recloser. The recloser phase and ground curves operate much slower than the 200T fuse characteristic that protects P4622. Since the recloser also carries more than 400A of load current, the fault locator ranks these nodes as the worst matched. Figure D.3 in Appendix D.2 shows a few of the worst matched nodes as calculated by the FLA. Several other nodes were listed a likely possibilities: P4496, P4498, P4508, P4509, P4513, P4515, P4520, L1279017, N7974, 1L5936, N7976, N7977, P4241, L1254806, L1254807, L1254808, L1254809, P4619, and P4622. These possibilities along with their total respective difference from the calculated best match is shown in Appendix D.2 Table D.2. 110 4.7.10 FLA Test Results Summary for Stewart Street Feeder Two line-to-ground faults were run on the Stewart Street 12.47kV in DEW to test the FLA. During both tests, more than 30 fault possibilities throughout the feeder were calculated by the FLA. The FLA calculated the fault location correctly during both simulations and was able to localize the fault to within ± 1 power pole span. Since these are ideal conditions, more testing is needed with the introduction of measurement and modelling errors. 111 4.8 4.8.1 Sensitivity Analysis: System Load Perturbations Introduction: Sensitivity Analysis One of the disadvantages of the proposed FLA is that the fault current solution depends directly on system loading at the time of the fault. In addition, the localization algorithm directly relies on the accuracy of the load flow solution. During Test Cases 1-3, we showed that the FLA was able to correctly identify all fault locations, however, we assumed the load was known and static. In this section we assume the load to be a gaussian random variable by which the known load is perturbed about a mean load operation point. By perturbing the load in this fashion, this introduces uncertainty about system loading conditions. 4.8.2 System Load Perturbations: Test Conditions and Procedures As we previously described, the uncertainty about system load can be modelled by a gaussian random variable Xi . To create the forecasted load data, we perturb the actual load table by the error variable e¯z . This forms the random variable equation: Xi = Zα ± e¯z (4.13) For a gaussian distribution, the probability that the load falls within n standard deviations of the mean(nσ) is described by: P (µ − xn < Xi < µ + xn ) 1 P (µ − xn < Xi < µ + xn ) = √ σ 2π Z µ+nσ e −(x−µ)2 2σ 2 dx (4.14) µ−nσ Evaluating the above integral leads to the following table via a error function: xn P (µ − xn < Xi < µ + xn ) σ 0.6826895 2σ 0.9544997 3σ 0.9973002 Assuming that 3σ are the limits of the probability function(.997 ≈ 1), the load error is described in Equation 4.15 below. It was assumed the perturbation error to be 30%, which gives a standard deviation of σ = .1. σ= perturbation error 3 (4.15) To simulate load uncertainty, each load’s real and reactive power is assumed to be normally distributed with a 30% error(σ = 0.1) with a mean power flow value of 1.0 per-unit(µ = 1.0). 112 A ”swing load” was chosen in the feeder such that the net system load is the same during each iteration. The swing load allows all loads in the system to be perturbed while assuring that the net system load is the same every iteration. By keeping the net power flow the same, we can test the FLA for every possible load scenario for a known load condition. Therefore, we can say that if we sum all k buses power flow every iteration, it will be equal to the net system power P0 , which will remain constant. P0 = k X Pn (4.16) n=1 In Figure 4.33, the histogram of 100 iterations of load perturbations is shown along with the probability density function. All system loads(except the swing load) are perturbed in this fashion and the fault locator’s performance is evaluated. In the next few sections, 100 iterations or more were performed to determine the FLA’s performance under various loading conditions. Figure 4.33: Normally Distributed Per-Unit Load Power. 113 4.8.3 System Load Perturbations on Test Case 1-No Localization During Test Case 1(Section 4.3), the proposed FLA was tested with no localization on the NF. Simple fault tables are used to rank faults from best to worst match. During Test Case 1, the FLA correctly identified the faulty node during each test. However, the system load conditions were assumed to be known. In this section, we repeat Test Case 1 with the addition of load uncertainty. As previously mentioned, the load uncertainty is modelled as a gaussian random variable by which the known load is perturbed about a mean load operation point. In this section, we consider several line-to-ground faults at various nodes in the network with perturbed loading. A line-to-ground fault was tested at the following nodes: Node 10 and Node 4. A simple MATLAB script was written to run the NF 100 times and record the results. A 30% load error was assumed(σ = 0.1) with a mean power flow value of 1.0 per-unit(µ = 1.0). The results are presented as percent success and failure over 100 iterations of perturbed loading. For the location of the faulted nodes, refer to the system one-line Figure 4.2. Fault at Node 10 with Perturbed Loading A bolted line to ground fault is placed at Node 10. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Results Observing the fault table for the NF(Table 4.1), Nodes 10 and 17 are almost indistinguishable under bolted ground fault conditions at either node. During the 100 iterations, the FLA was able to correctly identify the fault location as Node 10 67.0% of the time. The remaining 33%, the faulted node was identified as Node 17 incorrectly. Table 4.21: Success-Failure Rate on Node 10, Test Case 1(No Localization) Success/Failure Percent Identified Node Success Failure 67.00% 33.00% Node 10 Identified Correctly Node 17 Identified Incorrectly 114 Fault at Node 17 with Perturbed Loading A bolted line to ground fault is placed at Node 17. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Results Observing the fault table for the NF(Table 4.1), Nodes 17 and 10 are almost indistinguishable under bolted ground fault conditions at either node. During the 100 iterations, the FLA was able to correctly identify the fault location as Node 17 49.0% of the time. The remaining 51%, the faulted node was identified as Node 10 incorrectly. Table 4.22: Success-Failure Rate on Node 17, Test Case 1(No Localization) Success/Failure Percent Identified Node Success Failure 49.00% 51.00% Node 17 Identified Correctly Node 10 Identified Incorrectly Fault at Node 4 with Perturbed Loading A bolted line to ground fault is placed at Node 4. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 4 100.0% of the time. No other nodes were identified as faulty. Table 4.23: Success-Failure Rate on Node 4, Test Case 1(No Localization) Success/Failure Percent Identified Node Success 100.00% Node 4 Identified Correctly 115 4.8.4 System Load Perturbations on Test Case 2 In Test Case 2(Section 4.4), we introduce the capability of localization into the FLA which relies on load flow data results from a power flow algorithm. After the occurrence of the fault, the fault locator will attempt to determine which protective device operated to localize the fault to a particular zone of protection. To do this, the FLA relies heavily on load flow information that is used to calculate operating times and load rejection matching. Since measuring live load flow data at every point in the feeder is impractical(especially in large networks), the localization algorithm accepts tabulated load flow results from a radial power flow algorithm. Given that the load flow data is not real-time, there likely exists a difference in the actual and expected load values at any given point in the network. The adaptability of the FLA to perform under changing system load conditions is very important for practical use in a live network. To determine the algorithm’s flexibility, the localization algorithm was tested in the presence of perturbing load conditions to simulate load uncertainty. During Test Case 2, reclosers and substation breakers were inserted into the Notional Feeder(see Section 4.4 for details). This provided additional information to the fault locator, allowing an exact zone of protection to be pinpointed to localize the fault location. In this section, we repeat Test Case 2 with the addition of load uncertainty. As previously mentioned, the load uncertainty is modelled as a gaussian random variable by which the known load is perturbed about a mean load operation point. In this section, we consider several line-to-ground faults at various nodes in the network with perturbed loading. A line-to-ground fault was tested at the following nodes: Node 10 and Node 17. A simple MATLAB script was written to run the NF 100 times and record the results. A 30% load error was assumed(σ = 0.1) with a mean power flow value of 1.0 per-unit(µ = 1.0). The results are presented as percent success and failure over 100 iterations of perturbed loading. For the location of the faulted nodes, refer to the system one-line Figure 4.2. Fault at Node 10 with Perturbed Loading A bolted line to ground fault is placed at Node 10. Exactly 100 iterations are run to evaluate the FLA performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 10 100.0% of the time. No other nodes were identified as faulty. 116 Table 4.24: Success-Failure Rate on Load Perturbation Test for Node 10 Fault Success/Failure Percent Identified Node Success 100.00% Node 10 Identified Correctly Fault at Node 17 with Perturbed Loading A bolted line to ground fault is placed at Node 17. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Test Case 1. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 17 100.0% of the time. No other nodes were identified as faulty. Table 4.25: Success-Failure Rate on Load Perturbation Test for Node 17 Fault Success/Failure Percent Identified Node Success 100.00% Node 17 Identified Correctly 117 4.8.5 System Load Perturbations on Test Case 3-Fuse Saving During Test Case 2, we introduced protective devices such as reclosers and breakers to the Notional Feeder to protect it. During Test Case 3, we changed this and added fuses to the system to implement a fuse saving. To implement a common fuse saving scheme, the Notional Feeder protection system was reconfigured to contain 26 SandC T-Link Fuses and a main reclosing substation breaker. Pickups and time-dial settings were changed in the substation breaker to allow fuse saving coordination between all downstream fuses. The reclosing substation feeder breaker was set to one shot of fast before switching to the slow curve and allowing the fuse to blow. For more detailed information, see Section 4.5.6. Given the popularity of fuse saving schemes, further tests were needed to evaluate the effectiveness of the FLA under various load conditions. To test the FLA on a fuse saving coordinated feeder, the simulation conditions for Test Case 2 are reproduced again here in Test Case 3 with the addition of load perturbations. In this section, we consider several line-toground faults at various nodes in the network with perturbed loading. A line-to-ground fault was tested at the following nodes: Node 10 and Node 17. A simple MATLAB script was written to run the NF 100 times and record the results. A 30% load error was assumed(σ = 0.1) with a mean power flow value of 1.0 per-unit(µ = 1.0). The results are presented as percent success and failure over 100 iterations of perturbed loading. For the location of the faulted nodes, refer to the system one-line Figure 4.2. Fault at Node 10 with Perturbed Loading A bolted line to ground fault is placed at Node 10. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 10 100.0% of the time. No other nodes were identified as faulty. Table 4.26: Success-Failure Rate on Load Perturbation Test for Node 10 Fault with Fuse Saving Feeder Coordination. Success/Failure Percent Identified Node Success 100.00% Node 10 Identified Correctly 118 Fault at Node 17 with Perturbed Loading A bolted line to ground fault is placed at Node 17. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 17 100.0% of the time. No other nodes were identified as faulty. Table 4.27: Success-Failure Rate on Load Perturbation Test for Node 17 Fault with Fuse Saving Feeder Coordination. Success/Failure Percent Identified Node Success 100.00% Node 17 Identified Correctly 119 4.8.6 System Load Perturbations on Test Case 3-Fuse Blowing During Test Case 2, we introduced protective devices such as reclosers and breakers to the Notional Feeder to protect it. During Test Case 3, we changed this and added fuses to the system to implement a fuse saving. To implement a common fuse saving scheme, the Notional Feeder protection system was reconfigured to contain 26 SandC T-Link Fuses and a main reclosing substation breaker. Pickups and time-dial settings were changed in the substation breaker to allow fuse blowing coordination between all downstream fuses. For more detailed information, see Section 4.5. Given the popularity of fuse saving schemes, further tests were needed to evaluate the effectiveness of the FLA under various load conditions. To test the FLA on a fuse saving coordinated feeder, the simulation conditions for Test Case 2 are reproduced again here in Test Case 3 with the addition of load perturbations. In this section, we consider several line-toground faults at various nodes in the network with perturbed loading. A line-to-ground fault was tested at the following nodes: Node 10 and Node 17. A simple MATLAB script was written to run the NF 100 times and record the results. A 30% load error was assumed(σ = 0.1) with a mean power flow value of 1.0 per-unit(µ = 1.0). The results are presented as percent success and failure over 100 iterations of perturbed loading. For the location of the faulted nodes, refer to the system one-line Figure 4.2. Fault at Node 10 with Perturbed Loading A bolted line to ground fault is placed at Node 10. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 10 100.0% of the time. No other nodes were identified as faulty. Table 4.28: Success-Failure Rate on Load Perturbation Test for Node 10 Fault with Fuse Blowing Feeder Coordination. Success/Failure Percent Identified Node Success 100.00% Node 10 Identified Correctly 120 Fault at Node 17 with Perturbed Loading A bolted line to ground fault is placed at Node 17. Exactly 100 iterations are run to evaluate the FLA’s performance under varying load conditions. Simulation conditions for this fault were identical to the previous simulation testing in Section 4.8.3. Results During the 100 iterations, the FLA was able to correctly identify the fault location as Node 17 100.0% of the time. No other nodes were identified as faulty. Table 4.29: Success-Failure Rate on Load Perturbation Test for Node 17 Fault with Fuse Blowing Feeder Coordination. Success/Failure Percent Identified Node Success 100.00% Node 17 Identified Correctly 121 Chapter 5 FLA Testing Conclusions A total of four test cases were proposed to test the FLA using models in MATLAB and DEW software packages. During Test Cases 1-3, a Progress Energy modelled feeder in MATLAB was used to test the FLA under various conditions(called the Notional Feeder). During Test Case 4, the proposed FLA was tested on a large scale feeder(Stewart Street 12.47kV Feeder) modelled in DEW by Allegheny Power. It was noted that during Test Cases 1-4, system loading was considered to be known and static. Since this is not always the case in practice, a final test case was proposed with the addition of perturbed loading to introduce load uncertainty. During Test Case 1, the FLA was tested on the NF containing no protective devices with no localization. Test results showed that the FLA correctly identified the faulty node for each test during Test Case 1. However, test data showed that several nodes were nearly identical in short circuit current, i.e. Node 17 Phase-to-Ground fault test(Section 4.3.4). This test case illustrated the importance of the localization algorithm to accurately determine the true fault location if there are multiple possibilities. In Test Case 2, recloser and substation breaker models were added to the NF. Test results during this test case showed that the localization algorithm can effectively resolve multiple possibilities into one certain fault location. However, it was discovered that the FLA localization algorithm does have limitations. During a ground fault at Node 16(see Section 4.4.5 for details), the localization algorithm was unable to rank multiple possibilities. It was concluded that the localization algorithm does not provide any additional ranking information when multiple possibilities exist in the same zone of protection. In Test Case 3, the NF protection system was reconfigured to contain 26 SandC T-Link fuses and a main reclosing substation breaker to implement a fuse saving and fuse blowing protec- 122 tion scheme. During Test Case 3, the FLA correctly identified the faulty node for each test, except Node 8. While testing a fault at Node 8(see Section 4.5.11 for details), another inherent drawback was noted in the proposed FLA. In fuse blowing and fuse saving schemes, high speed fuses(N, QR and K) can melt before the current reaches a steady state value. This phenomena was observed in the NF model at Node 8, which is protected by a 50T fuse. Consequently, the fault locator failed to determine the location of the fault. Therefore, it was noted that high speed fuses may present a problem when fault locating with the proposed FLA. During Test Cases 1, 2 and 3, the Notional Feeder system model only consisted of 18 nodes, which is much smaller than most conventional feeders. In Test Case 4, a large scale feeder model was provided by Allegheny Power for FLA testing. The DEW feeder model consisted of more than 250 faulty node possibilities. During testing, the FLA correctly ranked and localized during all tests. However, multiple fault possibilities did occur in the same zone of protection during each test included in Test Case 4. This same drawback was noted during Test Case 2. Final testing of the FLA was performed again using NF model. In Test Cases 1-4, the load was assumed to be know and static, which is rarely the case in practice. Using the NF model, the system loads were perturbed to introduce load uncertainty. Test data showed that the localization algorithm provided a significant increased performance for faults at certain nodes in the NF. It was concluded that the proposed FLA, with the addition of localization, is not sensitive to small load changes. However, large errors in load flow modelling can result in incorrect ranking. 123 REFERENCES [1] M. M. Saha, J. J. Izykowski and E. Rosolowski. Fault location on Power Networks. pp. 333-360. 2010. [2] M. Dilek, R. Broadwater and R. Sequin, ”Computing distribution system fault currents and voltages via numerically computed Thevenin equivalents and sensitivity matrices,” Power Systems Conference and Exposition, 2004. IEEE PES, vol.1, pp. 244, 2004. [3] J. J. Grainger, ”Power System Analysis,” pp. 157. 1994. [4] W. F. Tinney, ”Compensation Methods for Network Solutions by Optimally Ordered Triangular Factorization,” Power Apparatus and Systems, IEEE Transactions on (Volume:PAS91 , Issue: 1 ), 1972. [5] G. Gross and H. W. Hong, A Two-Step Compensation Method for Solving Short Circuit Problems,” Apparatus and Systems, IEEE Transactions on (Volume:PAS-101 , Issue: 6 ), 1982. [6] R. C. Dorf , ”The Engineering Handbook,” pp. 112.7-112.10, 2004. [7] J. J. Burke and D. J. Lawre, , ”Characteristics of Fault Currents on Distribution Systems,” Power Apparatus and Systems, IEEE Transactions on (Volume:PAS-103 , Issue: 1 ), 1984. [8] I. D. Serna-Suarez, C. D. Ferreira-Sequeda, S. A. Martnez-Gutierrez, M. F. Suarez-Sanchez and G. Carrillo-Caicedo, ”Impact of static load models on the power distribution fault location problem ,” Transmission and Distribution Conference and Exposition: Latin America (TandD-LA), 2010 IEEE/PES, 2010. [9] N. Karnik, S. Das, S. Kulkarni and S. Santoso, ”Effect of load current on fault location estimates of impedance-based methods,” Power and Energy Society General Meeting, 2011 IEEE, 2011. [10] K. Zimmerman and D. Costello, ”Impedance-Based Fault Location Experience,” Rural Electric Power Conference, 2006 IEEE, 2006. [11] P. Gill, ”Electrical Power Equipment Maintenance and Testing,” pp. 544-545, 2008. [12] (7/1/2012). Discrete Fourier Transform. http : //en.wikipedia.org [13] K. Jinsang, M. E. Baran and G. C. Lampley, ”Estimation of Fault Location on Distribution Feeders using PQ Monitoring Data,” Power Engineering Society General Meeting. IEEE, 2007. [14] T. A. Short, D. D. Sabin and M. F. McGranaghan, ”Using PQ Monitoring and Substation Relays for Fault Location on Distribution Systems”, Rural Electric Power Conference, IEEE, 2007. 124 [15] Electric Power Research Institute, ”Distribution Fault Current Analysis,” EPRI 1209-1, 1983. [16] H. L. Willis, ”Power Distribution Planning Reference Book,” pp. 51-53, 2004. [17] T. A. Short, ”Electric Power Distribution Equipment and Systems,” pp. 252-253, 2004. [18] J. Machowski, J. Bialek and J. Bumby, ”Power System Dynamics: Stability and Control,” pp. 3.4.4.2-3.4.4.3, 2008. [19] Schweitzer Engineering Laboratories, ”SEL-351S Protection System Instruction Manual,” pp. 354-355, 2013. [20] Schweitzer Engineering Laboratories, ”SEL-651R Protection System Instruction Manual,” pp. 413-414, 2012. [21] S&C, ”S&C T-Speed Positrol Fuse Links Time-Current Characteristic Curves,” 1984. [22] M. Dilek, R. Broadwater and R. Sequin , ”Calculating short-circuit currents in distribution systems via numerically computed Thevenin equivalents,” Transmission and Distribution Conference and Exposition, IEEE PES (Volume:3 ), 2003. [23] Schweitzer Engineering Laboratories, SELU: PROT 401 Course Handbook,” pp. 18, 2013. [24] J. O’Malley, ”Schaum’s Outline of Basic Circuit Analysis,” pp. 295-296, 1992. [25] R. Das, ”Determining the Locations of Faults in Distribution Systems,” 1998. [26] A. A. Girgis, C. M. Fallon and D. L. Lubkeman, ”A Fault Location Technique for Rural Distribution Feeders,” Industry Applications, IEEE Transactions on (Volume:29 , Issue: 6 ), 1993. [27] J. S. Jung, ”Branch Current State Estimation Method for Power Distribution Systems,” 2009. [28] MathWorks, ”MATLAB 2010A Help File,” 2010. [29] U. Rao, ”Computer Techniques And Models In Power Systems,” pp. 444-447, 2008. [30] E. O. Schweitzer, ”A Review of Impedance-Based Fault Locating Experience,” Nebraska System Protection Seminar, 1990. Iowa- [31] W. Chen, ”Active Network Analysis,” pp. 284-285, 1991. [32] M. M. Saha, F. Provoost and E. Rosolowski, ”Fault location method for MV cable network Developments in Power System Protection, Seventh International Conference, 2001. 125 APPENDICES 126 Appendix A Notional Feeder Load Flow Data A.1 Notional Feeder Real Power Flow Data Bus Power Phase A Power Phase B Power Phase C Voltage Load 1 57.7500 kW 165.5500 kW 112.4200 kW 12.0 kV Load 2 651.4200 kW 171.7100 kW 100.1000 kW 12.0 kV Load 3 544.3900 kW 56.9800 kW 254.1000 kW 12.0 kV Load 4 145.5300 kW 112.4200 kW 245.6300 kW 12.0 kV Load 5 597.5200 kW 510.5100 kW 733.8100 kW 12.0 kV Load 6 535.1500 kW 530.5300 kW 520.5200 kW 12.0 kV Load 7 532.0700 kW 599.8300 kW 338.8000 kW 12.0 kV Load 8 - - 14.6300 kW 12.0 kV Load 9 20.0200 kW 10.0100 kW 85.4700 kW 12.0 kV Load 10 - 13.0000 kW - 0.240 kV Load 11 - 26.0000 kW - 0.240 kV Load 12 - 13.0000 kW - 0.240 kV Load 13 - 19.0000 kW - 0.240 kV Load 14 - 25.0000 kW - 0.240 kV Load 15 - 26.0000 kW - 0.240 kV Load 16 - 13.0000 kW - 0.240 kV Load 17 - 26.0000 kW - 0.240 kV Load 18 - 13.0000 kW - 0.240 kV Load 19 - 13.0000 kW - 0.240 kV Load 20 - 13.0000 kW - 0.240 kV Load 21 .. . .. . 19.0000 kW .. . .. . 0.240 kV .. . 127 Bus Power Phase A Power Phase B Power Phase C Voltage Load 22 - 19.0000 kW - 0.240 kV Load 23 - 19.0000 kW - 0.240 kV Load 24 - 19.0000 kW - 0.240 kV Load 25 32.7250 kW 25.5640 kW 50.7430 kW 12.0 kV Load 26 455.8400 kW 715.1760 kW 841.8410 kW 12.0 kV Load 27 15.8620 kW - - 12.0 kV Load 28 235.0810 kW 207.4380 kW 196.1190 kW 12.0 kV Load 29 319.3960 kW 317.8560 kW 95.3260 kW 12.0 kV Load 30 357.6650 kW 207.2070 kW 59.5980 kW 12.0 kV Load 31 499.5760 kW 424.4240 kW 846.4610 kW 12.0 kV Load 32 168.9380 kW 608.8390 kW 227.2270 kW 12.0 kV Total Load 5168.933 kW 4940.044 kW 4722.795 kW Σ=14831.772 kW 128 A.2 Notional Feeder Reactive Power Flow Data Bus Power Phase A Power Phase B Power Phase C Voltage Load 1 81.6200 kVAR 110.1100 kVAR 66.9900 kVAR 12.0 kV Load 2 332.6400 kVAR 80.0800 kVAR 56.9800 kVAR 12.0 kV Load 3 278.7400 kVAR 29.2600 kVAR 120.1200 kVAR 12.0 kV Load 4 74.6900 kVAR 57.7500 kVAR 120.1200 kVAR 12.0 kV Load 5 304.9200 kVAR 253.3300 kVAR 386.5400 kVAR 12.0 kV Load 6 272.5800 kVAR 261.8000 kVAR 264.8800 kVAR 12.0 kV Load 7 273.3500 kVAR 297.9900 kVAR 173.2500 kVAR 12.0 kV Load 8 - - 7.7000 kVAR 12.0 kV Load 9 10.0100 kVAR 1.5400 kVAR 43.1200 kVAR 12.0 kV Load 10 - 7.0000 kVAR - 0.240 kV Load 11 - 13.0000 kVAR - 0.240 kV Load 12 - 6.0000 kVAR - 0.240 kV Load 13 - 9.0000 kVAR - 0.240 kV Load 14 - 14.0000 kVAR - 0.240 kV Load 15 - 12.0000 kVAR - 0.240 kV Load 16 - 6.0000 kVAR - 0.240 kV Load 17 - 14.0000 kVAR - 0.240 kV Load 19 - 7.0000 kVAR - 0.240 kV Load 20 - 6.0000 kVAR - 0.240 kV Load 21 - 6.0000 kVAR - 0.240 kV Load 22 - 19.0000 kVAR - 0.240 kV Load 23 - 19.0000 kVAR - 0.240 kV Load 24 - 19.0000 kVAR - 0.240 kV Load 25 32.7250 kVAR 25.5640 kVAR 50.7430 kVAR 12.0 kV Load 26 455.8400 kVAR 715.1760 kVAR 841.8410 kVAR 12.0 kV Load 27 15.8620 kVAR - - 12.0 kV Load 28 235.0810 kVAR 207.4380 kVAR 196.1190 kVAR 12.0 kV Load 29 319.3960 kVAR 317.8560 kVAR 95.3260 kVAR 12.0 kV Load 30 357.6650 kVAR 207.2070 kVAR 59.5980 kVAR 12.0 kV Load 31 499.5760 kVAR 424.4240 kVAR 846.4610 kVAR 12.0 kV Load 32 168.9380 kVAR 608.8390 kVAR 227.2270 kVAR 12.0 kV Total Load 2569.644 kVAR 2384.478 kVAR 2248.4 kVAR Σ=7202.522 kVAR 129 A.3 12kV Capacitor Bank Data Bus Power Phase A Power Phase B Power Phase C Voltage Capacitor Bank 1 400 kVAR 400 kVAR 400 kVAR 12 kV Capacitor Bank 2 200 kVAR 200 kVAR 200 kVAR 12 kV Capacitor Bank 3 400 kVAR 400 kVAR 400 kVAR 12 kV Capacitor Bank 4 400 kVAR 400 kVAR 400 kVAR 12 kV Total 1400 kVAR 1400 kVAR 1400 kVAR Σ=4200 kVAR A.4 Transformer Bank Data Transformer MVA Rating Winding 1 Imp. Winding Imp. 2 69kV/12kV(∆-Wye) 20 MVA Z1 =0+0.055j pu Z2 =0+0.005j pu 12kV/240V(Single Phase) 262kVA Z1 =0+0.0192j pu Z2 =Z3 =0+0.0048j pu A.5 Source Impedance Data Source Source Resistance Rs Source Reactance jXs Source 1 69kV 0.0075 Ohms 0.0582j Ohms 130 A.6 A.6.1 Line Impedance Data Positive Sequence Line Impedance Data (1) (1) Line Resistance RLine Ω Inductance jXLine Ω Length(km) Line 1 0.1502 0.6309 7.1410 Line 2 0.0618 0.2597 2.9390 Line 3 0.0546 0.2294 2.5960 Line 4 0.0366 0.1536 1.7390 Line 5 0.0851 0.3575 4.0470 Line 6 0.0978 0.4106 4.6470 Line 7 0.0919 0.3861 4.3700 Line 8 0.0075 0.0315 0.3560 Line 9 0.0261 0.1095 1.2390 Line 10 0.0538 0.0066 0.2030 Line 11 0.1196 0.0146 0.4510 Line 12 0.0859 0.0105 0.3240 Line 13 0.1965 0.0240 0.7410 Line 14 0.0920 0.0113 0.3470 Line 15 0.2259 0.0276 0.8520 Line 16 0.1254 0.0153 0.4730 Line 17 0.0780 0.0095 0.2940 Line 18 0.0260 0.0032 0.0980 Line 19 0.0838 0.0103 0.3160 Line 20 0.1175 0.0144 0.4430 Line 21 0.1188 0.0145 0.4480 Line 22 0.0949 0.0116 0.3580 Line 23 0.3065 0.0375 1.1560 Line 24 0.0939 0.0115 0.3540 Line 25 0.0711 0.2984 3.3780 Line 26 0.0476 0.1998 2.2610 Line 27 0.0050 0.0211 0.2390 Line 28 0.0439 0.1846 2.0890 Line 29 0.1197 0.5028 5.6913 Line 30 0.0593 0.2491 2.8190 Line 31 0.0186 0.0780 0.8830 Line 32 0.0667 0.2801 3.1700 131 A.6.2 Negative Sequence Line Impedance Data (2) (2) Line Resistance RLine Ω Inductance jXLine Ω Length(km) Line 1 0.1502 0.6309 7.1410 Line 2 0.0618 0.2597 2.9390 Line 3 0.0546 0.2294 2.5960 Line 4 0.0366 0.1536 1.7390 Line 5 0.0851 0.3575 4.0470 Line 6 0.0978 0.4106 4.6470 Line 7 0.0919 0.3861 4.3700 Line 8 0.0075 0.0315 0.3560 Line 9 0.0261 0.1095 1.2390 Line 10 0.0538 0.0066 0.2030 Line 11 0.1196 0.0146 0.4510 Line 12 0.0859 0.0105 0.3240 Line 13 0.1965 0.0240 0.7410 Line 14 0.0920 0.0113 0.3470 Line 15 0.2259 0.0276 0.8520 Line 16 0.1254 0.0153 0.4730 Line 17 0.0780 0.0095 0.2940 Line 18 0.0260 0.0032 0.0980 Line 19 0.0838 0.0103 0.3160 Line 20 0.1175 0.0144 0.4430 Line 21 0.1188 0.0145 0.4480 Line 22 0.0949 0.0116 0.3580 Line 23 0.3065 0.0375 1.1560 Line 24 0.0939 0.0115 0.3540 Line 25 0.0711 0.2984 3.3780 Line 26 0.0476 0.1998 2.2610 Line 27 0.0050 0.0211 0.2390 Line 28 0.0439 0.1846 2.0890 Line 29 0.1197 0.5028 5.6913 Line 30 0.0593 0.2491 2.8190 Line 31 0.0186 0.0780 0.8830 Line 32 0.0667 0.2801 3.1700 132 A.6.3 Zero Sequence Line Impedance Data (0) (0) Line Resistance RLine Ω Inductance jXLine Ω Length(km) Line 1 0.8004 2.5107 7.1410 Line 2 0.3294 1.0333 2.9390 Line 3 0.2910 0.9127 2.5960 Line 4 0.1949 0.6114 1.7390 Line 5 0.4536 1.4229 4.0470 Line 6 0.5209 1.6338 4.6470 Line 7 0.4898 1.5365 4.3700 Line 8 0.0399 0.1252 0.3560 Line 9 0.1389 0.4356 1.2390 Line 10 0.1238 0.0838 0.2030 Line 11 0.2751 0.1861 0.4510 Line 12 0.1976 0.1337 0.3240 Line 13 0.4520 0.3057 0.7410 Line 14 0.2117 0.1432 0.3470 Line 15 0.5197 0.3515 0.8520 Line 16 0.2885 0.1951 0.4730 Line 17 0.1793 0.1213 0.2940 Line 18 0.0598 0.0404 0.0980 Line 19 0.1928 0.1304 0.3160 Line 20 0.2702 0.1828 0.4430 Line 21 0.2733 0.1848 0.4480 Line 22 0.2184 0.1477 0.3580 Line 23 0.7052 0.4769 1.1560 Line 24 0.2160 0.1460 0.3540 Line 25 0.3786 1.1877 3.3780 Line 26 0.2534 0.7949 2.2610 Line 27 0.0268 0.0840 0.2390 Line 28 0.2342 0.7345 2.0890 Line 29 0.6379 2.0010 5.6913 Line 30 0.3160 0.9911 2.8190 Line 31 0.0990 0.3105 0.8830 Line 32 0.3553 1.1145 3.1700 133 A.6.4 Positive and Zero Sequence Shunt Capacitance Data (1) (0) Line CLine (F) CLine (F) Length(km) Line 1 10−15 10−15 7.1410 Line 2 10−15 10−15 2.9390 Line 3 10−15 10−15 2.5960 Line 4 10−15 10−15 1.7390 Line 5 10−15 10−15 4.0470 Line 6 10−15 10−15 4.6470 Line 7 10−15 10−15 4.3700 Line 8 10−15 10−15 0.3560 Line 9 10−15 10−15 1.2390 Line 10 10−15 10−15 0.2030 Line 11 10−15 10−15 0.4510 Line 12 10−15 10−15 0.3240 Line 13 10−15 10−15 0.7410 Line 14 10−15 10−15 0.3470 Line 15 10−15 10−15 0.8520 Line 16 10−15 10−15 0.4730 Line 17 10−15 10−15 0.2940 Line 18 10−15 10−15 0.0980 Line 19 10−15 10−15 0.3160 Line 20 10−15 10−15 0.4430 Line 21 10−15 10−15 0.4480 Line 22 10−15 10−15 0.3580 Line 23 10−15 10−15 1.1560 Line 24 10−15 10−15 0.3540 Line 25 10−15 10−15 3.3780 Line 26 10−15 10−15 2.2610 Line 27 10−15 10−15 0.2390 Line 28 10−15 10−15 2.0890 Line 29 10−15 10−15 5.6913 Line 30 10−15 10−15 2.8190 Line 31 10−15 10−15 0.8830 Line 32 10−15 10−15 3.1700 134 A.7 Relay Settings and Fuse Characteristics Table A.1: Relay Settings for Substation Breaker A and Substation Breaker B Operation Number(Type) 1(Phase Relay) 2(Phase Relay) 1(Ground Relay) 2(Ground Relay) Pickup 1440 Amps 720 Amps 480 Amps 360 Amps Curve SEL-351S-6 SEL-351S-6 SEL-351S-6 SEL-351S-6 U5 U3 U5 U3 Time-Dial Curve Curve Curve Curve TD=1.1 TD=2.3 TD=1.8 TD=4.0 Table A.2: Relay Settings for Recloser A and Recloser B Operation Number(Type) 1(Phase Relay) 2(Phase Relay) 1(Ground Relay) 2(Ground Relay) Pickup Curve 1200 Amps 600 Amps 480 Amps 240 Amps ABB PCD 2000 STI ABB PCD 2000 EI ABB PCD 2000 STI ABB PCD 2000 EI 135 Time-Dial TD=0.9 TD=1.0 TD=1.3 TD=3.0 A.8 Fuse Characteristics Figure A.1: SandC T-Speed Fuse Minumum Melt Characteristics. 136 Figure A.2: SandC T-Speed Fuse Total Clearing Time Characteristics. 137 Appendix B Modelling of the Notional Feeder using MATLAB B.1 Introduction To test the proposed FLA, a PEC(Progress Energy Carolinas) example feeder was used(called the Notional Feeder). All parameters such as line impedance, transformer ratings and load data were provided and modelled in the MATLAB simulink software package. MATLAB was selected due to its capability to perform discrete simulations and packaged detailed models of transformers, lines and exponential loads. In this chapter, careful attention was given to the modelling of the system to provide the most accurate system model for testing the FLA. B.2 Modelling of Lines The modelling of lines in the Notional Feeder is done via the nominal PI line model. This line model is often used for short to medium length lines and includes a line inductance, resistance and capacitance as lumped parameters. When the line becomes appreciably long, this modelling introduces known errors. Since the distribution system contains short line sections, it was assumed that this model would suffice. Figure B.1 shows the nominal PI model used. In Figure B.1 the terms Rs , Rm and Ls ,Lm represent the self and mutual resistances and inductances due to mutual coupling between each of the three conductors. Phase and ground capacitances are also represented by Cp and Cg respectively. The RLC terms(Rs , Rm ,Ls ,Lm ,Cp and Cg ) are calculated from positive, negative and zero sequence impedance parameters of the line. Since MATLAB uses sequence components to calculate RLC terms, it must be assumed that the mutual coupling and self impedance terms are all equal. This means all the mutual impedances i.e., Zab = Zba and all the self-impedances Zaa = Zbb = Zcc are equal. Therefore, 138 Figure B.1: Nominal PI Line Model[28]. this reduces the line impedance matrix Zabc to the matrix shown in Equation B.5. And the sequence impedance matrix for the line segment between the two ends of Figure B.1: Z00 Z01 Z02 Z012 = Z10 Z11 Z12 Z20 Z21 Z22 (B.1) If we assume that all self and mutual terms are equal: Z0 0 Z+ Z012 = 0 0 0 0 0 Z− (B.2) Where Z00 = Z 0 , Z11 = Z + and Z22 = Z − . We also assume that the negative and positive sequence impedances are equal for this line segment: Z + = Z − We can transform the sequence impedance matrix to the phase impedance matrix using the following transform: Z0 1 Z012 = T 0 3 0 0 Z+ 0 139 0 0 3T −1 Z+ (B.3) Where T is: 1 1 T = 1 α2 1 α 1 (B.4) α α2 Where α2 = 16 120◦ . This yields the following result: Zabc = 2Z (1) Z (0) 3 + 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 2Z (1) Z (0) 3 + 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 Z (0) Z (1) 3 − 3 2Z (1) Z (0) 3 + 3 Zaa Zab Zac = Zba Zca Zbb Zcb Zbc Zcc (B.5) Using the above matrix, MATLAB calculates the RLC parameters as follows: Rs = 2R(1) R(0) + 3 3 (B.6) Ls = 2L(1) L(0) + 3 3 (B.7) Rm = R(0) R(1) − 3 3 (B.8) Lm = L(0) L(1) − 3 3 (B.9) The line capacitances can also be derived as: Cp = C (1) (B.10) 3C (1) C (0) (B.11) C (1) − C (0) In MATLAB Simulink each line is modelled using the Three Phase Nominal PI Line Section Cg = Block show in Figure B.2. Figure B.2: Line Model Block in MATLAB Simulink[28]. 140 B.3 Modelling of System Loads In the NF, all loads are modelled as static loads. Each load is described by a exponential function that directly varies the power flow as a function of voltage. Each composite load is described by the following power flow function: P (V, αp ) = P0 Q(V, αq ) = Q0 V V0 αp V V0 αq (B.12) (B.13) The above equations represent the consumed load at various voltages based on a nominal power and voltage. The terms P0 and Q0 represent the real and reactive power consumed a voltage V0 . The load voltage during operating conditions is represented by V . The terms αp and αq terms represent the real and reactive power sensitivity to changes in voltage. If we solve for the terms αp and αq using a relative sensitivity function we get: αp = ∂P P0 ∂V V0 (B.14) αq = ∂Q Q0 ∂V V0 (B.15) We can see intuitively that the coefficients αp and αq represent the normalized load sensitivity to voltage. Each of these terms represent an important factor in modelling consumer composite loads. As we approach αp = αq = 0 the load power consumption becomes less dependent on voltage and acts a constant power load. If we to approach αp = αq = 1, this would cause the load power flow to directly depend on voltage, thereby acting as a constant current load. When the terms αp = αq = 2, this causes the power flow to directly depend on the square of the voltage, thereby acting as a constant impedance load. Utilities and power research institutes have dedicated significant research to modelling typical consumer loads. Software to model these loads and implement them in algorithms are relatively inexpensive compared to obtaining real-time data. Modern protective relays and meters have become much cheaper, but the cost of real-time recording remains a significant cost. Usually most utilities estimate feeder load data using the following rules suggested by [16]: • Industrial areas are most typically closest to constant power loads (about 80/20 constant power/constant impedance). 141 • Residential areas with very strong summer-peaking loads usually have a 70/30 split of constant power/constant impedance loads. • Winter-peaking residential areas or those summer-peaking areas with low summer load densities per household (little air conditioning), tend to have a mix closer to 30/70 constant power/constant impedance loads. • Urban areas are usually about 50/50 constant power/constant impedance loads. A 50/50 mixture of power and impedance loads looks very much like and can be modelled as ”constant current.” • In rural and residential areas of developing countries, and commercial areas in economically depressed regions, loads generally tend to be about 20/80 constant power/constant impedance. It was assumed that the NF load could be represented as a urban load, representing 50/50 constant power/constant impedance loads. As indicated by [16], a 50/50 mix of constant power(motor loads) and constant impedance loads(resistive heating) can be approximated as a constant current load. Therefore, under un-faulted conditions, the loads in the NF are represented as constant current loads. B.3.1 Load Modelling Under Fault Conditions The load models given above in Equations B.12 and B.13 do not represent correct load behaviour under rapid voltage drop(fault) conditions[18]. Therefore, under faulted conditions, it is customary to approach load modelling as a piecewise function[29]. During voltage depressions, the constant current load model is switched to constant impedance. As recommended by [18], if the voltage is below 0.7 pu, the load models given above in Equations B.12 and B.13 are no longer valid and the load is then switched to constant impedance. α = 1 if V p load P (V, αp ) = α = 2 if V p load α = 1 if V q load Q(V, αp ) = α = 2 if V q load >0.7 pu (B.16) <0.7 pu >0.7 pu (B.17) <0.7 pu The equations above are used in the 3-Phase Dynamic Load model in MATLAB Simulink. The block representing each load is shown in Figure B.3. 142 Figure B.3: 3-Phase Dynamic Load Representing Exponential Load Functions. B.4 Modelling of Sources The system source is modelled a thevanin equivalent. The thevanin equivalent was provided by PEC and is represented by the thevanin equivalent source impedance Zs and thevanin voltage Vs : Figure B.4: System Thevanin Equivalent. To model this, a simple three phase source is used in MATLAB containing a series resistance and series inductance to model a thevanin equivalent of the system. The block configuration is show in Figure B.5. B.5 Modelling of Capacitor Banks The notional feeder consists of a total of four 12kV capacitor banks. Each capacitor bank is modelled as a constant impedance load with αp = αq = 2 in the exponential load equation 143 Figure B.5: Three Phase MATLAB Simulink Source. proposed in previous sections. Reactive power flow is proportional to the square of the voltage applied to the bank. The bank is represented by the exponential load as follows: Q(V, 2) = Q0 V = X0 V 2 V02 (B.18) Figure B.6: 12kV Capacitor Bank. B.6 Modelling of Multi-Winding Transformers All multi-winding transformers used in the notional feeder are modelled as show in Figure B.9. Each of the transformers serve two 150kVA loads. The transformer winding leakage inductance and resistance is specified for each winding as [L1 , L2 , L3 ] and [R1 , R2 , R3 ], respectively. The nominal winding voltages must also be specified as [U1 , U2 , U3 ] in addition to the system nominal 144 frequency fn and power rating Sn . Each multi-winding transformer is modelled with a nonsaturable core therefore the magnetization inductance and resistance Lm , Rm must be specified. All parameters can be found in Appendix A. Figure B.7: Three Winding Transformer. Figure B.8: MATLAB Multi-Winding Transformer Block. B.7 Modelling of Feeder Transformer The three phase feeder transformer used in the notional feeder are modelled as show in Figure B.9. This transformer steps 69kV sub-transmission down to 12kV for distribution. The transformer winding leakage reactance and resistance is specified for each winding as [X1 , X2 ] and [R1 , R2 ], respectively. The nominal winding voltages must also be specified as [V1 , V2 ] in addition to the system nominal frequency fn and 3-phase power rating Sn . Each multi-winding transformer is modelled with a non-saturable core therefore the magnetization reactance and resistance Xm , Rm must be specified. All parameters can be found in Appendix A. 145 Figure B.9: Per Phase Representation of 3-Phase Feeder Transformer. Figure B.10: MATLAB Three Phase Transformer. 146 Appendix C Distribution Fault Analysis Introduction to Short Circuit Analysis There are a variety of causes for faults occurring in distribution networks. Over-head lines are often exposed to environmental interference such as trees, lightning, and human intervention. Fault studies are often preformed to better understand how the system responds to environmental interference as well as protection of the system. Large scale distribution systems pose a unique set of challenges when preforming short circuit studies. It is often the case that these systems are very complex, containing thousands of customers and tens-of-thousands of nodes. Most classical short circuit programs using symmetrical components work well for balanced 3-phase systems. The main computational advantage for symmetrical components exists since the positive, negative and zero sequence networks can be considered separately. However, when unequal self or mutual impedances are considered, symmetrical components loose many of their advantages. Unequal self or mutual impedances create sequence component coupling. For this reason, short circuit analysis based on 3-phase models are more attractive. The following sections describe a fault analysis technique based on numerically calculated thevanin equivalents in the phase frame of reference. C.1 System Fault Currents and Voltages via Numerically Computed Thevenin Equivalents and Sensitivity Matrices There are several assumptions about the network that must be made before preforming any analysis. The following assumptions are presumed to be true[6]: • Circuit is comprised of linear components only; this is comprised of inductive, capacitive and resistive elements. • Slow acting control devices are considered to be frozen. This means that that all actively 147 controlled devices such as tap-changers or protective relays are in the same state at t = 0− as t = 0+ . • The substation bus is replaced by a thevanin equivalent. The thevanin equivalent component model is shown in Figure C.1. Figure C.1: System Thevanin Equivalent Component Model. • Load currents do not change during the fault. DEW’s algorithm for calculation of the loaded fault current can be broken down into several major steps: 1. Obtain all pre-fault voltages and currents. This requires a 3-phase power flow algorithm and detailed knowledge of the network(line parameters, load parameters,ect.) 2. Formation of the phase thevanin matrix. 3. Calculation of the fault voltages and currents. 4. Summation of pre-fault and fault currents using superposition. C.1.1 Thevanin’s Theorem and Superposition Principle We begin fault analysis by considering a typical power system shown below consisting of a source, loads, and a bus F . The basic power system fault can be modelled as a simple switch in series with a fault impedance. When the switch is in the closed position, the power system is considered to be faulted and fault current flows through the switch path. This is shown below in C.3. 148 Figure C.2: Power System containing a source, load buses and bus F . Figure C.3: Power System before a fault occurrence at bus F. If we measure the voltage across the switch in the open position, the voltage will be equal to the pre-fault bus voltage. If we replace the open switch by a voltage source equal in magnitude and angle as the pre-fault voltage, this will have no effect on the circuit. Therefore, we can model the open position of the switch by inserting a voltage source equal in magnitude and angle as the pre-fault voltage. This is show graphically in Figure C.4. If we want to represent a fault at bus f , we simply close the switch. We can represent the switch in the closed position by inserting a second voltage source equal in magnitude, but 180 degrees out of phase with the pre-fault voltage. This results in a voltage drop across the two sources as 0, yielding a closed switch. This is shown in Figure C.5. According to the principle of superposition, in a linear circuit containing several independent sources, the current or voltage of a circuit element equals the algebraic sum of the component voltages or currents produced by each individual source acting alone [24]. Using this theorem, we can conclude that the resultant voltages or currents are the sum of the currents/voltages before the fault occurred and the currents/voltages due to the fault itself. This is represented 149 Figure C.4: Open switch replaced by voltage source. Figure C.5: Closed Switch Replaced by Two Sources. graphically as the addition of Figure C.6 and Figure C.7. To begin let the pre-fault bus voltages and pre-fault bus current be denoted as V 0 and I 0 respectively. Also let the faulted bus voltages and fault current be denoted as Vf and If respectively. Using Figure C.8, we can establish a relationship between the pre-fault bus voltage, faulted bus voltage and the fault current. This relationship can be seen by reducing power network in Figure C.8 to a thevanin equivalent. We begin reducing the power network in Figure C.8 by open circuiting all current sources and short circuiting all voltage sources. In this model, we assume that the substation can be modelled as a thevanin equivalent source. Also, we assume the load model can be modelled as a constant current source. In Figure C.8 we are considering only the effect of the fault current itself, so we short circuit the substation source and open circuit the load current sources. Performing a simple KVL loop yields the following equation[22]: Vf = V0 − Zth · If 150 (C.1) Figure C.6: Circuit during pre-fault conditions. Figure C.7: Calculation of currents due to the fault itself. This equation represents the relationship between the system pre-fault voltages and faulted bus voltages at any bus k. This fundamental relationship is used later in this section to derive the phase thevanin matrix. C.1.2 Pre-Fault and Faulted Systems in DEW To better understand how DEW calculates fault currents under loaded conditions, we start by investigating the pre-fault and faulted networks. In Section C.1 we said that the superposition theorem states that the resultant currents are the sum of the currents before the fault occurred and the currents due to the fault itself. This is respesented by Equation C.2 below. If −loaded = I 0 + If (C.2) We also showed in Section C.1 that Figure C.6 and Figure C.7 represented the currents flowing before the fault and the currents due to the fault itself respectively. In this paper, 151 Figure C.8: Converting the network to a thevanin equivalent. we will refer to these circuits as the pre-fault and faulted networks. In order begin our fault analysis we need to obtain the pre-fault voltage at the faulted bus N . In order to do this, we call a 3-phase power flow algorithm to solve for the system voltages and currents(MATLAB and DEW contain a powerflow tool). The pre-fault system to be solved by the power flow algorithm is in Figure C.9, consisting of a substation(converted to a thevanin equivalent), several load buses, and bus N . Figure C.9: Pre-Fault system showing several loads and bus N(future faulted bus). Let us consider bus N to be the future faulted node. The pre-fault system voltages returned 152 by the power flow algorithm are of the form: i Van i Vbn i Vcn The pre-fault load currents are expressed as: i ILoad−A i ILoad−B i ILoad−C The stored load matrix holds all load flow of every bus up to the nth bus: 1 SLoad−A 1 SLoad−B 1 SLoad−C .. . n SLoad−A n SLoad−B n SLoad−C We can represent the faulted system, by short circuiting voltage sources, open circuiting current sources and adding a voltage source of the same magnitude but 180 degrees out of phase with the pre-fault voltage at bus N . This is shown in Figure C.10. Figure C.10: Faulted System with Fault applied at Node N. 153 Before we can begin to calculate fault current in Figure C.10, we must convert the system into a thevanin equivalent impedance looking into bus N. This requires a 3x3 matrix consisting of self and mutual equivalent impedances for all 3-phases. This is called the phase thevanin matrix. The matrix terms Zaa , Zbb , Zcc represent the self impedances of phase a, b and c respectively. The remaining terms(off diagonal) represent mutual impedances between phases, for example Zab represents the mutual impedance between phases a and b. Zaa Zab Zac Zth = Zba Zbb Zca Zcb Zbc Zcc (C.3) Many times, manufactures of cabling for distribution systems will only supply positive, negative and zero sequence impedances for a line segment(s). By applying a reverse transformation, we can go from the symmetrical component frame of reference to the phase frame. Z0 0 Z012 = 0 0 Z+ 0 0 Z− 0 (C.4) We can define the relation between the sequence component frame and phase frame as: 1 1 T = 1 α2 1 α 1 α α2 (C.5) Where α2 = 16 120◦ . Transformation of the impedance is not a straightforward procedure, so we begin here: Vabc = Zth · Iabc T · V012 = Zth · T · I012 V012 = T−1 · Zth · T · I012 V012 = Z012 · I012 Therefore: Z012 = T−1 · Zth · T Zth = T · Z012 · T−1 In the DEW software package, this conversion can be done for you. When clicking on a 154 distribution cable, we can define the positive, negative, and zero sequence impedances or you can specify Zabc . C.1.3 Forming the Phase Thevanin Matrix Forming the phase thevanin matrix(PTM) begins by analysing the system network. Using the system network model, we follow the following steps to obtain the PTM: • Load: The constant current load is scaled such that the load current flow is ≈ 0. This is done via a scaling factor ζi . ζi 1 ILoad−A 1 ILoad−B 1 ILoad−C .. ≈0 . n ILoad−A n ILoad−B n ILoad−C • Fault: The fault is removed from the faulted bus, and a test load is inserted. Figure C.11: Pre-Fault system with scaled loads and test load inserted at the faulted bus. When forming the phase thevanin matrix, a test load is inserted sequentially at each phase of the faulted node and power flow is performed. The result of the power flow on the test load is the test load voltage and current. The phase thevanin matrix represents the relationship between the voltages changes and the current changes at the faulted node before and after the test load is inserted. By making the applied system pre-fault load very small, this greatly reduces the 155 time needed to run power flow on the test load. Before the test load is inserted, a power flow is performed and the pre-test load voltages are determined. Building the phase thevanin matrix can be broken into the following steps: 1. Remove the fault from the faulted bus. 2. Scale the loads using the scaling factor ζi . 3. Run a power flow algorithm on the system to obtain the pre-test voltages Vkn where k = a, b, c Van Vbn Vcn 4. Insert a test load at the faulted bus on Phase A, then run power flow to determine test (1) the test load current Ia (1) and voltage Vkn where k = a, b, c. This is show in Figure C.12. (1) Van (1) Vbn (1) Vcn Figure C.12: Test load inserted on Phase A of the faulted node. 156 5. Insert a test load at the faulted bus on Phase B, then run power flow to determine test (2) the test load current Ib (2) and voltage Vkn where k = a, b, c. This is show in Figure C.13. (2) Van (2) Vbn (2) Vcn Figure C.13: Test load inserted on Phase B of the faulted node. 6. Insert a test load at the faulted bus on Phase C, then run power flow to determine test (3) the test load current Ic (3) and voltage Vkn where k = a, b, c. This is show in Figure C.14. (3) Van (3) Vbn (3) Vcn 7. Form the phase thevanin martix using equation C.6. Zth = (1) Van −Van (1) Ia (1) Vbn −Vbn (1) Ia (1) Vcn −Vcn (1) Ia (2) Van −Van (2) Ib (2) Vbn −Vbn (2) Ib (2) Vcn −Vcn (2) Ib 157 (3) Van −Van (3) Ic (3) Vbn −Vbn (3) Ic (3) Vcn −Vcn (3) Ic (C.6) Figure C.14: Test load inserted on Phase C of the faulted node. C.1.4 System Fault Characteristics Before performing analysis of the system under faulted conditions, we must study the fault itself. Distribution systems are often constructed using overhead cabling, exposing it to a wide variety of human and environmental interference. Utilities often record the root cause of faults for future study: Lightning, Tree Contact, Ice/Snow, Animals, Vandalism, Construction, Vehicle Accidents, Wind, Equipment Failure, and Conductor ”Dig-Ins” are most common. Figure C.15: Fault Root Causes and Percent Occurrence[7]. 158 Table C.1: Fault types and their frequency of occurrence[23]. Fault Type Occurrence Percentage Three Phase Fault Phase-to-Phase Phase-to-Phase-Ground Single Line to Ground 5% 15% 10% 70% Distributions faults are usually classified by the number of conductors that are involved. For example, a single conductor shorted to ground is called a single line to ground fault(SLG). When multi-phase faults occur we specify these as phase-to-phase(LL), phase-to-phase-toground(LLG) or 3-phase faults(3P). • 3-Phase Fault: A general three phase fault involves short circuiting all three phases to one common point, hence the name: three phase fault. Three phase faults can normally be regard as the rarest but most severe type of fault. Usually 3-phase faults begin as phaseto-phase or phase-to-ground faults. This characteristic is important to note because most fault location algorithms assume the fault type is non-evolving1 . • Phase-to-Phase and Phase-to-Phase-Ground Faults: A general phase-to-phase fault involves short circuiting two phases to one common point. If the fault is phase-to-phaseground, the common point is short circuited to ground. Phase-to-phase faults and Phaseto-Phase Ground faults are considered less severe than a 3-phase fault but more severe than single phase fault. Phase to phase faults rarely occur on underground line segments and mostly occur on overhead lines. • Single Line to Ground Fault: A general single line to ground fault involves short circuiting a single line directly to ground. Single line to ground faults are the most common fault occurring on power systems. For fault locating purposes, most analysis is centered around this fault type. Many faults occur by contacting trees, asphalt, gravel and dirt with quite different and unpredictable fault impedances. Many tests have shown that conductors contacting the wet soil, dry soil, concrete and rocks result in highly variable fault impedances. In general most utitlites assume the fault impedance to be negligible or approximately zero. According to 1 This can be extremely problematic for most fault locating algorithms. The reasons for this will be cover in later chapters. 159 studies done by the EPRI and utilties in [7], a fault impedance of 0 ohms proved to be a valid assumption. EPRI stated the following: “Good fault location can be done by assuming a bolted fault–no fault arcing resistance. Results from the EPRI fault study published in the early 1980’s showed that actual fault currents were close to the calculated value. The EPRI study found that calculated fault currents were approximately 2 percent higher than the measured value. Therefore, we assume that fault resistance cannot play a drastic role, but some faults may have enough arc length to make the bolted-fault assumption less accurate than desired. C.1.5 3-Phase Faults We first consider the general case of a 3-phase fault shown in Figure C.16. Each phase consists of its own fault impedance Za , Zb , Zc and a common point impedance Zf . We begin our analysis by re-arranging Equation C.1: V0 − Vf = Zth · If Figure C.16: Model of a 3 Phase Fault. Where, our pre-fault voltages are: i Van i V0 = Vbn i Vcn We also define are fault voltages as: f Van f Vf = Vbn f Vcn 160 (C.7) And our resultant fault currents as: Ia If = Ib Ic If we evaluate Equation C.1.8 we get the following equation: i Van f Van Ia i f Vbn − Vbn = Zth Ib f i Vcn Vcn Ic In order to solve for the If vector, we must solve our faulted bus voltage vector Vf in terms of fault currents and fault impedances. This can be done by applying a KVL to Figure C.16. V f = Ia · Za + Zf · If an f KV L Vbn = Ib · Zb + Zf · If f Vcn =I ·Z +Z ·I c c f f We can equate If in terms of Ia , Ib and Ic : If = Ia + Ib + Ic V f = Ia · Za + Zf · (Ia + Ib + Ic ) an f KV L Vbn = Ib · Zb + Zf · (Ia + Ib + Ic ) f Vcn = I · Z + Z · (I + I + I ) c c f a b c If we substitute we get: i Van Ia · Za + Zf · (Ia + Ib + Ic ) Ia i Vbn − Ib · Zb + Zf · (Ia + Ib + Ic ) = Zth Ib i Vcn Ic · Zc + Zf · (Ia + Ib + Ic ) Ic To simplify notation, we will define Zth as: a11 a12 a13 Zth = a21 a22 a23 a31 a32 a33 Substitution yields: 161 i Van Ia · Za + Zf · (Ia + Ib + Ic ) a11 a12 a13 Ia i Vbn − Ib · Zb + Zf · (Ia + Ib + Ic ) = a21 a22 a23 Ib i a31 a32 a33 Ic Ic · Zc + Zf · (Ia + Ib + Ic ) Vcn Solving for the pre-fault voltage vector gives the following equation: i Van i Vbn = i Vcn | Za + Zf g + a11 Zf g + a12 Zf g + a13 a21 + Zf g a22 + Zb + Zf g a23 + Zf g a31 + Zf g a32 + Zf g {z a33 + Zcc + Zf g Ib Ic } ψi Ia Solving for the fault currents gives: Ia Ib = Ic | −1 Za + Zf g + a11 Zf g + a12 Zf g + a13 a21 + Zf g a22 + Zb + Zf g a23 + Zf g a31 + Zf g a32 + Zf g {z a33 + Zcc + Zf g i Van i Vbn i Vcn (C.8) } ψi−1 For a bolted fault with no arcing resistance: Ia a11 a12 a13 −1 i Van i Ib = a21 a22 a23 Vbn i Ic a31 a32 a33 Vcn | {z } −1 Zth C.1.6 Phase-to-Phase-Ground Faults Figure C.17: Model of a Phase-Phase-Ground Fault. 162 (C.9) We first consider the general case of a phase-to-phase-ground fault shown in Figure C.17. Each phase consists of its own fault impedance Zb , Zc and a common point impedance Zf . In this case phase A is the only un-faulted phase, with Ia = 0. We begin our analysis by re-arranging Equation C.1: V0 − Vf = Zth · If Where, our pre-fault voltages are: ! i Vbn V0 = i Vcn We also define are fault voltages as: f Vbn Vf = ! f Vcn And our resultant fault currents as: Ib If = ! Ic If we evaluate Equation C.1.8 we get the following equation: i Vbn i Vcn ! − f Vbn ! f Vcn Ib = Zth ! Ic In order to solve for the If vector, we must solve our faulted bus voltage vector Vf in terms of fault currents and fault impedances. This can be done by applying a KVL to Figure C.17. V f = I · Z + Z · I b b f f bn KV L f Vcn = Ic · Zc + Zf · If We can equate If in terms of Ib and Ic : If = Ib + Ic V f = I · Z + Z · (I + I ) c b b f b bn KV L f Vcn = Ic · Zc + Zf · (Ib + Ic ) If we substitute we get: i Vbn i Vcn ! − Ib · Zb + Zf · (Ib + Ic ) Ic · Zc + Zf · (Ib + Ic ) 163 ! = Zth Ib Ic ! To simplify notation, we will define Zth as: Zth = a22 a23 ! a32 a33 Substitution yields: i Vbn ! Ib · Zb + Zf · (Ib + Ic ) − i Vcn Ic · Zc + Zf · (Ib + Ic ) ! = a22 a23 ! Ib a32 a33 ! Ic Solving for the pre-fault voltage vector gives the following equation: i Vbn ! a22 + Zb + Zf = i Vcn ! a23 + Zf a32 + Zf {z ! Ic a33 + Zc + Zf | Ib } ψi Solving for the fault currents gives: Ib Ic ! = !−1 a22 + Zb + Zf a23 + Zf a32 + Zf a33 + Zc + Zf {z | i Vbn i Vcn ! (C.10) } ψi−1 For a bolted fault with no arcing resistance: Ib ! Ic = a22 a23 a32 a33 {z | −1 Zth C.1.7 !−1 i Vbn ! i Vcn } Phase-to-Phase Faults Figure C.18: Model of a Phase-Phase Fault. 164 (C.11) We first consider the general case of a phase-to-phase fault shown in Figure C.18. In this case the fault impedance between Phase A and Phase B is Zf . In this case phase A is the only un-faulted phase, with Ia = 0. We begin our analysis by re-arranging Equation C.1: V0 − Vf = Zth · If Where, our pre-fault voltages are: ! i Van 0 V = i Vbn We also define are fault voltages as: f Van Vf = ! f Vbn And our resultant fault currents as: Ia If = ! Ib If we evaluate Equation C.1.8 we get the following equation: i Van i Vbn ! − f Van ! f Van = Zth Ia Ib ! (C.12) To simplify notation, we will define Zth as: Zth = a11 a12 ! a21 a22 Substituting for Zth gives the following equations: i f Van − Van = a11 Ia + a12 Ib (C.13) f i Vbn − Vbn = a21 Ia + a22 Ib (C.14) We begin by identifying that during a phase-to-phase fault, Ia = −Ib = If . Subtracting C.13 from C.14 and substituting Ia = −Ib : 165 f i i f Van − Vbn − (Van − Vbn ) = [(a11 + a12 ) − (a12 + a21 )] · Ia (C.15) f f If we measure Van and Vbn ,then subtracting gives: f V f − Vbn = If Zf an (C.16) f f Van − Vbn = Ia Zf We can see that Equation C.16 give us the voltage across the fault impedance. We can easily substitute If = Ia . We can use this relationship by substituting the second equation in C.16 into Equation C.15. When we solve for the fault current we get: Ia = −Ib = If = i −Vi Van bn (a11 + a22 ) − (a12 + a22 ) · Zf (C.17) For a bolted fault with no arcing resistance: Ia = −Ib = If = C.1.8 i −Vi Van bn (a11 + a22 ) − (a12 + a22 ) (C.18) Single Line-to-Ground Faults Line to ground faults are the easiest of fault types to calculate. We first consider the general case of a phase-to-ground fault shown in Figure C.18. In this case the fault impedance between Phase A and Ground is Zf . In this case phase A is the only faulted phase, with Ib = Ic = 0. We begin our analysis by re-arranging Equation C.1: V0 − Vf = Zth · If i Where, our pre-fault voltages are: V 0 = Van f We also define are fault voltages as: Vf = Van And our resultant fault currents as: If = Ia We can also reduce Zth to: Zth = a11 i −Vf =a I If we evaluate Equation C.1.8 we get the following equation: Van an 11 f 166 Figure C.19: Model of a Phase-to-Ground Fault. f f Substituting If = Ia and Van = Za If gives: Van − Za If = a11 Ia We can solve for the fault current If = Ia : Ia = If = i Van a11 + Zf (C.19) i Van a11 (C.20) For a bolted fault with no arcing resistance: Ia = If = C.2 Verification of DEW Fault Current Calculation: Example Feeder When performing short circuit studies in DEW, the phase-thevanin matrix, load-flow analysis and calculation of the fault current magnitude are all done without presentation to the user. In this section, we show the step-by-step execution of DEW’s fault analysis under loaded conditions while also illustrating that it is sufficient for fault locating applications. We begin our analysis by considering a simple radial feeder shown in Figure C.20. To maintain the focus on the algorithm itself, simple values were chosen for line impedance values and load conditions. As shown in the figure, this feeder consists of three load buses connected to a 13.8kV source via three line segments. As described in previous sections, we begin our fault analysis by considering the pre-fault conditions of the circuit. To obtain pre-fault quantities, the DEW 3-Phase Power Flow tool is utilized. This tool performs power flow on the network model and reports voltages, currents 167 Figure C.20: Simple Radial Feeder with three load buses. and their corresponding angles. As shown in Figure C.20, three-phase loads are connected to buses 1,2 and 3 rated at 90kW/43.6kVAR. Power flow was performed using a constant current load model. To verify that the DEW power flow solution is accurate, the solution is verified with MATLAB Simulink Power Flow Tool. A MATLAB script was written to calculate 3-phase pre-fault voltages, currents, and their corresponding angles. The power flow results from DEW and MATLAB are shown in Tables C.2, C.3. Table C.2: L-G Voltage Results of DEW vs. MATLAB Powerflow Script Quantity Bus Bus Bus Bus Bus Bus Bus Bus Bus 1 1 1 2 2 2 3 3 3 L-G L-G L-G L-G L-G L-G L-G L-G L-G DEW Power Flow Tool Phase Phase Phase Phase Phase Phase Phase Phase Phase A Voltage B Voltage C Voltage A Voltage B Voltage C Voltage A Voltage B Voltage C Voltage 7.962 7.962 6 7.962 6 7.958 7.958 6 7.958 6 7.956 7.956 6 7.956 6 6 -.0812 kV -120.0812 kV 119.9188 kV 6 -.1354 kV -120.1354 kV 119.8646 kV 6 -.1625 kV -120.1625 kV 119.8375 kV MATLAB Power Flow Script 7.9619 7.9619 6 7.9619 6 7.9583 7.9583 6 7.9583 6 7.9565 7.9565 6 7.9565 6 6 -0.0814 kV -120.0814 kV 119.9186 kV 6 -0.1355 kV -120.1355 kV 119.8645 kV 6 -0.1626 kV -120.1626 kV 119.8374 kV We begin our fault analysis by choosing a fault location and a fault type. In this example we will be using a 3-Phase bolted fault(Rf = 0Ω) at Bus 1. Referring back to Equation C.9 it can be seen that the Phase Thevenin matrix and Pre-Fault Bus Voltages are needed to calculate the resultant fault current. Since we have obtained the pre-fault voltages via power-flow(Tables C.2, C.3), our next step will require the formation of the phase thevenin matrix. 168 Table C.3: Current Results of DEW vs. MATLAB Script Quantity Source Phase A Current Source Phase B Current Source Phase C Current Line 2 Phase A Current Line 2 Phase B Current Line 2 Phase C Current Line 3 Phase A Current Line 3 Phase B Current Line 3 Phase C Current Load 1 Phase A Current Load 1 Phase B Current Load 1 Phase C Current Load 2 Phase A Current Load 2 Phase B Current Load 2 Phase C Current Load 3 Phase A Current Load 3 Phase B Current Load 3 Phase C Current DEW Power Flow Tool MATLAB Power Flow Script 12.55 6 25.9224 A 12.55 6 -145.9224 A 12.55 6 94.0776 A 8.36 6 -25.9449 A 8.36 6 -145.9449 A 8.36 6 94.0551 A 4.18 6 -25.9585 A 4.18 6 -145.9585 A 4.18 6 94.0415 A 4.18 6 -25.8772 A 4.18 6 -145.9300 A 4.18 6 94.0686 A 4.18 6 -25.9314 A 4.18 6 -145.9300 A 4.18 6 94.0686 A 4.18 6 -25.9585 A 4.18 6 -145.9585 A 4.18 6 94.0551 A 12.5328 6 -25.9222 A 12.5328 6 -145.9222 A 12.5328 6 94.0778 A 8.3536 6 -25.9446 A 8.3536 6 -145.9446 A 8.3536 6 94.0554 A 4.1763 6 -25.9582 A 4.1763 6 -145.9582 A 4.1763 6 94.0418 A 4.1792 6 -25.8774 A 4.1792 6 -145.8774 A 4.1792 6 94.1226 A 4.1773 6 -25.9316 A 4.1773 6 -145.9316 A 4.1773 6 94.0684 A 4.1763 6 -25.9582 A 4.1763 6 -145.9582 A 4.1763 6 94.0418 A 169 To form the Phase Thevanin Matrix we refer back to the procedure outlined in Section C.1.3. Building the phase thevanin matrix can be broken into the following steps: 1. Scale the loads using the scaling factor ζi . A scaling factor of ζi = 10−3 was used [22]. 2. Run a power flow algorithm on the system to obtain the pre-test voltages at the faulted node(Bus 1) Vkn where k = a, b, c. Van 7.962kV 6 − .0182◦ Vbn = 7.962kV 6 − 120.0182◦ Vcn 7.962kV 6 119.9188◦ 3. Insert a test load at the faulted bus(Bus 1) on Phase A, then run power flow to determine (1) test the test load current Ia (1) and voltage Vkn where k = a, b, c. This is show in Figure C.12. A test load value of Rtest = 100 Ω was used. The test load current was found to (1) be: Ia = 792.7523 A6 − 5.7327◦ . (1) Van 7.9275 kV 6 − 5.7327◦ (1) Vbn = 7.9674 kV 6 − 120.0008◦ (1) 7.9674 kV 6 119.9992◦ Vcn 4. Insert a test load at the faulted bus(Bus 1) on Phase B, then run power flow to determine (2) test the test load current Ib (2) and voltage Vkn where k = a, b, c. This is show in Figure C.13. A test load value of Rtest = 100 Ω was used. The test load current was found to (2) be: Ib = 792.7523 A6 − 125.7327◦ . (2) Van 7.9674 kV 6 − 0.0008◦ (2) Vbn = 7.9275 kV 6 − 125.7327◦ (2) 7.9674 kV 6 119.9992◦ Vcn 5. Insert a test load at the faulted bus(Bus 1) on Phase C, then run power flow to determine (3) test the test load current Ic (3) and voltage Vkn where k = a, b, c. This is show in Figure C.14. A test load value of Rtest = 100 Ω was used. The test load current was found to (3) be: Ic = 792.7523 A6 114.2673◦ . (3) Van 7.9674 kV 6 − 0.0008◦ (3) Vbn = 7.9674 kV 6 − 120.0008◦ (3) 7.9275 kV 6 114.2673◦ Vcn 170 6. Form the phase thevanin matrix using equation C.6. The result is as follows: (7.962 kV 6 −.0182◦ )−(7.9275 kV 6 −5.7327◦ ) 7.9286 −5.7327◦ kA Zth = 0 0 0 (7.962 kV 6 −120.0182◦ )−(7.9275 kV 6 −125.7327◦ ) 7.92756 −125.7327◦ kA 0 0 0 0 Zth = 0 1j 0 0 0 1j −1j 0 0 0 −1j 0 0 0 −1j Z−1 th = 0 · (C.21) 1j (C.22) (C.23) Using Equation Equation C.9, we get the result: Iaf −1j 0 0 −1j 0 0 {z Ibf = Icf | 0 −1 Zth 7.962 kV 6 − .0182◦ 7.962kV 6 − 120.0182◦ 7.962 kV 6 119.9188◦ −1j } (C.24) 0 Which yields the following: Iaf 7962 A6 − 90.0182◦ Ibf = 7962 A6 149.9818◦ 7962 A6 29.9188◦ Icf We can calculated the fault current seen by the substation under loaded conditions by using the principle of superposition as described in previous sections: If −loaded = I 0 + If Iaf −loaded 7962 A6 − 90.0182◦ 12.5328 A6 − 25.9222◦ Ibf −loaded = 7962 A6 149.9818◦ + 12.5328 A6 − 145.9222◦ Icf −loaded 7962 A6 29.9188◦ 12.5328 A6 94.0778◦ Therefore the current seen at the substation during loaded fault conditions are: 171 Iaf −loaded 7967.32 A6 − 90.01◦ Ibf −loaded = 7967.32 A6 149.98◦ 7967.31 A6 29.98◦ Icf −loaded To validate this calculation, a 3-Phase bolted fault was place at Bus 1. DEW gives the result shown in Figure C.21 which is If −loaded = 7967 A. Figure C.21: DEW Event Report showing the current seen at the substation for a bolted 3-Phase fault at Bus 1. 172 Table C.4: MATLAB Simulink Fault Current Results Quantity MATLAB Simulink Fault Current Results 7967.1 A 6 − 89.9◦ 7967.1 A 6 150.1◦ 7967.1 A 6 30.06◦ Phase A Fault Current Phase B Fault Current Phase C Fault Current C.2.1 Validation with MATLAB Simulink Model To verify and validate DEW fault analysis, a model of Figure C.20 was built in MATLAB Simulink. The model consists of a 13.8kV L-L source, three lines of impedance Zline = 1j and three load buses with constant current loads. A bolted 3-Phase fault (Rf = 0)was applied and yielded the results in Table C.4. 173 Appendix D Supplemental FLA Simulation Results for Stewart Street 12.47kV Feeder D.1 Pole P4622 Supplemental Recorded Results 174 Figure D.1: Worst Matched Locations for a fault at P4622 as calculated by the FLA. 175 Figure D.2: Other Likely Fault Locations for a fault at P4622 as calculated by the FLA. 176 Table D.1: Other Likely Fault Possibilities for P4622 Node P4509 P4513 P4515 P4520 P4522 N7974 1L5936 N7976 L1254807 L1254808 L1254809 L1279017 P4498 N7977 P4241 L1254804 P4268 Rank Upstream Device 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427566(25T) FUSE654427566(25T) FUSE654427566(25T) FUSE1052482716(40T) FUSE1052482716(40T) FUSE1052482716(40T) FUSE1146924279(25T) FUSE654421586(25T) FUSE1071439054(15T) FUSE654427484(25T) FUSE1052482746(200T) FUSE1052482746(200T) 177 D.2 Pole P4266 Supplemental Recorded Results Figure D.3: Worst Matched Locations for a fault at P4266 as calculated by the FLA. 178 Figure D.4: Other Likely Fault Locations for a fault at P4266 as calculated by the FLA. 179 Table D.2: Other Likely Fault Possibilities for P4266 Node L1254806 L1254807 L1254808 L1254809 P4619 P4622 L1279017 N7974 1L5936 N7976 N7977 P4241 P4508 P4509 P4513 P4515 P4520 P4496 P4498 Rank Upstream Device 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 FUSE1052482716(40T) FUSE1052482716(40T) FUSE1052482716(40T) FUSE1052482716(40T) FUSE654421506(65T) FUSE654421506(65T) FUSE1146924279(25T) FUSE654427566(25T) FUSE654427566(25T) FUSE654427566(25T) FUSE1071439054(15T FUSE654427484(15T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654427653(65T) FUSE654421586(25T) FUSE654421586(25T) 180