Fault Location in High Voltage Shunt Capacitor Banks

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8-9-2017 1200 AM

Fault Location in High Voltage Shunt Capacitor Banks Fault Location in High Voltage Shunt Capacitor Banks

Hessamoddin Jouybari Moghaddam The University of Western Ontario

Supervisor

Dr Tarlochan Sidhu

The University of Western Ontario

Graduate Program in Electrical and Computer Engineering

A thesis submitted in partial fulfillment of the requirements for the degree in Doctor of

Philosophy

copy Hessamoddin Jouybari Moghaddam 2017

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Abstract

This thesis is focused on developing and investigating methods for locating internalfailures in High Voltage (HV) Shunt Capacitor Banks (SCBs) Integrating fault locationalgorithms into capacitor bank protective relays has become more vital with SCBs beingmore widely in use and unbalance being a major occurrence Specifically this is ofimportance for large (high voltage) SCBs which have a wider search space in terms ofthe number of elements and units that comprise the bank Localizing the fault locationproblem is an attempt towards reducing the outage (repair) time of SCBs with advantagessuch as planning preventive maintenance and reducing unscheduled outages of the SCBs

The challenges for determining the location of internal failures and continuous moni-toring of the SCBs for this application are first no outward indication for the commonfusing technologies of SCBs (internally fused and fuseless) second the offsetting (bal-ancing) effect of subsequent failures against the low impact of the previous failures (ieambiguous failures) third compensating for other sources of unbalance such as manu-facturing tolerances gradual capacitance changes and system unbalances and last lessthan ideal number of available measurements

In this thesis first the ultra sensitive protection unbalance protection that is theconventional method for detecting internal failures is reviewed This protection strategywould be the backbone for fault location methods In the area of monitoring internalfailures and fault location of SCBs very little research work has been reported in theliterature A chapter will cover the existing methods that are either directly related tothis topic or indirectly perform the same application Furthermore a relevant method inthe literature is investigated in more details

Intimate connection exists between bank designs and unbalance protection methodsTherefore different configurations have different advantages or shortcomings in terms offault location Having reviewed various connections the ones that are more common orhave more challenges in terms of available measurements are intended for proposing newmethods for internal failure determination or enhancing the fault location algorithms

In a separate chapter first a new indicating quantity that employs automatic cal-ibrating factors is proposed The method overcomes the mentioned challenges and isfurther adapted to suit three of the common SCB grounding arrangements The indi-cating quantity is referred to as Superimposed Reactance method and can be integratedinto voltage-based unbalance protection functions to enhance the extracted informationfrom detected failures Then current-based unbalance protection methods for doublewye banks are considered and a fault location method that applies a combination ofself-tuning and auto-setting of k-factors is proposed for this type of banks

In another part of the proposed methodrsquos chapter envision of additional unbalanceprotection functions is discussed While it is seldom economic to add voltage or currenttransducers for solely fault location purpose two common protection philosophies withadditional measurements are discussed in terms of fault location applicationIn the last part of the chapter provisions for the proposed algorithm security and alsothe proposed methods usage and information display are presented

The performance of the investigated methods of the literature and the proposed meth-ods are assessed in a separate chapter Various internal failure scenarios and external

disturbances are studied to both examine the algorithm security and dependability Sim-ulations consider capacitor banks adapted from the literature and also actual banks inexisting utility systems

The work is extended by discussing other applications rather than only fault locationdetermination for the proposed methods accordingly online monitoring aspect is elabo-rated In summarized tables the proposed method output operands are compared withthe present methods in the literature Fuse saving for externally fused banks is anotherapplication of the proposed methods which is verified using an illustrative scenario Acommercial relay is also tested by play back of COMTRADE files from PSCAD simu-lations to demonstrate the shortcomings of conventional unbalance relaying methods interms of ambiguous failures online monitoring in comparison with the proposed methods

Keywords capacitor failure condition monitoring fault location fault report fuseinternal failure online monitoring preventive alarm protective relays shunt capacitorbanks

Dedication

To my parents and my grandma

Acknowlegements

I would like to express my sincere gratitude to Dr Tarlochan Singh Sidhu for his guidancesupport and continuous encouragement throughout the course of this research It hasbeen a great privilege to pursue my higher education under his supervision

I give great thanks to my parents Mr A Jouybari and Mrs Z Sani and mygrandma Mrs S Pouzesh for their love support encouragement and patience

I am thankful to my friends in London ON for helping me through the difficult timesand for their support and care

I gratefully acknowledge the financial support provided by NSERC and GE GridSolutions to pursue this research work

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Figures viii

List of Tables xvi

List of Appendices xvii

1 Introduction 111 Problem statement and research objectives 1

111 Challenges 2112 Motivation 3113 Research objectives 7

12 Thesis outline 813 Summary 9

2 Fault Location Fundamentals Unbalance Protection 1021 Introduction 1022 Phase voltage differential 1023 Unbalance method for capacitor banks grounded through a neutral capacitor 1224 Unbalance method for capacitor banks grounded through a CT with re-

sistive burden 1325 Phase current unbalance protection for fault location 1526 Neutral voltage unbalance for double wye ungrounded configurations with

isolated neutrals 1727 Neutral voltage unbalance for double wye ungrounded configurations with

tied neutrals 1728 Summary 18

3 SCBs Fault Location Literature Survey 1931 Introduction 1932 Literature Survey 1933 Investigation and review of the SEL method 21

331 Single Wye Ungrounded SCB 21332 Double Wye Ungrounded SCB with Neutral Current Measurement 24333 Double Wye Ungrounded SCB with Isolated Neutrals 26334 H-bridge banks with CT in each phase and PT at the tap point 29

34 Summary 29

4 The Proposed Fault Location Methods 3241 Introduction 3242 Superimposed Reactance (SR) for Ungrounded Single Wye SCB 34

421 Determining the involved phase 34422 Estimating the number of failed elements 37

43 Adapted SR for Single Wye SCB Grounded through a Capacitor 37431 Determining the involved phase 37432 Estimating the number of failed elements 39

44 Adapted SR for Single Wye SCB Grounded through a CT 40441 Determining the involved phase 40442 Estimating the number of failed elements 41

45 Enhanced Compensated Neutral Current for Ungrounded Y-Y SCB 42451 Determining the involved phase and section 42452 Estimating the number of failed elements 44

46 Enhanced Compensated Neutral Current for Grounded Y-Y SCB 45461 Determining the involved phase and section 45462 Estimating the number of failed elements 47

47 Envision of Additional Unbalance Protection Elements 48471 Additional Voltage Differential Element 49472 Additional Neutral Unbalance Element 51473 Conclusion for applicability of additional protection elements to

fault location 5548 Provisions for Algorithms Security and Applications 55

481 Compensation for Gradual Changes in the Reactance 56482 Required Data for the Application Setting 57483 The Proposed Algorithms Flowchart 59484 Blinder Counting Schemes and Blocking the Algorithm 59485 Usage and Information Display for Bank OperatorsService Crews 62

49 Summary 62

5 Evaluation of the Proposed and the Investigated Methods 6351 Introduction 6352 Single Wye Ungrounded 7053 Single Wye Grounded Through a Capacitor 7954 Single Wye Grounded via CT 8355 Y-Y Ungrounded with Neutral Current Unbalance 8556 Y-Y Grounded with Neutral Current Unbalance 9257 Case Studies with Additional Protection Elements 97

571 Y-Y Ungrounded with Neutral Voltage Unbalance-Tied Neutrals 97

572 Additional Voltage Differential Element 98573 Conclusion on the Results for Additional Protection Elements 106

58 The SEL Method for Y-Y Ungrounded with Isolated Neutrals 10659 Further Investigation on Algorithms Reliability 108

591 Simultaneous Failures 108592 Susceptibility to External Disturbances 108593 Regular Updating of the k-factors 158

510 Proposed Methods Verification for an Existing Utility System 160511 Summary 165

6 Proposed Methods Applications and Online Monitoring 16661 Introduction 16662 Online Monitoring vs Fault Location 166

621 Failurersquos Involved Phase Determination Methods 167622 Failurersquos Involved Phase and Section Determination Methods 168

63 Demonstrating Fuse Saving for Externally Fused SCBs 17464 Comparing Conventional Unbalance Relaying of a Commercial Relay 176

641 The open loop test set-up 176642 Relay outputs analysis 176

65 Summary 179

7 Summary Conclusions and Future Works 18071 Summary and Conclusions 18072 Future Works 183

Bibliography 184

A Simulation Settings 189

B Simulated System and Specifications of the SCBs 190

C Plot of Additional Signals During External Unbalance 194

D Additional Simulation Results on Measurement Accuracy 203

E Further on SCBrsquos Protection and Internal Failures 208E1 Other protection functions for SCBs 208E2 Resistive Potential Devices (RPDs) 209E3 Rack bonding 209

Curriculum Vitae 211

List of Figures

11 High Voltage Shunt Capacitor Banks (Scale Illustration) 212 Masking or offsetting effect 413 Externally fused capacitor unit [1] 514 Internally fused capacitor unit [1] 615 Fuseless capacitor unit [1] 6

21 SCB with phase voltage differential protection [2] 1122 Single wye SCB grounded through a capacitor 1323 Single wye SCB grounded via CT with a resistive burden 1324 Single wye SCB grounded via CT with a resistive burden application of

a neutral unbalance relay capable of ratio compensation and phase shifting 1425 Phase current unbalance protection(a) SCB with window type CTs at

neutral connection (b) SCB with H-bridge configuration [2] 1526 Neutral Voltage Unbalance Protection for Double Wye Ungrounded Con-

figurations with Isolated Neutrals [2] 1727 Neutral Voltage Unbalance Protection for Double Wye Ungrounded Con-

figurations with Tied Neutrals [2] 17

31 The SEL methodrsquos single Y configuration and available measurements 2232 The SEL method fault location logic for single wye 2233 The SEL methodrsquos double wye configuration and available measurements 2635 Double Wye Ungrounded Configurations with Isolated Neutrals 2736 The SEL fault location logic for double wye with isolated neutrals 2834 The SEL methodrsquos fault location logic for double wye (fuseless) 3037 Measurements for fault location of H-bridge banks 3038 The SEL fault location logic for H-bridge banks 31

41 Effect of fusing on the change of reactance 3342 Ungrounded single wye shunt capacitor bank 3443 Measurements available for single wye SCB grounded through a capacitor 3844 Single wye bank grounded through a CT 4045 Ungrounded double wye shunt capacitor bank 4246 Grounded double wye shunt capacitor bank 4647 Grounded double wye neutral current unbalance protection restraint su-

pervision [3] 4748 230 kV Grounded Fuseless Bank with Tapped Voltage Measurement in

Each Section 49

49 A phase of a double wye SCB with voltage differential protection 50410 138 kV Ungrounded Fuseless Bank 52411 Derivation of neutral voltage based on perunit phase capacitance after

failure 53412 Neutral voltage estimate for asymmetrical Y-Y SCBs 54413 Per unit capacitance of the 25C rating vs temperature for capacitors

impregnated with Faradol 810 insulating fluid [4] 57414 General characteristic plane of the proposed fault location methods 59415 Flowchart of the proposed SR based fault location methods 60416 Flowchart of the proposed enhanced current based fault location methods 60417 Pickup and counting scheme 61

51 Interpretation guide for fault location principle variations 6452 Margin evaluation without measurement noise (fuseless wye SCB) 6553 Margin evaluation without measurement noise (fused double wye SCB) 6654 Fault location principle smaller counter settings for a single wye SCB 6755 Successful detection of close internal failure [counter set on 10] single wye

SCB 6756 Fault location principle smaller counter settings for a double wye SCB 6857 Successful detection of close internal failure [counter set on 10] double

wye SCB 6858 Counter setting and detection of close consecutive failures 6959 Fault location output for close consecutive failures 69510 SR magnitude jump and reset for close consecutive failures 70511 SR variations single failure in phase A Case 1-1 71512 Fault location output single failure in phase A Case 1-1 72513 The SEL method detection angle single failure in phase A Case 1-1 72514 The SEL method fault location output single failure in phase A Case 1-1 73515 SR variations single failure in phase A Case 1-2 73516 Fault location output single failure in phase A Case 1-2 74517 The SEL method detection angle single failure in phase A Case 1-2 74518 The SEL method fault location output single failure in phase A Case 1-2 75519 SR variations single failure in phase A Case 1-3 75520 The proposed fault location output single failure in phase A Case 1-3 76521 The SEL method detection angle single failure in phase A Case 1-3 76522 The SEL method fault location output single failure in phase A Case 1-3 77523 SR variations Case 1-4 78524 Fault location output Case 1-4 78525 SR variations for a single element failure in phase A Case 2-1 80526 Fault location output single failure in phase A Case 2-1 80527 Zoomed magnitude of the SR Case 2-1 81528 SR variations Case 2-2 81529 Fault location output Case 2-2 82530 Fault location counters Case 2-2 82531 SR variations Case 3-1 83

532 Fault location counters Case 3-1 84533 Fault location output Case 3-1 84534 SR variations Case 3-2 85535 Fault location counters Case 3-2 86536 Fault location output Case 3-2 86537 Compensated neutral current variations single failure in phase B right

section Case 4-1 87538 The proposed fault location output single failure in phase B right section

Case 4-1 88539 The SEL method detection angle single failure in phase B right section

Case 4-1 88540 The SEL method fault location output single failure in phase B right

section Case 4-1 89541 Compensated neutral current variations single failure in phase C right

section Case 4-2 90542 The proposed fault location output single failure in phase C right section

Case 4-2 91543 The SEL method detection angle single failure in phase C right section

Case 4-2 91544 The SEL method fault location output single failure in phase C right

section Case 4-2 92545 Compensated neutral current variations Case 4-3 93546 The proposed fault location output Case 4-3 93547 Compensated neutral current variations Case 4-4 94548 The proposed fault location output Case 4-4 94549 Zero sequence current and uncompensated differential neutral current

Case 5-1 95550 Compensated neutral current variations Case 5-1 96551 The proposed fault location output Case 5-1 96552 The measured neutral voltage for rightleft section single element failures 98553 Phase A fault location principle voltage differential protection 99554 Phase B fault location principle voltage differential protection 99555 Phase C fault location principle voltage differential protection 100556 Phase A fault location output voltage differential protection 100557 Phase B fault location output voltage differential protection 101558 Phase C fault location output voltage differential protection 101559 Phase A fault location principle simultaneous failures 102560 Phase B fault location principle simultaneous failures 103561 Phase C fault location principle simultaneous failures 103562 Fault location output simultaneous failures 104563 87-3 fault location principle for three phases simultaneous failures 104564 Phase A 87-3 fault location alarm simultaneous failures 105565 Phase B 87-3 fault location alarm simultaneous failures 105566 Phase C 87-3 fault location alarm simultaneous failures 105

567 The SEL method detection angle single failure in phase C right sectionCase 6-1 106

568 The SEL method fault location output Case 6-1 107569 Measured and compensated differential voltage Split wye bank with iso-

lated neutrals 107570 Compensated Neutral Current Fault location malfunction for simultane-

ous failures 109571 Voltage based fault location malfunction for simultaneous failures 110572 Proposed method performance under power system fault Case 8-1 111573 Jumps in magnitude of the proposed principle under power system fault

Case 8-1 112574 Jumps in magnitude of the proposed principle under power system fault

(Case 8-1 with high impedance fault) 112575 Proposed method dependability under power system fault Case 8-1 113576 The proposed method fault location principle Case 8-2 113577 The proposed method fault location method counter Case 8-2 114578 Proposed method principle under power system fault Case 8-3 115579 Proposed method output under power system fault Case 8-3 115580 Plot of the SR Case 8-4 116581 The proposed fault location counter during open pole Case 8-4 116582 SR Magnitude jumps Case 8-4 117583 The SEL method fault location principle Case 8-1 117584 The SEL method output Case 8-1 118585 The proposed fault location principle for Case 9-1 119586 The proposed fault location counter for Case 9-1 119587 The proposed fault location principle for Case 9-2 120588 The proposed fault location counter for Case 9-2 120589 The proposed fault location principle for Case 9-3 121590 The proposed fault location counter for Case 9-3 121591 The proposed fault location principle magnitude for Case 9-3 122592 The proposed SR variations Case 9-4 SCB grounded via capacitor 122593 The proposed method output Case 9-4 SCB grounded via capacitor 123594 The proposed fault location principle for Case 10-1 124595 The proposed fault location counter for Case 10-1 125596 The proposed fault location output for Case 10-1 125597 The proposed fault location principle for Case 10-2 126598 The proposed fault location principle magnitude for the opened phase in

Case 10-2 126599 The proposed fault location counter for Case 10-2 1275100The proposed fault location output for Case 10-2 1275101Case 10-3 Unit failure and external unbalance case study SCB grounded

via CT (a) the proposed SR variations (b) output of the fault location 1285102Proposed method compensated neutral current Case 11-1 1295103Proposed method output Case 11-1 130

5104Algorithm security considering counter pickup and count updown pro-cess Case 11-1 130

5105Variations in the proposed principle magnitude under power system fault 1315106Variations in the proposed principle magnitude without power system fault1315107Proposed compensated neutral current Case 11-2 1325108Proposed method output Case 11-2 1335109The proposed fault location principle Case 11-3 1345110Algorithm security considering counter pickup and count updown pro-

cess Case 11-3 1355111The proposed fault location output Case 11-3 1355112The proposed fault location principle Case 11-4 1365113Algorithm security considering counter pickup and count updown pro-

cess Case 11-5 1395117The proposed fault location output Case 11-5 1395118The SEL method principle for Case 11-1 1405119The SEL method output for Case 11-1 1405120The SEL method principle Case 11-3 1415121The SEL method output Case 11-3 1425122The SEL method principle Case 11-4 1425123The SEL method output Case 11-4 1435124Positive sequence and negative sequence line currents Case 11-4 1435125The SEL method principle Case 11-5 1445126The SEL method output Case 11-5 1445127The SEL method compensated neutral current magnitude Case 11-5 1455128Case 12-1 (a) Zero sequence current (b) uncompensated differential neu-

tral current 1455129The proposed fault location principle Case 12-1 1465130Counter of the proposed fault location method Case 12-1 1465131Case 12-2 (a) Zero sequence current (b) uncompensated differential neu-

tral current 1475132The proposed fault location principle Case 12-2 1485133Counter of the proposed fault location method Case 12-2 1485134The proposed fault location principle Case 12-3 1495135The proposed fault location output Case 12-3 1495136The SEL method referenced angle for fault location under external unbal-

ance Case 13-1 1505137The SEL method fault location output Case 13-1 1505138Measured and compensated differential voltage under external unbalance

Case 13-1 1515139Voltage unbalance during power system fault Case 13-1 152

5140Case 13-2 Referenced angle for the SEL method under ground-fault ofthe phase with failed elements 152

5141Phase B fault location principle Case 14-1 first failure 153

514287-3 fault location principle for three phases Case 14-1 first failure 154

5143Phase C fault location principle Case 14-1 second failure 154

514487-3 fault location principle for three phases Case 14-1 second failure 155

5145Phase A fault location output Case 14-1 155

5146Phase B fault location output Case 14-1 156

5147Phase C fault location output Case 14-1 156

5148Third (87-3) differential element alarms Case 14-1 157

5149Third (87-3) differential element counters Case 14-1 157

5150K-factors regular updates impact on the security of SR based fault locationmethod 159

5151K-factor regular updates impact on the security of enhanced neutral cur-rent based fault location method 159

5152The proposed SR fault location principle for Case 15-1 160

5153The proposed SR fault location counter for Case 15-1 161

5154The proposed SR fault location output for Case 15-1 161

5158The proposed fault location principle for Case 15-3 164

5159The proposed fault location counter for Case 15-3 164

5160The proposed fault location output for Case 15-3 165

61 Involved phase determination criterion for the SEL method-each coloredzone represents one phase 169

62 Magnitude of the operating function of the SEL method note the impactof offsetting against the previous failures 169

63 Assertion and de-assertion of the output operand for the SEL method 169

64 Online monitoring Application for Involved Phase Determination 171

65 Involved phase and section determination criterion for the SEL method-each colored zone represents one phasesection 172

66 Drop out and masking apparent in the SEL operating function magnitude 172

67 Missing consecutive failures for the SEL method 173

68 Online monitoring Application for Involved Phase and Section Determi-nation Decision Criteria 173

69 Online monitoring Application for Involved Phase and Section Determi-nation Outputs 174

610 Fault location report for externally fused SCBs (a) the proposed SR mag-nitude and angle variations (b) involved phase and number of shortedparallel element groups 175

611 Relay oscillography records for voltage based unbalance protection 177

612 Relay oscillography records for current based unbalance protection 178

B1 230 kV internally fused ungrounded single wye SCB 190

B2 230 kV fuseless ungrounded single wye SCB 191

B3 230 kV internally fused ungrounded double wye SCB with single stringper phase for each section 191

B4 230 kV fuseless ungrounded double wye SCB 191

B5 Schematic of the simulated power system 192

B6 Single line diagram of the existing utility system 192

C1 Neutral voltage and zero sequence voltage internal failure only (the bankand system have pre-existing unbalance too) 195

C2 Neutral voltage and zero sequence voltage simultaneous internal failureand shunt power system fault 195

C3 Neutral voltage and zero sequence voltage internal failure in one phase ofthe SCB while the same phase of the line is open 196

C4 Neutral measurements for a scenario including an internal failure occurrence197

C5 The proposed fault location counter for an internal failure occurrence 197

C6 Neutral measurements for a scenario including an internal failure occur-rence during a power system phase to phase fault 198

C7 The proposed fault location counter for the scenario of Fig C6 198

C8 Neutral measurements for a scenario including an internal failure occur-rence during a power system phase to ground fault for the same phase 199

C9 The proposed fault location counter for the scenario of figure C8 199

C10 Neutral measurements for a scenario including an internal failure occur-rence during a power system phase to ground fault in another phase 200

C12 Neutral measurements for a scenario including an internal failure occur-rence during an open pole in the same phase 201

C14 Compensated and uncompensated neutral current for fault in phase B andinternal failure in phase B 202

C15 Compensated and uncompensated neutral current for fault in phase A andinternal failure in phase B 202

D1 Superimposed Reactance Magnitude case I system unbalance and capaci-tor unbalance case II capacitor unbalance only case III system unbalanceonly 203

D2 Superimposed Reactance Magnitude case I no measurement noise caseII 50 dB SNR case III 50 dB SNR and 6 ratio error 204

D3 A closer look at the SR considering Neutral CT ratio error 205

D4 Full cycle DFT frequency response 206

D5 Frequency response of the applied anti aliasing filter 206

D6 Low pass filter and DFT filter application on the measured signal 207

D7 Low pass filter and DFT filter application on the measured signal forsystem with ten times richer harmonic sources 207

E1 Resistive divider for voltage sensing in SCBs [1] 210E2 SampC 15 VA Potential Device Schematic [5] 210

List of Tables

51 Increment in the magnitude of the superimposed reactance case 1-4 7952 k-factor values for phase A case 1-4 7953 Increments in the magnitude of the compensated neutral current in percent

of the rated current for single element failures 8954 K1 magnitude (pu) | phase (deg) sets for case 4-4 92

61 Method Comparison for Internal FailuresOnline Monitoring (Ungrounded Wye Banks) 167

62 Method Comparison for Internal FailuresOnline Monitoring (Ungrounded Y-Y Banks) 170

B1 System Parameters 192B2 Utility Banks Construction Data 192B3 Construction data for single wye SCB and each bank of the double wye SCB193B4 Construction data for the single wye SCB with externally fused units 193

List of Appendices

Appendix A Simulation Settings 189Appendix B Simulated System and Specifications of the SCBs 190Appendix C Plot of Additional Signals during External Unbalance 194Appendix D Additional Simulation Results on Measurement Accuracy 203Appendix E Further on SCBrsquos protection and internal failures 208

Chapter 1

Introduction

11 Problem statement and research objectives

Today complex transmission systems demand increasing amount of reactive power sup-port which is to be supplied by transmission providers Shunt Capacitor Banks (SCBs)Figure 11 are critical power system apparatus that are mainly installed for this VARdemand Benefits from installation of SCBs includes relatively inexpensive voltage sup-port power factor correction providing VAR support for distributed energy resourcesand keeping FACTS devices within their capacity limits Relieving reactive power re-quirements itself leads to reduction of losses and can also help to postpone investmentsin transmission and generation capacities Although SCBs are not new in terms ofapplication and their introduction to power system there has been little research onadvanced methods for their protection The reason for less interest in developmentof SCBs advanced dedicated relays is because SCBs are historically considered a rel-atively low-volume market [6] Referring back to early research on SCBs monitoring andprotection papers and patents include discussing the general protection methods [7ndash9]special logics for discrimination between an internal fault and a system fault for a ca-pacitor battery [10] effects of system disturbances on security of protection functionsfor SCBs [1112] detection of high impedance ground faults within a SCB that benefitsfrom perphase voltage differential protection [13] and direct impedance measurementsfor unbalance detection [14]

Fault location for various power apparatus is different in the level of selectivity andsearch space reduction For example for transmission lines fault location can point outthe exact distance at which the fault has occurred For SCBs the less than ideal numberof available measurements limits the fault location to the affected phase detection andin case of double wye connections to the affected wye section There are a few recentpublications for fault location in SCBs The faulted phase determination is adequateenough to narrow the search area and reduce the investigation time for locating the faultby at least 666 In addition in single wye SCBs with tapped potential transformers(PT) or in double wye SCBs with neutral current transformers (CT) this search areacan be reduced by 833 because in these configurations each phase has two sectionsthat are distinguishable in terms of failure location As a result IEEE guide for pro-

2 Chapter 1 Introduction

Figure 11 High Voltage Shunt Capacitor Banks (Scale Illustration)

tection of SCBs [2] recommends fault location logics as effective methods to speed uptroubleshooting and repair of the banks Summing up higher availability of supportingreactive power is an advantage that the current research is looking for

111 Challenges

Failure of an elementunit will increase the voltage stress on the remaining series ele-mentsunits The more the number of the failed units the greater the stress and thusless time between the failures As a result cascading failure is the condition that mustbe taken care of by not missing the detection of any failure inside the SCB

Knowing the location of the failure (ie the phase and for double wye configurationsthe wye section containing the fault) would eventually result in increasing the total in-service time of SCBs This is realized by either minimizing the searching time for thefailed elements in the repair process or by enabling advance preventive maintenanceschedules Few available measurements and metering accuracies make the fault locationtechniques to be challenging especially when considering the effect of a single elementfailure among hundreds of elements in the measured signals

11 Problem statement and research objectives 3

Another challenge is the masking or offsetting effect which stands for the conditionat which a subsequent failure cancels out the unbalance seen by the relay and thusmakes the failure location detection false or insensitive For H-bridge SCBs the maskinghappens when a second failure occurs in the opposite diagonal of an existing failure Fordouble wye SCBs same phase faults on both sections may become hidden from the relaySimilarly same number of element failures on all three phases in a section are the casesthat may not be detected Also failures on two phases in a section can be mis-detectedfor a failure in the other phase of the other section Comparably in single wye SCBswhen failures exist in all three phases the bank might seem balanced to the relay andfailures in two phases may become mis-detected for an unbalance in the other phaseFigure 12 illustrates these scenarios

In order to introduce highly sensitive fault location methods the technique must alsobe able to accurately and completely compensate for the inherent unbalances in the SCBand the system voltage unbalances In addition gradual capacitance changes due totemperature variations and aging should be compensated Shading effect is also anothersimilar case which occurs at times that part of the SCB may be under direct sunlightwhile the other part is in the shade Compensating for these slight and low rate changesat regular time interval has to be considered in a fault location method

112 Motivation

In the following parts it is explained why the fault location function is an emerging crucialrequirement for capacitor bank protection and monitoring relays in the modern electricalpower systems

The popular design requires sensitive relaying

Single phase capacitor units constitute a shunt capacitor bank With these units con-nected in parallel and series the desired voltage rating and reactive power rating wouldbe achieved In a similar way capacitor elements form a capacitor unit with their paralleland series combination

Capacitor units in their early generation needed fuses because they were very vulner-able to case rupture (as there was no control over minor internal faults until they becamea major fault) These Externally fused banks are known for higher operating costs andbank unavailability A capacitor unit with a blown fuse requires the capacitor bank tobe taken out of service and hence reduces the time that SCB is available and benefitsthe system Because pollution corrosion and fluctuating climatic conditions reduce thereliability of external fuses they have to be checked and replaced periodically [1] Figure13 shows an externally fused capacitor unit

In another fusing method called Internally fused the isolation of a failed capacitorelement allows the capacitor bank to remain in service The design reduces the vul-nerability to faults from animals climbing inside the bank Figure 14 demonstrates aninternally fused design for capacitor units

High quality insulating materials has made the role played by SCB fuses to becomesecondary The prevalent dielectric type for the HV power capacitors is polypropylene

Maybe Mis-detected for

May not be detected

H-Bridge

Double Wye

Single Wye

Figure 12 Masking or offsetting effect

Figure 13 Externally fused capacitor unit [1]

film These films are impregnated with synthetic fluid such as Faradol 810 or otherbiodegradable PCB free oils [15] As a result fuseless designs have been introduced Theyhave the advantage of being cheaper and having lower losses ie RI2 losses associatedwith capacitor can as capacitor fuses are not present in these bank designs Heavyduty welding of the two foil electrodes within the failed element minimizes the chance ofcontinued arcing [16] Figure 15 illustrates this design Depending on whether the groupsof capacitor units are connected in series or in seriesparallel from phase to neutralcapacitor banks without fuse may also be called unfused instead of fuseless [17] Theoperating voltage level changes according to the arrangement of units [3] ie unfusedbanks are normally used for systems with voltages below 345 kV for voltages equal orhigher than this value fuseless banks are in service

In short while the fuseless units are superior in terms of lower losses associatedwith fuses both of fuseless and internally fused technologies are advantageous to theexternally fused designs With instantaneous disconnectionshorting out of the faultyelement these designs prevent from cascading element failures inside the capacitor unitsAlthough manufacturers have adopted these technologies for higher availability of theSCB and lower maintenance costs but internally protected capacitor units have the dis-advantage of low transient withstand capability of their low rating fuses [18] and novisual indication for the unit with failed elementsndash all film capacitors even do not bulgewhen a failure occurs [19] Historically SCBrsquos maintenance is a time-consuming task

Figure 14 Internally fused capacitor unit [1]

Figure 15 Fuseless capacitor unit [1]

for utilities [20] With unbalance being a major occurrence due to the dielectric fail-ure developing methods for determining the involved phase is an advancement for SCBprotection and control relays This helps the crew by reducing the search space to aparticular phase for repair and preparing the bank faster for service

The increased frequency of failures in todayrsquos grid

Modern grids work close to their operation limits and over-voltage duty is placed ontransmission systems by todayrsquos load flow requirements Utilities have also reported anincrease in the frequency of failures in SCBs in recent years [21] Integrating fault locationalgorithms into capacitor bank protective relays has become more vital with SCBs beingmore widely in use Specifically this is of importance for large (high voltage) SCBs whichhave a larger search space in terms of the number of elements and units that comprisethe bank

Outage times and incidents in Canada

The Canadian Electricity Association reports major transmission equipment statisticsannually For shunt capacitor banks considering failures of capacitors bushings andinsulation SCBs at different voltage levels have had time consuming repair and recoveryof service For banks with 60 kV-109 kV voltage rating the average repair time (forcedunavailable time) studied over a period of five years 1998-2002 has been reported tobe 5552 hours- same statistic for banks of 200 kV-299 kV has been 1406 hours Thetotal outage time over this interval at 60 kV-109 kV has been 231520 hours for 417 SCBoutages A single bank outage incident at extra high voltage level 600 kV- 799 kV hasresulted in 10 hours of repair or replacement time [22] The recent SCB installations insouth western Ontario and a recent incident in greater Toronto area originating from SCBswitching and grounding issues can also be mentioned as local examples that motivateresearch topics on protection and monitoring of SCBs For details on installation ofseven 230 kV SCBs in transmission stations across south western Ontario see [23] Forthe incident at Richview Transformer station that resulted in substantial damage to the230 kV SCBs and their breakers see [24]

113 Research objectives

The thesis objectives are

bull To investigate a relevant commercial fault location method and to do performanceanalysis for that under special challenging scenarios

bull To develop an enhanced fault location technique for SCBs protected with neutralcurrent unbalance protection (both grounded and ungrounded) in order to preventambiguous indications and provide live report of number of failures

bull To introduce a new fault location indicating quantity for banks with voltage basedunbalance protection in order to detect consecutive failures and provide live reportof number of failed elements The method is intended to be applicable to differentgrounding arrangements

bull To expand the concept of fault location to online monitoring for fuse saving inexternally fused banks

bull To apply self-tuning and auto-setting to voltage differential unbalance protection

bull To investigate and discuss applicability of neutral voltage unbalance estimation forfault location of double wye SCBs

bull To discuss the proposed methods advantages to a conventional unbalance protectionmethod alarms by testing a commercial relay

Furthermore all of the developed fault location methods have the following properties

bull Making the best out of the available measurements

bull Deploying k-factor auto-setting and self-tuning concept

bull Compensating for pre-existing inherent unbalance in the SCB (manufacturing tol-erances) and system voltage unbalance

bull Compensating for gradual changes in the capacitance (aging temperature impacts)

bull Determining consecutive failures location

bull Determining number of failed capacitor elements

bull Verified for reliable operation considering system harmonics system voltage unbal-ance measurement noise and power system disturbances

12 Thesis outline

Chapter 2 gives an overview of the unbalance protection methods whose purpose is toremove the bank from service for any fault that is likely to cause further damage De-pendent on the connection type and available transducers several unbalance protectionmethods exist The chapter covers these methods and explains the theory of them Incase there are adjustments for the methods that increase their sensitivity it is explainedin this chapter to help in forming the basis for fault location algorithm developmentThe conventional operating functions that help in discriminating internal failures fromother unbalance signals are elaborated in this chapter

Chapter 3 presents the current literature in the area of fault location in SCBs Thechapter includes investigation of the relevant methods theories Because the presentmethods are restrictively disclosed only in the form of patents rather than academic pa-pers where applicable this chapter is intended to find out the assumptions and derivationapproach of these existing methods in the literature

Chapter 4 introduces the proposed methods in this thesis The chapter includes faultlocation principle development equations and any other estimationcalculation that is

13 Summary 9

used to add a property such as detection of number of failed elements to the proposedmethods The proposed methods cover different connections and fusing technologiesinternally fused and fuseless designs as well as both grounded and ungrounded configu-rations Algorithm application settings margins and blinder settings are discussed in thischapter as well A discussion on additional measurements application is also provided

Chapter 5 presents the simulation study and validation of the proposed fault locationtechniques Power System Computer Aided Design (PSCAD) software is used for gener-ating the voltage and current signals and then a relay model developed in MATLAB isused to playback and process the signals for fault location purpose Evaluations are cate-gorized to two different sections the ones that focus on various internal failure scenariosand the ones that are for validation under special conditions like external unbalances

Chapter 6 discusses applications of the proposed methods such as fuse saving forexternally fused SCBs and extending the fault location function to an online monitoringsystem A commercial relayrsquos conventional unbalance protection is tested by play backof the PSCAD records to demonstrate the advantage of the proposed methods featuresfor integration into this conventional unbalance relaying

Chapter 7 summarizes the presented work This chapter is followed by a list ofreferences Appendix A gives a more detailed information on software settings for thesimulation study Appendix B provides the simulated system and SCB specificationsAppendix C presents some additional plots for the algorithm evaluation Appendix Dprovides additional results on measurement and phasor estimation accuracy Appendix Egives further information for interested readers on capacitor banks and their protection

13 Summary

This chapter has briefly introduced the role and importance of high voltage shunt ca-pacitor banks in power systems The problem of fault location and its application havebeen explained Challenges and motivation for the present research have been outlined-followed by the thesis organization A literature review and investigation of a relevantfault location method will be discussed in the following chapter

Chapter 2

Fault Location FundamentalsUnbalance Protection

21 Introduction

SCBs protection consists of system protection schemes and bank protection schemes [2]System protection schemes are required to handle abnormal system conditions such asoverundervoltages and excessive transient overcurrents within a system and to discon-nect the entire shunt capacitor bank in order to prevent further damage to the capacitorsOn the other hand bank protection schemes are required to protect faults within thecapacitor bank The main concerns in bank protection are unbalance problems withinthe bank due to faulted capacitor units or elements [13] This is due to the fact that mildinternal faults do not render high currents for external fuses or over current protectionoperation Accordingly unbalance relaying would be the proper sensitive solution forprotection against internal failures and it can trip the element failures much faster [18]This chapter presents the theory of unbalance protection methods as the main existingschemes that are in connection with internal failures in SCBs Unbalance protectionmethods are the backbone of fault location methods They use the evaluated unbalancefor detection of abnormalities in a device The known relationships among the measuredvoltagescurrents taken around the SCB are used to monitor the changes in impedancesindirectly Unbalance protection methods have to be designed to eliminate or reduceunbalances due to capacitor tolerances and temperature drifts [2] The rest of the chap-ter introduces various unbalance relaying methods It should be noted that unbalancerelaying methods with particular fault location schemes proposed in the literature willbe covered in a separate literature review chapter More information on protection anddesign of SCBs is presented in Appendix E

22 Phase voltage differential

The phase voltage differential protection is selected to illustrate how phase differencebetween electrical quantities can determine whether an internal failure has occurredAssume a solidly grounded wye SCB with potential transformer in each phase at a tap

22 Phase voltage differential 11

point Figure 21

Figure 21 SCB with phase voltage differential protection [2]

For each phase of the bank the following equation would be true

VTAP =X2

X1 +X2

VBUS (21)

Note that to date all-film capacitor units losses combined with buswork losses are solow [25] that in references and also in IEEE Std C3799-2012 [2] the impedance of thecapacitor bank is considered to be purely negative reactive Following the previousequation a constant is defined as

X1 +X2

The protection operating signal and the self-set value for the constant are defined as

VOP = VTAP minusK VBUS (23)

KSET =| VTAP

| (24)

It is worth noting that for ungrounded SCBs the voltage terms in (23) which are usuallymagnitudes will be replaced with phasors measured with respect to the neutral voltage[3] The actual value for the constant KACT in the operating signal equation will changeas a result of an internal failure Therefore by replacing the actual tap voltage in termsof this k-factor the following equation can be derived for the operating signal

VOP = (KACT minusKSET )times VBUS (25)

By analyzing the vectorial position of the operating signal with the bus voltage (inphase or out of phase) it can be determined that the failure is in the upper side of the

12 Chapter 2 Fault Location Fundamentals Unbalance Protection

tapped point or the lower In some references the differential voltage (23) is formedfrom magnitudes of the voltage phasors [26] while in other references the operatingvoltage is the vectorial difference [27] Considering the k-factor nature (24) which mustbe an absolute value to make the fault location based on (25) valid in the vectorialdifference case the phase angle difference between the tap voltage and the bus voltagecan introduce standing unbalance in the operating signal For fuseless SCBs instead ofa midpoint tap voltage the voltage across low voltage capacitors forms the tap voltageThis is because strings are not connected at the midpoints in multi-string fuseless designsThe described unbalance protection is phase segregated and very simple that can also beused for locating an internal failure This is applicable only for wye connected SCBs withtapped potential transformer Voltage difference between the tap voltages of the parallelbanks for double wye grounded SCBs is also an alternative similar unbalance protectionin which again three separate single phase voltage differential relays are used to detectunbalance for each phase independently Special configurations with the tapped voltagetransformers connected at the phase side of grounding capacitors also exist [2] [1] Theprinciples of the other fault location detection algorithms are similar in basics to theexplained method

23 Unbalance method for capacitor banks grounded

through a neutral capacitor

In IEEE Std C3799 [2] unbalance protection of a bank grounded via a capacitor isexplained Depending on the grounding impedance the configuration could either beconsidered as an ungrounded SCB (relatively large grounding impedance) or a groundedSCB with relatively small grounding impedance The first case is discussed thoroughlyin the next sections The latter is the same as the presented phase voltage differentialprotection

For the sake of brevity only the equation set which explains the operating signalassuming equal phase reactances is brought hereBy Ohmrsquos law in the SCB shown in Figure 22 we have

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

)times (minusjXN) = VN (26)

which is equivalent to

3V0 times jXN = jX times VN + jXN times 3VN (27)

which allows for introducing the following protection function

Vop =| 3V0 minus (X

+ 3)times VN | (28)

This protection function is a neutral voltage unbalance protection with a ratio compen-sation In the upcoming section for the proposed methods we will show that this ratioof neutral reactance to phase reactance adds a third factor to the fault location principle

24 Capacitor banks grounded through a CT with resistive burden 13

XA XB XC

Figure 22 Single wye SCB grounded through a capacitor

through a CT with resistive burden

In IEEE Std C3799 [2] unbalance protection of a bank grounded via CT with a resistiveburden is explained

Figure 23 Single wye SCB grounded via CT with a resistive burden

Again we assume that the three phase reactances are equal and thus denoted byX Another assumption for the sake of simplicity would be the CT ratio of 11 In [2]

instead of the primary value of the ground current its secondary value based on theburden and the voltage across it is used for deriving the protection functionConsidering a SCB as in Figure 23 the following balance equation holds true

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

which can be simplified as

3V0 + jX

Rtimes VR = 0 (210)

which demonstrates that the neutral voltage at the bus V0 is balanced by a voltageassociated with the bank neutral (shifted and with a compensation ratio j X

RtimesVR) Thus

a neutral voltage unbalance relay can be used for implementation of such a protectionscheme see Figure 24

Figure 24 Single wye SCB grounded via CT with a resistive burden application of aneutral unbalance relay capable of ratio compensation and phase shifting

To further simplify the operating function knowing that VRR

= 3I0 and defining asimple pickup value Vpickup the protection function actuation can be describe as

| 3V0 + 3j X I0 |gt Vpickup (211)

which is more simplified in (212)

| Z0 minus (minusjX) |gt Vpickup3 | I0 |

This relates the protection function to the apparent zero sequence monitoring of thebank The zero sequence impedance can be measured having the ground current and thebus voltages however the protection assumes a fixed and equal reactance for the threephases of the bank It is worthwhile to note that no reference in the current literature hasdiscussed fault location for this scheme Thus we have addressed this in the proposedmethods chapter

25 Phase current unbalance protection for fault location 15

25 Phase current unbalance protection for fault lo-

cation

Figure 25 illustrates application of phase unbalance for protection of different capacitorunits connections inside a capacitor bank

Figure 25 Phase current unbalance protection(a) SCB with window type CTs at neutralconnection (b) SCB with H-bridge configuration [2]

Because phase unbalance provides unbalance measurement per phase deriving theequation sets and logics that can be used for fault location is rather straight forwardFor two parallel banks with window CT at the neutral of each phase the differentialcurrents measured per phase will be useful for sensitive unbalance protection and faultlocation when compared to two individual CTs per phase summated electrically Withreference to Figure 25 part (a) the following can be written for phase A

IDIF = IA1 minus IA2

IA = IA1 + IA2

Using the identical voltage that the two parallel banks are working with we haveIDIF = VA

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

Before the failure the vectorial relationship between phase current and the differentialneutral current of the same phase is

IDIF = IAZA2minusZA1

ZA2+ZA1or

Iop = IDIF minus IAKA = 0(215)

where Iop is the operating protection signal which is nulled by compensating the inherentunbalance via the KA By approximating the impedances with their pure reactance thisk factor can be expressed as

KA asympXA2 minusXA1

XA2 +XA1

Failure of any capacitor element in either of the strings 1 or 2 changes the valueof KA to say KAf If we represent the new differential current with KfIA then theoperating signal would become

Iop = IA(KAf minusKA) (217)

According to (216) and Figure 41 the phase angle difference between the phase currentand the operating current defined by (217) can only be 180 or 0 dependent on thefusing and the string that involves the failed element Thus the location of the internalfailure can be found for each phase (string 1 or 2) Note that phase B and C arerespectively duplicated in the equations and explanations

Same idea applies for H-configured banks This time the operating signal will be thedifference between line current and the bridge current with a correlating k factor definedby circuitry laws In Figure 25 (b) IH will be zero if the voltage difference between thetwo points of A1 and A2 is zero For phase A using the identical voltage that the twoparallel strings are working with and by voltage division one can find out that this zerovoltage difference implies the following balance equation

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

Any unbalance will make the bridge current non-zero as

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

As a result failures in the upper left section (Z1) of the bridge and failures in lower rightsection (Z

prime1) of the bridge will cause same phase relation between the phase current and

the bridge current Same story applies for upper right (Z2) and lower left sections (Zprime2)

Note that phase B and C are respectively duplicated in the equations and explanations

26 Neutral voltage unbalance Y-Y ungrounded with isolated neutrals 17

26 Neutral voltage unbalance for double wye un-

grounded configurations with isolated neutrals

Figure 26 illustrates another unbalance protection method for double wye banks Thetwo sections in this protection scheme are not parallel Applying fault location con-sidering pre-existing inherent unbalance for such a protection scheme is not applicableThis is due to the fact that as the neutrals of the two sections are isolated no relationcould be found between the phase reactances Thus the number of unknown k factorswill be more than the known equations With regard to this configuration in the nextchapter we will discuss the proposed method of [27] which is based on some simplifyingassumptions

Figure 26 Neutral Voltage Unbalance Protection for Double Wye Ungrounded Config-urations with Isolated Neutrals [2]

grounded configurations with tied neutrals

Figure 27 illustrates another unbalance protection method for double wye banks This

Figure 27 Neutral Voltage Unbalance Protection for Double Wye Ungrounded Config-urations with Tied Neutrals [2]

unbalance protection is not sensitive to third harmonic components or system voltageunbalance [2] However it does not address bank inherent unbalance and thus it is not ascommon as the unbalance protection with neutral current Again this protection schemeis not favorable in terms of fault location Which is because unlike the double wye con-nections with a CT in the tied neutral the neutral quantity does not help to discriminatebetween failures in the rightleft sections ie there is no phase angle difference in theneutral voltage phasor We will elaborate more on this in neutral voltage estimationSection 472

28 Summary

This chapter introduced the fundamentals of detection of problems within the capaci-tor units Known relations of currents and voltages based on presumed symmetry inthe impedances of the bank are used in developing operating functions whose level isevaluated against thresholds for tripping the bank and preventing from cascading fail-ures The chapter mainly introduced unbalance protection basics for configurations thatalready have per phase unbalance measurements to give an idea of the fundamentalsof fault location Various unbalance relaying methods were introduced including someuncommon unbalance protection schemes In the following chapter a survey and theoryinvestigation will be presented for the patents and publications for SCBs fault locationThe focus of the present thesis would be on configurations that do not have per phaseunbalance indication common connections will be studied in more detail

Chapter 3

SCBs Fault Location LiteratureSurvey

31 Introduction

This literature survey reviews the existing approaches in locating internal element fail-ures for HV-SCBs The review has two parts The first part will cover explanation ofthe properties and application of existing fault location methods The second part in-vestigates one of the references in more detail as the relevant and fairly disclosed faultlocation method in the literature

32 Literature Survey

Detection of unbalances inside power coupling devices has been a concern for the industryin the past decades The aim has been disconnecting the device eg SCB to preventfrom cascading failures [28] Particularly several patents and papers on the protection ofSCBs have been published [7ndash102930] However the issue of fault location detection forthree phase SCBs have recently attracted more attention Identifying the failed elementamong the numerous elements constituting the bank requires measurement of voltageacross the capacitors or calculation of the impedance or current flow by deploying severalCTs This simple idea of direct measurements is complex for application and roughlyspeaking is an impractical approach Therefore research to at least identify the involvedphase has emerged in the recent years

Fault location determination is complex for configurations that do not benefit fromphase segregated protection methods ie where the unbalance is not measured per phaseExamples of these are single wye and double wye configurations with neutral voltageunbalance protection or neutral current unbalance protection respectively As discussedin the former chapter configurations that apply per-phase unbalance measurements donot introduce a concern in terms of fault location For example phase current unbalanceand H-bridge current unbalance both imply measured unbalance in each phase via CTsThe H-bridge configuration can even include potential transformers at tap points to makeits simple fault location immune to ambiguous failures [27] Fault location for solidly

20 Chapter 3 SCBs Fault Location Literature Survey

grounded single wye banks is also reported to be straight forward because normallythey are protected with voltage differential function across each phase that inherentlydetermines the faulted phase [31] see section 2

In [4] a string differential current based approach is presented which in fact is onlyapplicable for specially designed banks with extra available measurement points Theconfiguration discussed in [4] has 4 strings per phase Each string current is comparedtwice ie with its two adjacent strings In addition to this intra phase current unbalanceprotection a common string (zero sequence) current unbalance protection has also beenintroduced in [4] This zero sequence measurement is accomplished using 4 separatesumming blocks and helps in finding the involved string for cases that there are equalnumber of failed elements in two adjacent strings of the intra phase unbalance protection

The method presented in [25 32 33] is an impedance measurement based approachthat benefits from compensating temperature effects on impedance variation Real timemeasured impedances are averaged to fine tune the nameplate values A mho character-istic in the impedance plane is used for detecting changes in impedance of strings Tomaintain the sensitivity of the method the radii of the offset mho adapts with changesin the temperature For security reason in case of large scale system disturbances thefunction is blocked Such an approach for fault location and the method of [4] can becategorized in a separate group of methods as they require measurement of all stringcurrents which is not usually the case in terms of availability of measurement points andinstalled CTs The basis of the rest of the fault location methods for SCBs is phase anglecomparison [10] which is employed to determine the involved phase [2634]

The method introduced in [26 31 34] is faulted phase identification for ungroundedwye SCBs and faulted phase and section identification for ungrounded double wye SCBsThe idea is further discussed in [27 35] for several other simple connections A fixedreference ie positive sequence voltage for SCBs with neutral voltage protection andpositive sequence current for SCBs with neutral current measurement has been definedfor the phase angle evaluation of a determined compensated quantity The suggestedmethods of these references neglect the negative sequence component of the voltageor current to derive the expected value for each phasersquos fault Furthermore in thesereferences detection of number of failed elements consecutive failures and compensationfor partial shading and gradual changes in the capacitance as a result of aging andtemperature variations is not discussed Details of these methods will be elaborated inthe next part of this chapter

In the reference [36] a method which does not use the neutral measurements andthus is applicable to both ungrounded and grounded SCBs is introduced The methodcompromises the simplicity of unbalance protection and instead of four measurementsdeploys all three phase currents and voltages for SCB protection Also the fault locationbasis is very similar to [34] with the only difference of comparing current based operatingquantity angle to positive sequence voltage phase angle presuming the 90 degree phaseshift between phase currents and bus voltages for ideal capacitors In the mentionedreference compensated negative sequence current cancels out the effect of imbalancesnot related to internal capacitor failures Having the present time measurements and themeasurements from commissioning time the predetermined factor indirectly takes intoaccount the temperature variations However such an approach does not address the

33 Investigation and review of the SEL method 21

shading effect Moreover consecutive failure detection and determination of number offailed elements have not been considered in [36]

In [37] an algorithm for fault location is presented for double wye connected SCBswhich relies on comparison between consecutive measurements of the normalized un-balance current phase angle with respect to one of the phases In terms of the choiceof only one phase current considerations rise for algorithm security Because in casesteady state changes in the network symmetry are expected then per-unitizing based ona single phase current is not the proper choice The compensation method in [37] for pre-existing unbalance and consecutive failures is based on determining step changes in theper-unitized neutral current This implies that by consecutive measurements the goalof compensation is achieved indirectly The start tracking and end tracking momentshave not been clarified for these consecutive measurements Detection of the numberof failed elements is reported to be done by scaling the rms of neutral current to therms of a selected phase current (perunit) for an offline simulation based look-up tableDetails on how such an algorithm can be adapted to suit commercial relaying functionsare not provided Moreover in [37] it is claimed that by using the per unit value of theneutral current it becomes independent of system transients and less dependent of thetemperature changes however such a method can not address the shading effect Sameidea of measurement of step changes has also been developed in [21] for H-bridge banksThe proposed method in [37] is unproven in terms of angle of the step change The angleof the neutral current referenced to the phase current per se can not identify consecutivefailures and also it is not immune to pre-existing unbalance In this reference angle of thestep change is a vague term as the angle between the two subsequent unbalance currentswould be close to zero In addition the method does not introduce any compensation orresetting procedure

In conclusion because the details of the operating equations are also not disclosedfor [37] method of SEL [31] was chosen for comparison and review The following sectionprovides the calculations required to prove the derivation approach for the SEL methoddiscussed in [2734]

33 Investigation and review of the SEL method

The explanations in this section are mainly from references [2734] But we have investi-gated the details on derivation of the equations and assumptions because they were notdisclosed We refer to these referencesrsquo approach for fault location as the rdquoSEL methodrdquothroughout this thesis by this we mean the method of SEL Inc

331 Single Wye Ungrounded SCB

Figure 31 shows the respective measurements SELrsquos compensated voltage term (intro-duced as unbalance quantity) is defined as follows

∆VG = V BUSA + V BUS

B + V BUSC minus 3VN minus (η1 (V BUS

B minus VN) + η2 (V BUSC minus VN)) (31)

η1 and η2 are defined as scale factor settings based on the relay measurements that resetthe unbalance quantity

By comparing the phase angle of the ∆VG with the phase angle of the positive sequencevoltage the involved phase will be determined through the logic shown in Figure 32 Notethat the phase differences include a 15 blinder to avoid mis-detection of unbalances notresulting from capacitor failures The first inputs of the OR gates are for fuseless banksand the second ones stand for fused banks cases (implying 180 phase shift for change inthe sign of reactance variation in case of failure)

Figure 31 The SEL methodrsquos single Y configuration and available measurements

Figure 32 The SEL method fault location logic for single wye

Here we will investigate how they have come up with this equation and fault locationmethod For fault location purpose we have to write the equations while assuminga failure The assumption is that capacitor bank impedances can be approximated aspure reactances Also at this point it is assumed that all three phases have the same

reactance (X) before the failure takes place We start by writing a KCL at the neutralof Figure 31

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

where the bus voltages are denoted without the BUS superscript Considering a failurein phase A and rewriting the equations in another form we have

minus 3VN = 3timesminus VA

Xfminus VB

Xminus VC

where the reactance of phase A after failure is denoted by Xf Adding and subtractingthe underlined terms in the nominator results in

minus3VN = 3timesminus VA

Xfminus VA

minus VBXminus VC

rArr minus3VN = 3timesVA( 1

Xminus 1

Xf)minus 3V0

Multiplying the nominator and denominator of the right side by X and then adding 3V0to both sides gives

3V0 minus 3VN = 3timesVA(1minus X

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

rArr 3V0 minus 3VN = 3times (VA(1minus X

Xf)minus 3V0 + V0

2 + XXf

and consequently we derive

3V0 minus 3VN = 3times(VA minus V0)(1minus X

+ 2(36)

3V0 can be replaced with sum of the bus voltages Also the denominator on the rightside of the equation is a positive number as X

Xfasymp 1 It is also clear that VA minus V0 =

V +A +V minusA Considering that V minusA V +

A in a normal power system operation we can fairlyapproximate that ang(VA minus V0) = angV +

A By employing the same approach for phases Band C we can write

ang∆VG = ang(3 (VA + VB + VC)minus 3VN) = ang(V +p ) + ang(1minus X

) (37)

where V +p denotes the positive sequence component of the voltage of the involved phase

(p) For fuseless SCBs X gt Xf and for fused ones Xf gt X Therefore the algorithm ofFigure 32 can be verified However the assumption of equal reactances in (32) makes

the method vulnerable to inherent unbalance in the SCB Thus to increase the security ofthe method the authors of [2734] have subtracted a compensating factor of the followingform η1 (V BUS

B minusVN) + η2 (V BUSC minusVN) from VA +VB +VC minus 3VN to define ∆VG as (31)

To determine η1 and η2 in (31) we write a KCL at the neutral of Figure 31

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

where the bus voltages are denoted without the BUS superscript By multiplying thisequation by XA we have

VA minus VN +XA

(VB minus VN) +XA

(VC minus VN) = 0 (39)

By adding and subtracting the underlined terms as follows

VA+VB +VCminusVNminus2VN +VNminusVB +VNminusVC

(VBminusVN)+XA

(VCminusVN) = 0 (310)

By further simplification and factoring appropriate terms we have

VA + VB + VC minus 3VN minus ((XA

minus 1)(VB minus VN) + (XA

minus 1)(VC minus VN)) = 0 (311)

By comparing 31 and 311 we can determine

η1 =XA

minus 1 (312)

η2 =XA

minus 1

It is important to note here that (37) can not be simply derived assuming the generalcase where the capacitors of three phases are not equal

332 Double Wye Ungrounded SCB with Neutral Current Mea-surement

For a failed capacitor to withstand the discharge transient current flow from parallelcapacitors there is a limit for the total stored energy in a parallel connected groupTo keep the sensitivity of unbalance protection schemes while not violating this limitsplitting the bank into two wye sections is the preferred solution This makes double wyebanks a common connection in HV-SCBsFor the double wye configuration the SEL unbalance quantity is defined as

60KN = IN minus (K1 middot ICAPB +K2 middot ICAP

C ) (313)

variables of which are measured currents according to Figure 33 By comparing the phaseangle of the 60KN with phase angle of the positive sequence current the faulted phasewill be identified through the logic shown in Figure 34 For double wye configuration

depending on the CT polarity and the direction of the neutral current the phase anglerelationship with failures in the left bank and right bank is distinguished Figure 34is based on the assumption that the phase CT matches the neutral CT polarity and isfor fuseless banks In case of fused banks the legend would be reverse for right and leftsection faults

The way that such a method has been derived can be explained through the followingequationsWriting KCL at the left neutral node (Figure 33)

IN = I lA + I lB + I lC (314)

where the superscript l denotes the left section current in the corresponding phase Byperforming a current division this KCL can be written in terms of the phase currents as

IN = KAIA +KBIB +KCIC (315)

where we have omitted the rdquoCAPrdquo from notation of the phase currents and

Kp =Xr

X lp +Xr

p AB or C (316)

in which the superscripts r and l denote the corresponding right section and left sectionreactances In order to find the k-factors that should be set for inherent unbalancecompensation the KCL equation can be rewritten in the following way

IN = KAIA +KAIB

minusKAIB

+KBIB +KAIC minusKAIC +KCIC (317)

Because I0 would be zero as there is no path to ground in this configuration we have

IN = (KB minusKA)IB + (KC minusKA)IC = αAIB + βAIC (318)

which is in fact the neutral current prior to an internal failure that is caused by anyother unbalance ie pre-existing unbalanceAs a result and by simply changing the way k-factors are denoted the SEL fault locationprinciple constants (313) are found to have the following values

K1 = KB minusKA

K2 = KC minusKA

Assuming an element failure in the left section of phase A which causes the k-factor inphase A to get a new value of KAf namely after failure k-factor

KAf =Xr

the neutral current becomes

IN = KAf IA +KBIB +KCIC

= KAf IA minusKAIA +KAIA +KBIB +KCIC (321)

the compensated neutral current is then defined to be

INcompensated = IN minus INpreminusfailure = IN minus (K1IB +K2IC)

= (KAf IA +KBIB +KCIC)minus (KAIA +KBIB +KCIC)

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

Having this equation derived the logic of Figure 34 can be explained through the fol-lowing notesFirst of all considering that IminusA I+A in a normal power system operation we can fairlyapproximate that angIA = angI+A Second the positive sequence component of differentphases have 120 phase shift with respect to each other Third (322) implies that thephase angle of the compensated neutral current has zero or 180 phase shift (dependingon the section of the failure location) with respect to the phase angle of the phase in whichthe elementunit has failed The phase angle difference between the compensated neutralcurrent and the phase current is also dependent on the fusing method (ie impedancechange direction in case of failure see Figure 41) Putting these together the phasecomparison demonstrated in Figure 34 has been devised by SEL Inc to determine theinternal failure location Note that for a fused bank the legend for the right section andthe left section will replace each other

Figure 33 The SEL methodrsquos double wye configuration and available measurements

333 Double Wye Ungrounded SCB with Isolated Neutrals

Fig 35 shows the measurements that are available based on the neutral voltage unbal-ance protection (59NU) for this configuration

Figure 35 Double Wye Ungrounded Configurations with Isolated Neutrals

Similar to ungrounded double wye banks with neutral current unbalance protectionthe measured neutral quantity is expected to be zero for two healthy bank sections Thisis because both neutrals will have the same value which is equal to V0 Therefore bydesign the two sections could be of different rated reactances which is not consideredby the SEL method Here we will investigate the SEL method for this configuration iethe equations are developed for this purpose The final assumptions concluded for thismethod will be used to clarify why this particular SEL method is susceptible to externaldisturbance case studies in the future chapters

Assume that all phase reactances are equal to X With a failure in the left section ofphase A that makes the reactance Xf we can write two KCLs at the neutrals

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

Subtracting the later equations from each other we can express the result in terms ofthe neutral voltage difference defined by (325)

VNlNr = VNl minus VNr (325)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

Simplifying the later equation gives

VNlNr3

minus 1

X)(VA minus VNl) (327)

If we multiply both sides by X and using the following notation

XSpu =X minusXf

we can express the identity as

3VNlNr = XSpu(VA minus VNl) (329)

By defining an unbalance quantity from (329)

∆VG = VNlNr minusXSpu

3(VA minus VNl) (330)

one can get an idea of the parameter estimations in the SEL operating quantity whichis

∆VG = VNlNr minusKV + (331)

where K is the phasor setting that resets the principleThe SEL fault location logic assuming a 15 blinder is shown in Figure 36 The principlephase angle is referenced to the positive sequence bus voltage phase angle denoted asDVGA As a result the concluded assumptions are as followsFor a normal power system operation when assuming VNl VA fairly it can be approx-imated that ang(VAminusVNl) = angV +

A (because the neutral voltage is almost equal to residualvoltage when pre-existing unbalance is neglected) Similar idea is true for other phasesand therefore a general phase angle relationship can be written for (329)

angVNlNr = ang(V +p ) + ang(1minus X

) (332)

where V +p denotes the positive sequence component of the faulted phase voltage For

fuseless SCBs X gt Xf and for fused ones Xf gt X

Figure 36 The SEL fault location logic for double wye with isolated neutrals

34 Summary 29

Because K is expected to get a small value the phase angle of the compensatedquantity referenced to positive sequence voltage phase angle is approximately the sameas its uncompensated referenced phase angle which was verified in (332) In equationform this is

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

= angVNlNr minus angV + (333)

334 H-bridge banks with CT in each phase and PT at the tappoint

In accordance with the descriptions in section 25 the fault location principle using thebridge unbalance current is expressed as follows in [27]

60p = IHp minusKpIp (334)

Which is derived from (217) and (219)In order to determine which quadrant of each phase of an H-bridge has the failed

element both phase voltage and phase current unbalance protections should be appliedThe reason is as per section 22 voltage differential protection can distinguish whetherthe upper part of a tap is faulty or the lower part Also as per section 25 the phasecurrent unbalance itself can only distinguish between the failure of the two diagonals ofthe bridge

Figures 37 and 38 demonstrate the configuration measurements and the fault loca-tion logic based on a 15 blinder respectively It is worthy to note that in Figure(38)DV A points out to (23)

34 Summary

This chapter covered the current fault location methods and where applicable elaboratedon some of them in detail Assumptions and properties of the methods were extractedto help out in proposing new methods for fault location in HV SCBs Next chapter willpresent the proposed ideas and algorithms

Figure 34 The SEL methodrsquos fault location logic for double wye (fuseless)

Figure 37 Measurements for fault location of H-bridge banks

34 Summary 31

Figure 38 The SEL fault location logic for H-bridge banks

Chapter 4

The Proposed Fault LocationMethods

41 Introduction

This chapter presents the proposed methods for fault location in HV SCBs The config-urations for which new ideas have been developed or the fault location is proposed forthe first time are introduced and the equation sets that form the fault location principlesare elaborated Flowchart of the algorithms and application settings are also explained

Accuracy of an internal failure detection method is directly related to how it candiscriminate between pre-existing unbalances in the bank and the subsequent failuresAccordingly operating function k-factors are determined to develop sensitive fault loca-tion methods

Although the initial difference between reactances of different phases is minimizedthrough manufacturing methods [4] see Section 51 but still there would be a differencein the total phase reactances Thus different reactances need to be assumed for the threephases Because temperature affects the reactance and even at times part of the SCBmay be under direct sunlight while the other part is in the shade (aka shading effect)k-factors should be updated at regular time intervals This helps to compensate for thegradual changes A separate section in this chapter will explain this algorithm property

Common connections and fusing technologies are considered in the proposed faultlocation methods development The selected configurations are complex in terms ofderivation of the unbalance equations with the expected available measurements Theproposed logics consider whether the bank is internally fused or fuseless to account forthe increase or decrease in the magnitude of the reactance after the fault see Figure 41

In the following sections of this chapter first a new indicating quantity is definedbased on the measured voltages around single wye SCBs and it is denoted as super-imposed reactance This complex value forms the basis for the proposed fault locationmethods in three different grounding arrangements Originally the principle is developedfor single wye ungrounded SCBs with neutral voltage unbalance protection and thenit is adapted to become suitable for two other connections grounded through CT andgrounded through capacitor After these an enhanced fault location method is intro-

41 Introduction 33

Figure 41 Effect of fusing on the change of reactance

duced for grounded and ungrounded double wye SCBs with neutral current unbalanceprotection The proposed fault location methods not only incorporate the properties ofthe present methods in the literature but also put forth solutions for more application is-sues while making the most out of the in-use measurements This is in consistent with the

34 Chapter 4 The Proposed Fault Location Methods

common practical unbalance protection functions The algorithm development includesassumption of different phase and section reactances due to manufacturing tolerance Theproposed methods are devised with less simplifications to keep the fault location sensitiveto slightest failures while it is immune to noise harmonics and external unbalances

42 Superimposed Reactance (SR) for Ungrounded

Single Wye SCB

421 Determining the involved phase

XA XB XC

Figure 42 Ungrounded single wye shunt capacitor bank

Assume a single wye ungrounded SCB Figure 42 Writing KCL at the neutral nodeconsidering a failure in phase A gives

) =VAXAf

where XAf denotes the reactance of phase A after the elementunit failure Adding andsubtracting the underlined terms will simplify this very first equation

minus 1

) =VAXAf

minus VAXA

Multiplying both sides by XA will give

VN =(VA

XAXAfminus VA) + VA +KA

BVB +KACVC

( XAXAfminus 1) + 1 +KA

B +KAC

where we have defined two pre-failure reactance ratios as follows

42 Superimposed Reactance (SR) for Ungrounded Single Wye SCB 35

Having (43) we can add and subtract VB and VC to the numerator The internalunbalance of the SCB makes the neutral voltage to change from the zero sequence voltageAlso V0 can be considered to be a representative of the power system (voltage) unbalanceThus to account for the power system unbalance it is tried to abstract the differencebetween the residual voltage V0 and the neutral voltage by adding and subtracting V0from (43)

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

CVC + VC minus VCXAminusXAf

XAf+ 1 +KA

B +KAC

minus V0

Simplifying the previous equation one can derive

VN =(VA minus V0)

XAminusXAfXAf

+ (KAB minus 1)(VB minus V0) + (KA

C minus 1)(VC minus V0)XAminusXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

For auto-setting of the constants in (46) and thus representing the inherent unbalancein the SCB we have to evaluate this equation prior to an internal failure By assuming

XAf = XA (47)

we will have

VNest = αA(VB minus V0) + βA(VC minus V0) + V0 (48)

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

In (48) the neutral voltage is denoted by VNest as it is an estimation of neutral voltagewithout direct measurement of it Using (48) we can solve for αA and βAFor a failure in phase A of the SCB the corresponding k-factors in terms of their relativeαA and βA are

1 + 2βA minus αA

1minus βA minus αA

αA + αAKAC + 1

1minus αA

The k-factors can also be set directly using the following equations A simple KCL atthe neutral point implies

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

or equivalentlyVA minus VNXAXA

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

Thus for each phase the k-factors can be set separately eg for phase A we can write

(VB minus VN)KAB + (VC minus VN)KA

C = VN minus VA (415)

Equation (415) is a set of two equations for real and imaginary parts of the voltageterms Hence the two unknowns k-factors can be found and set for fault locationAfter setting the k-factors the following terms can be defined to simplify (46)

γA = (KAB minus 1)(VB minus V0) + (KA

C minus 1)(VC minus V0) (416)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

Note that γ is not a constant but a continuously monitored factor for each phase XSpu

denotes the superimposed reactance and both its magnitude and phase angle will bemonitored Therefore the general form for (46) becomes

(XSpup + λp)(VN minus V0) = (VA minus V0)XSpu

p + γp (419)

which implies

XSpup =

γp minus λp(VN minus V0)VN minus Vp

By applying the same procedure when assuming failures in phase B or C the equationfor k-factors γ andλ of the two other phases can be found as follows

For phase B KB

C =KAC

KBA = (KA

B)minus1

γB = (KBC minus 1)(VC minus V0) + (KB

A minus 1)(VA minus V0)λB = 1 +KB

A +KBC

For phase C KC

A = (KAC )minus1

γC = (KCA minus 1)(VA minus V0) + (KC

B minus 1)(VB minus V0)λC = 1 +KC

A +KCB

The latter equation-sets for the two other phases demonstrate that the k-factors arerelative to each other As a consequence upon a failure the magnitude of the two otherphase principles also will change Fault location using XSpu implies that measuring the

43 Adapted SR Single Wye SCB Grounded through a Capacitor 37

equivalent reactance in terms of the measured voltages introduces an accurate way tolocate the internal unbalance caused by element failures

With reference to (418) and the sign of the reactance difference (before and afteran internal failure) we know the expected phase angle of the perunit superimposedreactance For fuseless banks because Xp gt Xpf it is expected that in case of failurethe angle of XSpu for the faulted phase would be around 0 we will consider a tolerancefor security reason as it will be explained in Section 484 Similarly for fused banksthe expected phase angle for XSpu is (about) 180 because Xp lt Xpf In order tomake a unique phase angle boundary for both fused and fuseless banks it is proposed toincorporate a sign factor to (418) This factor is defined as follows

+1 for fuseless banks

minus1 for fused banks(423)

Therefore after failures the phase angle of the superimposed reactance will lie aroundzero As a result the superimposed reactance would be

XSpup = Ksg

422 Estimating the number of failed elements

For detection of the number of failed elements and also activation of the phase anglecomparison logic a referencethreshold value can be set simply using the superimposedreactance magnitude based on (418) Accordingly one advantage of the proposed princi-ple is that there is no need for derivative calculation to find a base for number of elementfailures detection The defined superimposed reactance as per (418) can be set as a basefor this purpose using the SCB nameplate values assuming failure of a single elementSee Section 482 for more detailed equations

43 Adapted SR for Single Wye SCB Grounded

through a Capacitor

We will investigate application of the proposed superimposed reactance concept for faultlocation of single wye SCBs grounded through a capacitor Applying KCL at the neutralpoint of the shown SCB in Figure 43 with a presumed internal failure in phase A resultsin the following balance equation

= VN(1

) (425)

Adding and subtracting the following underlined terms results in

XA XB XC

Figure 43 Measurements available for single wye SCB grounded through a capacitor

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

(426)Multiplying both sides by XA reintroducing the superimposed reactance as per (418)and defining the k-factors as per (44) with a third k-factor introduced by the followingdefinition

VAXSpuA + 3V0 + VB (KA

B minus 1) + VC (KAC minus 1) = VN(1 +KA

B +KAC +KA

N +XSpuA ) (428)

Adding and subtracting three terms of KAp V0 for the three k-factors can introduce

an equation which looks similar to the proposed principle for ungrounded banks as per(424)

(VNminusVA)(XSpuA ) = (VBminusV0)(KA

Bminus1)+(VCminusV0)(KACminus1)minus(VNminusV0)(1+KA

B+KAC+KA

N)minusKANV0

(429)The following terms can be defined to simplify the last equation

γprime

A = (KAB minus 1)(VB minus V0) + (KA

λprime

A = 1 +KAB +KA

C +KAN (431)

Comparing with the γ and λ terms derived for ungrounded wye SCBs (416) and (417)it can be shown that

γprimeA = γA

λprimeA = λA +KA

43 Adapted SR for Single Wye SCB Grounded through a Capacitor 39

Therefore the resultant fault location principle would be

XSpup =

γprimep minus λ

primep(VN minus V0)minusK

VN minus Vp(433)

where the superscript p denotes the phase for which the superimposed reactance isestimatedTo derive the self-setting equations KCL is applied at the neutral point of the SCBshown in Figure 22 which results in the following balance equation

= VN(1

) (434)

this can be rewritten as

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

a more organized presentation of the later equation is

VN(1 +KAN)minus VA = KA

B(VB minus VN) +KAC (VC minus VN) (436)

As can be seen the number of k-factors is three but only two equations ie real andimaginary segments of (436) exist for deriving them (all of the k-factors are real numbersrepresenting reactance ratios) Accordingly since the grounding capacitive reactance issmaller than phase equivalent capacitive reactance the Kp

N would be much larger thanthe phase k-factors which are normally about unity Based on the neutral capacitor andthe phase capacitor values [3] a typical phase to neutral k-factor would be around 10 Asa result even with element failures development in any of the three phases the change inthe third k-factor from its pre-set value would be trivial and thus it is assumed that thisk-factor is constant for the fault location purpose ie there is no need to update thisquantity once it is set based on rated capacitor values It should be noted that accordingto IEEE Std C3799 [2] the ratio of phase reactance to grounding reactance (the thirdk-factor) does also appear as a ratio compensation property in the operating voltage forneutral voltage unbalance protection of this configuration and it is set constant using thecapacitor rated values

To determine the number of failed elements and also to trigger the phase angle compari-son logic a reference value can be set for superimposed reactance magnitude using (433)It is an advantage of this proposed principle that there is no need for derivative calcu-lation in quantifying element failures with a reference index The defined superimposedreactance as per (433) can be set as a base for this purpose using the SCB nameplatevalues assuming the minimum failure of one element See Section 482 for more detailedequations

through a CT

We will investigate application of superimposed reactance for fault location of this con-figuration Figure 44 illustrates the corresponding SCB unbalance protection schemeFaults will cause residual current to flow through the low ratio grounding CT and the

XA XB XC

Figure 44 Single wye bank grounded through a CT

resistive burden will develop an associated voltage VR For the sake of simplicity a CTratio (CTR) equal to the aforementioned resistance is assumed This way VR and theprimary ground current (IG) values can be equivalently expressed in the equations Sameassumption has been applied in the technical data provided in [2]

IG =VRR

CTR = VR (437)

Same assumption has been applied in the technical data provided in [2] CTR of 505and R of 10 ΩApplying KCL at the neutral point gives the following equation

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

Considering an internal failure in phase A that changes the phase A reactance to XAf plus addingsubtracting the specified terms will simplify the previous equation

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

44 Adapted SR for Single Wye SCB Grounded through a CT 41

With the same definition for superimposed reactance as per (418) and the k-factors asper (44) the rearranged balance equation would be

VA(XSpuA ) + 3V0 + VB(KA

B minus 1) + VC(KAC minus 1) = minusjXAVR (440)

In (440) the before failure phase reactance XA can be approximated with its ratedvalue denoted by X In terms of algorithm reliability the applicability of this assumptionfor consecutive failures will be investigated in Chapter 5 Nevertheless this assumptionis considered to be acceptable as the rated reactance is similarly applied in the operatingvoltage of the corresponding protection method defined in IEEE Std C3799 [2] To givean example for a 230 kV 8437 Mvar SCB with a value of 627 Ω for X a change of lessthan 01 after an element failure and less than 18 upon a unit failure was observedin the phase reactance Therefore even for detecting consecutive failures the assumptionshould still hold trueThe general equation for the SR developed from (440) and considering phase sequenceas p pprime and pprimeprime would become

XSpup =

Vp + VpprimeKppprime + VpprimeprimeK

ppprimeprime + jXVR

minusVp(441)

For self-setting the k-factors we have to evaluate the former equation prior to an internalfailure eg when XAf = X This results in nulling out the superimposed reactanceTherefore the real and imaginary parts of the following identity can be solved for findingthe two k-factors

KABVB +KA

CVC = minusjXVR minus VA (442)

The equation sets for phase B and C are analogous to (442) The final fault locationlogic would be the same as the one explained for ungrounded wye SCBs Also it is worthnoting that like the ungrounded wye case the principle should be multiplied by a signfactor as per (423) This makes the angle boundary become unique for both fused andfuseless banks

For detection of the number of failed elements and also activation of the phase anglecomparison logic a reference value can be defined to be compared with the superimposedreactance magnitude using (441) Accordingly unit and phase construction (numberof series and parallel connections ratings of elements and the bank) are the requiredinformation for estimating pre-fault and post-fault phase reactances It is worthy to notethat as the proposed SR is a per unit quantity the thresholds are not susceptible to agingof the capacitors

45 Enhanced Compensated Neutral Current for

Ungrounded Y-Y SCB

Double wye connection is a prevalent connection in HV-SCBs which helps to keep thetotal stored energy in a parallel connected group of capacitors within the limits whilemaintaining the sensitivity of unbalance protection Neutral current unbalance protection(ANSI 60N) is selected for development of the proposed fault location method since this isthe most common unbalance protection used for double wye banks Also this unbalanceprotection does not benefit from per phase unbalance quantity measurement which makesit challenging in terms of fault location

451 Determining the involved phase and section

Figure 45 Ungrounded double wye shunt capacitor bank

Figure 45 illustrates the circuit diagram and available measurements for an un-grounded double wye SCB with neutral current unbalance protection Using the leftsection currents denoted by superscript l the measured neutral current is identical to

IN = I lA + I lB + I lC (443)

Performing current division helps to relate the left section currents to measured phasecurrents

where the phase coordinate k-factors are defined as

Kp =Xr

X lp +Xr

p AB or C (445)

45 Enhanced Compensated Neutral Current for Ungrounded Y-Y SCB 43

in which the superscripts r and l denote the corresponding right section and left sectionreactances

Assuming an element failure in the left section of phase A that changes the leftsection reactance of this phase to X l

Af and thus yielding to a new k-factor for phase Asignified by KAf

KAf =Xr

X lAf +Xr

the neutral current would change to

IN = KAfIA +KBIB +KCIC (447)

Subtracting (447) from (444) nulls out any pre-existing unbalance and helps the neu-tral current change caused by the internal failure to stand out The result is noted bycompensated neutral current IComp

ICompN = (KAfIA +KBIB +KCIC)

minus(KAIA +KBIB +KCIC)

= (KAf minusKA)IA (448)

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

Equation (449) clarifies that for the phase in which the element has failed the ICompN

would be either in phase or out of phase with the corresponding phase current dependingon direction of change in the affected reactance see (450)

angICompN = angIA + ang(X l

A minusX lAf ) (450)

However ICompN should be expressed in terms of the measured current and adjustable

setting In this regard the neutral current of (444) is re-written in terms of symmetricalcomponents Note that as there is no path to ground I0 is zero for this configurationthus we have

IN = K1I1 +K2I2 (451)

Interestingly the k-factors are found to be complex conjugates of each other which canbe proved as followsRewriting the KCL equation of (444) in terms of symmetrical components gives

IN = KA(I1 + I2) +KB(a2I1 + aI2) +KC(aI1 + a2I2) =

I1(KA + a2KB + aKC) + I2(KA + aKB + a2KC) (452)

where a = ej2π3 Since KABC are real values and a2 = alowast the two k-factors are proved

to be complex conjugates of each other In order to solve for K1 the following approachhas been applied

First equation (451) is multiplied by Ilowast1 and then the conjugate of equation (451) ismultiplied by I2

Ilowast1 middot IN = Ilowast1 middot (K1I1 +K1lowastI2) (453)

I2 middot IlowastN = I2 middot (K1lowastIlowast1 +K1I

lowast2 ) (454)

subtracting the results gives

Ilowast1 IN minus I2 IlowastN = K1 |I1|2 minusK1 |I2|2 (455)

therefore we have

K1 =Ilowast1 IN minus I2 IlowastN|I1|2 minus |I2|2

Equation (456) uses the current measurements to auto-set the k-factors To ensure de-pendability of the unbalance k-factors the auto-set can be done using the average ofseveral successive measurements of phase and neutral currentsBy replacing the derived k-factors in the compensating term of K1I1 + K2I2 and sub-tracting it from the neutral current one can use the phase angle difference between thecalculated quantity and the phase currents to determine the faulted phase and section Tomake the phase comparison demonstrated in (449) adjustable for internally fused andfuseless banks a sign factor Ksg is defined that makes the final fault location principleto be expressed as

ICompN = Ksg (IN minus (K1I1 +K2I2)) (457)

Moreover depending on whether the element has failed in the left section or right sectionof the SCB (449) will get an additional negative sign As a result to make the decisionboundary uniquely around 0 phase angle difference between IComp

N and the faulted phasecurrent Ksg is defined as followsFor fuseless SCBs

+1 Left Section Evaluation

minus1 Right Section Evaluation(458)

For internally fused SCBs

minus1 Left Section Evaluation

+1 Right Section Evaluation(459)

The consequence of an element failure in one of the sections is the change in the reactancevalue The effect on the neutral current magnitude should therefore be evaluated to set areference for fault location application With reference to (444) and (445) the derivativeof the neutral current can be used to derive the required setting The procedure wouldbe similar to neutral current unbalance pickup setting calculations [3] It is worthy tonote that as in the common design for double wye ungrounded SCBs the left and rightsection of the bank may not have the same reactance so the reference value for detection

46 Enhanced Compensated Neutral Current for Grounded Y-Y SCB 45

of number of failed elements should be set separately for each section To find the changein the neutral current with development of a single element failure in the left section afailure is assumed in one of the phases say phase A

d INdX l

=d(KAIA +KBIB +KCIC)

IA (460)

which gives the following identity

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

Similarly for a failure in the right section of phase A one can derive

d INdXr

(X lA +Xr

A)2IA (462)

Same equations hold true for phase B and C To form the derived equations as a settingthe phase current is replaced by rated current Ir and the absolute value of the derivativeis re-written in terms of limits Both the change in reactance and the change in neutralcurrent are expressed in perunit values Left section reactance is selected as the base forreactance change and the rated phase current as a base for the neutral current change

∆ IN(pu) =

∆X l

A(pu) times Kx

(Kx+1)2Left section setting

∆XrA(pu) times 1

(Kx+1)2Right section setting

where the following relationship exists between left section reactance and right sectionperphase reactance

Xr = KxXl (464)

When ∆X(pu) is calculated for a single element failure the ∆ IN(pu) will form a basefor detection of number of failed elements that is also used to set a magnitude thresholdfor triggering the phase comparisonDetails on application settings and how the setting quantities are calculated for a givenSCB are provided in Section 482

Grounded Y-Y SCB

Developing a fault location method for grounded double wye banks with neutral unbal-ance protection would be almost similar to ungrounded ones As there is a pass to groundin this configuration the zero sequence current exists in the neutral current Howevereven sensitive unbalance protection methods [38] have had to ignore the effect of zero

sequence current This is because compensating the pre-existing unbalance caused byall three sequences of current ie setting the three k-factors requires a set of threeequations while we always have just a set of two (real and imaginary parts of the neu-tral current) As a result the zero sequence current is left uncompensated [2] Suchan assumption does not render loss of reliability for the protection and fault locationThe reason is first the two sections of these grounded banks are manufactured to beidentical in impedance (factory matched) Second a window CT measuring the vectorialdifference between the neutral currents is applied Furthermore as it will be seen inthis section manufacturing tolerance in the parallel banks impedance (mismatch) willcause a small aggregated k-factor multiplied by the zero sequence current in the expectedneutral current calculation which makes the effect of zero sequence to be negligible [3]Figure 46 illustrates this configuration with its corresponding measurements for neutralunbalance protection

Figure 46 Grounded double wye shunt capacitor bank

The pre-failure neutral current can be expressed in an approach similar to (315) and(445) The current through the window CT in the neutral is referred to as IN

IN = I lN minus IrN = (K lA minusKr

A)IA + (K lB minusKr

B)IB + (K lC minusKr

= KAIA +KBIB +KCIC (465)

where the k-factors are

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

If we transform (465) from phase coordinates into sequence components [3] it becomes

IN = KA(I1 + I2 + I0) +KB(a2I1 + aI2 + I0) +KC(aI1 + a2I2 + I0)

= I1(KA + a2KB + aKC) + I2(KA + aKB + a2KC) + I0(KA +KB +KC)

I1(KA + a2KB + aKC) + I2(KA + aKB + a2KC)

= K1I1 +Klowast1I2 (467)

As stated before the term corresponding to zero sequence current is neglected toenable auto-set of unbalance k-factors The coefficient of I0 itself is likely to get a verysmall value as the k-factors of different phases defined by (466) might be of varying signsFurthermore the resultant k-factors will be complex conjugate of each other since KA isa real value and a2 = alowastSince for severe system voltage unbalance the quality of compensation factor would belower than its actual required value reference [3] suggests a percent restraint see Figure47 for a commercial protection operating signal In the evaluation section it will beshown that restraint supervision is not necessary for supervised monitoring applicationssuch as fault location

Figure 47 Grounded double wye neutral current unbalance protection restraint super-vision [3]

The compensated neutral current for fault location would be the vectorial differenceof actual measured neutral current with the expected value of it derived as per (467)Therefore same equations as ungrounded SCBs will be used for fault location and k-factor calculation see equations (457) (458) and (459)

Similar to ungrounded double wye SCBs we need to first find out the neutral currentderivative with respect to one of the sections of a selected phase (reactance) Then theabsolute value of the derivative should be related to a minimum expected change in thereactance ie one element failure The difference from the ungrounded configurationis the identity which relates the value of the phase coordinate k-factors to the phasereactances as per (466) For grounded SCBs the two sections (the two parallel banks)

are factory matched which means the base for number of failed elements would be thesame for them The mentioned derivation could be expressed as

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

By taking the same procedure for a failure in the right section we will get similar resultsthough with opposite effect on the magnitude of the neutral current see (469) This wasexpected due to the differential property of the measured current through the neutralwindow CT

d INdXr

(X lA +Xr

A)2IA (469)

Again note that the expected value for XrA and X l

A are the same for this configurationand in the next equation we will denote both as X Also to set the function for aparticular SCB the phase current in (468) may be taken as its magnitude which will bedenoted as the SCBs primary perphase current Ir Thus the final base for detection ofnumber of failed elements would be

∆ INIr

2X(470)

in which ∆X denotes the absolute value of the change in one of the locationsrsquo reactancesuch as phase A left section as a result of an element failure in that location X denotesthe reactance of that location The last equation can be interpreted in per unit form aswell

∆ IN(pu) =∆X

2(pu) (471)

47 Envision of Additional Unbalance Protection El-

ements

The suitability of a fault location method depends on capacitor bankrsquos configuration andthe available monitoring points Locating internal failures could be an additional relayingelement to be added to a capacitor bank protection and control relay Thus it is seldomeconomic to add voltage or current transducers whose application could be for solelyfault location As a result this chapter by discussing two actual SCB configurationswill consider examining utility perspectives that already deploy additional unbalanceprotection elements

47 Envision of Additional Unbalance Protection Elements 49

471 Additional Voltage Differential Element

Figure 48 depicts the provided configuration

Figure 48 230 kV Grounded Fuseless Bank with Tapped Voltage Measurement in EachSection

The left string of each phase depicted along with the rack reference is in parallelwith a group of capacitor units shown on the right side of each phase Therefore theconfiguration is double wye with three differential elements per phase The aim is tolocate the faults on left and right (top of the LV capacitors) of each phase For eachsection of the SCB ie right and left the tap voltage is assessed against the bus voltagewith a k-factor that resets the signal

Vop = VBUS minus ksetVTAP (472)

The fault location philosophy is as explained in Section 22 As can be seen in Figure 48an additional differential function is included in the protection IED of this SCB namely87-3 with the following definition

Vop = V LTAP minus ksetV R

TAP (473)

Note that the kset values will take different values for the three differential functions

Estimating the number of failed elements

Sensitivity analysis of the differential protection function can be used to define a basefor the number of failed elements determination The incremental change in the voltagedifferential operating quantity can be found by taking the operating signal derivativewith respect to the reactance considering a change of reactance in the correspondingpart For the provided fuseless bank design the top section failures are of concern thuswe assume a failure in one of the sections suppose left and top ie XL

1 see Figure 49The lower part of the section is assumed to have constant reactance for this purpose XL

2 Bus voltage is also noted as Vp

Figure 49 A phase of a double wye SCB with voltage differential protection

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

Replacing the kset with its value as XL

d Vop = dXL times VpXL

In per-unit form and assuming that the bus voltage is equal to 1 per-unit we can re-writethe last equation in general as

∆Vop(pu) = ∆X(pu) (476)

in which the base for per unitizing the reactance is the corresponding section total reac-tance We will show in the evaluation results that the third differential function 87-3

gives a reliable auxiliary alarm which is helpful in case of bus VT failures A difference tonotice is that the voltages and the k-factor that comprise the operating function of 87-3have much less magnitudevalue than the corresponding ones in 87-1 and 87-2 More-over simultaneous failures could be detected successfully this is due to independence ofequations for each phase and section k-factors (87-1 and 87-2 functions) which allows toreset each function without disturbing the detection of failed elements in the rest of thephase and sectionsThe 87-3 function is not capable of detecting simultaneous left and right section failuresIn this regard sensitivity analysis can show the effect of the corresponding simultaneousfailures for 87-3 operating functionWith reference to Fig 49 the derivative of 87-3 function in Fig 48 can be expressedas follows First with respect to left section top of the tap failures

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

in per unit and assuming that the bus voltage is equal to 1 per unit we can re-write thelast equation in a general form as

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

in which the base for per-unitizing the reactance is the corresponding section total reac-tanceSame procedure with respect to the right section top of the tap failures gives

d VopdXR

=d(minusksetVp XR

XR1 +XR

= minusksetVpminusXR

(XR)2(479)

again in per-unit and assuming that the bus voltage is equal to 1 pu we can re-write thelast equation in a general form as

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

From (478) and (480) plus the fact that the right and left sections of the SCB of Fig48 have different reactances we conclude that upon simultaneous failures in left andright sections the magnitude of the operating function of 87-3 will get changed less thanthe expected jump for a single left section element failure An illustrative scenario willbe provided in Section 5

472 Additional Neutral Unbalance Element

Based on IEEE Std C3799 [2] for large and HV capacitor banks failure of a singleelement results in a very small operating signal This implies the need for ultra sensitiveunbalance protection A backup (redundant) neutral voltage unbalance protection isgenerally provided this will also help to reduce the chance of missing canceling failures

Neutral voltage is sensitive enough for protection purposes in case of mirrored failures inboth sections (simultaneous masking) while neutral current is not Similarly provisionsmight be made to back up voltage transformer based protections with current based onesor with back up VTsFigure 410 depicts a configuration in which both neutral current and neutral voltage aremeasured

Figure 410 138 kV Ungrounded Fuseless Bank

A single string on the left side of the illustration represents one wye section which isin parallel with a group of units forming the right wye section Thus the configurationis generally the same as what we discussed for double wye ungrounded banksAs it was mentioned the additional neutral PT could be an asset for protection howeverin terms of fault location the answer is different Since with neutral unbalance protection

a complete and successful fault location was demonstrated the only point that might beof concern is for simultaneous failures Which again for both neutral voltage unbalanceand neutral current unbalance it was shown that fault location is not applicable Sincethe added neutral measurement does not bring any per-phase measured quantity evenapplying both of the neutral current based and neutral voltage based fault locations inparallel will not introduce any benefitIn the next subsection we will discuss rdquoestimationrdquo of the neutral voltage without usingthe actual measurement to envisage any prospective application for fault location

Estimation of the Neutral Voltage

IEEE C3799 [2] introduces formulas for deriving the perunit magnitude of unbalancequantities for protection purposes A voltage based perunit value can be converted tothe primary quantity using system line to neutral voltage as a base and as reportedby [26] the formulas give an error of less than 1 when compared to simulationsA detailed explanation and a perceived new application of the formula presented in [2]for the neutral voltage calculation is discussed here By assuming a failure in eachsection of a Y-Y SCB the perunit capacitance of the phase can be calculated eitherusing the formulas of [2] or by taking the perunit value of the alternative one presentedin Section 482 Suppose the perunit capacitance is Cp for the affected phase then usingthe suggested instant of time analysis in IEEE Std C3799 the neutral voltage can bederived as follows For the instant of time that the affected phase bus voltage is at itspositive peak and considering 120 phase angle shift between the bus voltages the twoother phases are at their half of negative peak value Therefore we can make themparallel with a resultant phase capacitance of 2 pu Fig 411 presents the equivalentcircuit for that instant of time

Vp1 Vp2 || Vp3

Cp 2 pu

Figure 411 Derivation of neutral voltage based on perunit phase capacitance afterfailure

where V p1 is the phase with the failed element(s) and the two other phases aresignified with V p2 and V p3 A voltage division helps to express the neutral voltage inperunit

(1minus VN)Cp = (VN + 05)times 2 (481)

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

The last equation is the suggested formula in IEEE C3799

Discussion on Neutral Voltage Estimation for Y-Y Banks

Although at first an estimation for the neutral voltage seems to be a useful quantityhowever as it will be discussed it cannot be relied on for faulted section identificationin double wye banks [39]Fig 412 shows the circuit diagram for cut-set analysis of two single element failurescenarios in the left and the right section of an asymmetrical Y-Y SCB respectivelySuppose the reactance of the involved phase say phase A changes (noted by prime

VPXrsquol

Xrsquor

Cut Set

Figure 412 Neutral voltage estimate for asymmetrical Y-Y SCBs

symbol in Fig 412) Then for the described two scenarios the following equation setholds true

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Adding and subtracting the underlined terms to the corresponding equation givesVAminusVN

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Naming the neutral voltage of the first scenario VN1 and second scenario as VN2 helps to

48 Provisions for Algorithms Security and Applications 55

re-write the equation set as3VN1(

) = (VA minus VN1)(1

Xprimel

minus 1Xl

3VN2(1Xl

) = (VA minus VN2)(1Xprimerminus 1

This implies that the resultant neutral voltage from same level of failures in the left andthe right sections are the same if and only if the change in the two sections capacitance(reciprocal of reactances) are equal or equivalently

VN1 = VN2 lArrrArr Cprime

l minus Cl = Cprime

r minus Cr (486)

Referring to the configurations in Fig B4 and Fig 410 it is recognized that thecommon design for the asymmetrical SCB configurations implies slight differences in thetwo sections design such as difference in the per phase parallel strings number for afuseless bank Therefore the change in the phase capacitance after a failure would bethe same for the two sections and that gives equal neutral voltage magnitude which cannot help in determining the faulted section

473 Conclusion for applicability of additional protection ele-ments to fault location

The successful determination of simultaneous failures was verified for the additionaltapped voltage differential element This has been due to fault location indicating quan-tities independence for each phase and section This allows to reset each function withoutdisturbing the detection of failed elements in the rest of the phase and sections It wasalso concluded that the auxiliary alarms of the tap to tap differential element will beuseful in case of loss of bus VTs Sensitivity analysis proved the possible malfunction ofthis auxiliary alarm for simultaneous left and right section failures

Neutral voltage estimation applicability to involved section identification in capacitorelement failures was discussed and mathematical reason behind the unhelpfulness of thisquantity was also provided

48 Provisions for Algorithms Security and Applica-

In this section the provisions made to increase the proposed algorithms security andalso considerations for deploying the methods in actual relays are presented Theseinclude immunity to gradual reactance changes applying security counting scheme andinformation on the required data for relay settings plus displaying the fault locationresults for the bank repair crew and operators Flowcharts of the proposed methods arealso shown which include these provisions

481 Compensation for Gradual Changes in the Reactance

Similar to the difference in the perceived temperature in the sun and the shade for hu-mans there could be a considerable temperature variance for substation equipments tobe in the shade or under direct sunlight Solar radiation can greatly change the tem-perature of an equipment heating it above the air temperature Although temperaturedifference of around 10C is the usual expected value but extreme examples of possi-ble 30C difference have also been reported [40] In power capacitors solar heating canchange the capacitance for three different reasons [19]

bull Changing the dielectric film usually polypropylene

bull Changing the dielectric fluid mineral oil or other fluid

bull Heating of the dielectric fluid causes expansion better permeating the film

Some of the unbalance protection methods like voltagecurrent differential can reduceunequal solar heating effect [2] as the affected part of the quantities cancel out each otherThis is of higher importance for fuseless banks with lots of series elements By consideringa regular updating for the k-factors and hence making the algorithm immune to gradualchanges in the capacitance actual failures within the SCB can be distinguished reliablyIn order to detect sudden changes due to capacitor failures the k-factor updating isblocked with the very first considerable increase in the magnitude of the fault locationprinciple Upon detection of the failure the regular update process will be triggered againto ensure detection of subsequent failures The regular updating of k-factors is also calledrdquoself-tuningrdquo and the initial setting of them which is also applied upon failure detectionin our proposed methods is referred to as rdquoauto-settingrdquo [38]In order to find out the rate of this update so that the element failures do not getmissed or rdquolearnedrdquo by the algorithm we evaluate a worst case scenario for a partialshading We refer to IEEE standard for shunt power capacitors [41] the maximumambient temperature defined in this standard for operation of SCBs is 55C Consideringthe aforementioned 30C difference between one phase under direct sunlight and theother resting in the shade and using Figure 413 a gradually reached superimposedreactance defined by equation (418) of 15 can be anticipated for the worst casescenario Considering the fact that it takes hours for the 30C temperature differenceto be reached this anticipated amount is not comparable with even one single elementfailure effect References [38] and [42] have reported the fact that capacitor failures canbe distinguished from changes due to ambient temperature because of thermal inertia ofcapacitor cans For example for single element failures in single wye SCBs the magnitudeof the superimposed reactance will change 03 or even less in around 10 ms On theother hand it will take thousands of seconds for the worst case scenario of a shadingeffect to be able to mimic such a change Simulation results in the next chapters confirmthese calculated values See Table 51 and Figure 523 in Section 5As a conclusion to enhance the dependability of the proposed methods the k-factorsmust be updated after detection of each failure or after repair of the SCBs and toenhance the security of the proposed methods k-factors have to be updated at regularintervals of say once or twice an hour To avoid interference with the fault location this

regular updating should be blocked for a short while once an internal failure is suspectedie when the phase angle comparison is triggered

Figure 413 Per unit capacitance of the 25C rating vs temperature for capacitorsimpregnated with Faradol 810 insulating fluid [4]

482 Required Data for the Application Setting

The required data to set up the proposed fault location methods [43 44] is summarizedin this section We will also present that how the bank and capacitor unit constructioninformation could be used for setting calculations The following nomenclature showsthe required information from a usercustomer to set the application

Su Series groups in the unit

N Parallel elements in a group

P Parallel units in a group

Pst Parallel strings per phase

S Series groups line to neutral (or to neutral capacitor)

Qu Rated kVAR of each unit

Vu Rated voltage (kV) of each unit

Q Rated MVAR of the SCB (three phase)

V Rated line to line voltage of the SCB (kV)

f Rated operating frequency

Where the element capacitance is not provided directly capacitance of each element canbe calculated using the ratings and construction information of each capacitor unit see(487)

Ce = Cutimes Su

SutimesQuN times V u2 times ω

times 103 (487)

where ω denotes the angular frequency in rads and Ce and Cu denote element ca-pacitance and unit capacitance in microF respectively Based on the provided constructioninformation for both the bank and its units the after failure and before failure capaci-tance are calculated by the fault location algorithm considering a single element failureFor double wye banks the ratio of the nominal section reactances and the rated primaryper phase current of the SCB are also calculated as follows

Kx =Xr

Irated =Qradic3Vtimes 10minus3 (A) (489)

The before failure per phase capacitance is

C = Cutimes P times PstS

For fuseless banks according to definition [3] P equals unity The after failure per phasecapacitance for each section would be

Cutimes PS

(Pstminus 1) +Cutimes PS minus 1

(Cuf + (P minus 1)times Cu) (491)

where Cuf denotes the after single element failure unit capacitance Depending on thefusing method this capacitance will get one of the following values

Cuf =CetimesNSuminus 1

Fuseless Bank (492)

Cuf = (CetimesNSuminus 1

) (Cetimes (N minus 1)) Fused Bank (493)

Note that the operator implies the following identity

C1 C2 = (1

)minus1 (494)

Same equations apply for each section of the double wye bank The corresponding ca-pacitive reactances are also calculated where needed as X = 1

Cω To ensure method

reliability and for the purpose of threshold setting a safety factor of 09 is applied tothe calculated change in the fault location principle magnitude for single element fail-ures The resultant threshold would be the measure for phase comparison activation inthe proposed fault location methods and also a base for the number of failed elementsdetermination

483 The Proposed Algorithms Flowchart

A characteristic plane relative to the proposed fault location methods is presented in Fig-ure 414 For voltage based fault locations the magnitude threshold is set for the percentsuperimposed reactance For current based fault locations the magnitude threshold is setfor the compensated neutral current in percent of the rated current If the magnitudegoes beyond a specified minimum value then the angle comparison will be activated Itshould be noted that for double wye SCBs the angles evaluated by this characteristicare compensated neutral current angle referenced to each phase current angle As a re-sult the angle boundaries are set around zero phase angle Figures 415 and 416 show

Figure 414 General characteristic plane of the proposed fault location methods

more detailed algorithm steps by flowchart for the proposed SR based methods and theenhanced current based methods respectively

484 Blinder Counting Schemes and Blocking the Algorithm

Depending on how close the decision principle is to the security margins the blinderscan be defined Blinders are the tolerance from the zero degree angle zone proposedfor angle comparison for fault location purpose With 15 degrees safety margin forthe proposed methods an acceptable and reliable operation has been observed for thesimulated scenarios

With regard to the deployed counting scheme dependent on the counter limit thatchanges the status of the fault location (aka pick-up delay) the minimum required timebetween detectable consecutive faults can be investigated The counter is set on 30 whichrequires about 2 cycles of the fundamental frequency in order to change the status of

Figure 415 Flowchart of the proposed SR based fault location methods

Figure 416 Flowchart of the proposed enhanced current based fault location methods

the fault location report This setting is also intentional to make the principle variationsand the k-factor reset action visible in the evaluation figures Using this presumed securesetting we performed our investigation on minimum required time between two detectablefailures Simulations show that for a detection time of 30 ms the proposed methodswould be able to determine fault location of a semi-simultaneous consecutive failure asclose as 40 ms to the previous failure However in practice low pick up delays are notpreferred Because the role of magnitude criteria becomes very decisive and thus duringtransients it may result in loss of the algorithm security For this compromise reducingthe counter setting is not suggested as fault location determination is not time critical itis for postmortem actions (repair time reduction) and also it is unlikely for two failuresto happen exactly at the same time in different locations In practice the countingthreshold pick up delay can be set to say 100 ms and would able to detect consecutivefailures that are as close as say 200 ms to each other Nevertheless the proposed methodsare superior in terms of detection time as we also note that the more the number of thefailures the more the chances for cascading failures and thus the less time between themConsequently the detection time in locating the failures before tripping the SCB couldimprove the repair time for the capacitor bank and more availability of it in service

Fig 417 demonstrates the pickup and operation of the fault location based on thecounting scheme Because the voltage stress on the healthy elements in the SCB depends

Figure 417 Pickup and counting scheme

on the previous failed elements an adaptive pick up and pick up delay can be selectedThis way tripping the bank can also be initiated from the fault location when the numberof failed elements reaches a predefined limit for each phase

As it will be shown in the next chapter there are cases for some configurations whereit is suggested for security reason to block the fault location function in a protectiverelay In case during this short time that the fault location is blocked failures occur inother locations the algorithm will not be able to detect any subsequent failure unlessit gets reset upon unblocking This is because without resetting the principle it willretain variations due to a missed failure Thus the trade off would be between missingfailures in the same location during the blocking time due to resetting the k-factorsupon unblocking and not resetting the k-factors by relying on the fact that such afailure scenario is pretty unlikely [21] Therefore we have not suggested resetting thek-factors after the blocking interval A safer approach could be resetting them once nofailure is detected for a while after the unblocking moment

485 Usage and Information Display for Bank OperatorsServiceCrews

The fault location algorithm is intended to be integrated into the unbalance relaying ofSCB protection relays to provide advance alarms that often reduce the search space (bydetermining failure location) for planned maintenance Commercial numerical relays forSCB protection and control [345] report the sequence of event records They can captureand time tag state changes of relaying elements For every fault event the followingitems can be captured affected phasesection location number of failed elements andtime stamp of the faultevent Numerical relays can communicate fault information toHMISCADA relay setup tools using communication protocols Users can latch the frontpanel display of target messages ie faulty phase number of elements etc Moreoverdesignated LEDs of microprocessor-based annunciators [46] can be configured to indicatethe phase with failed capacitor elements to technicians that arrive at the substation

49 Summary

This chapter introduced the theories of the proposed methods and applications for faultlocation in HV-SCBs First the Superimposed Reactance (SR) concept was presented aspart of the fault location for single wye SCBs with neutral voltage unbalance protectionsecond the SR was adapted for applying fault location to two other grounding arrange-ments Then the neutral current unbalance protection was adapted to suit fault locationmethods for double wye grounded and ungrounded SCBs A discussion on applicabilityof additional protection elements was also provided Algorithmsrsquo characteristics such ascompensation for gradual changes in capacitance settings calculations and the flowchartof the proposed methods were also explained In the next chapter simulation study ofthese proposed methods will be presented

Chapter 5

Evaluation of the Proposed and theInvestigated Methods

51 Introduction

This chapter covers evaluation of the proposed methods also where applicable the SELmethod [45] is simulated for comparison Transient time-domain simulation studies areconducted to demonstrate the effectiveness of the proposed fault location schemes usingPSCADEMTDC software package The required voltage and current waveforms arerecorded in COMTRADE 1 format which is an standard file format for transient wave-form and event data of electrical power systems Anti-aliasing filters are applied to theoutputs of the transducer models Then the records are played back for a relay modeldeveloped in MATLAB Accordingly waveforms are resampled at 64 samples per thepower frequency cycle Depending on the signal type the relay model applies decayingDC removal filter or CVT transient filter and then uses full cycle Discrete Fourier Trans-form (DFT) for phasor estimation Phase angle compensation for the delays introducedby the filters have also been considered Phasor estimation and fault location algorithmare executed every 4 samples See Appendix A for more details

Because we deal with internal failures of the SCB the test power system is selectedto be a three phase source connected to the SCB via a transmission line SCBs are sim-ulated according to their configurations and designs See Appendix B for details of theSCB designs under study

In regard to simulation of the pre-existing unbalance in the SCB based on [4 21]capacitance of the units has a maximum acceptable tolerance of 10 from the averagevalue In practice this is rarely more than 7 In addition having this deviationmentioned on the unit nameplate the capacitor units are arranged in a way that theSCBs have equalized capacitance in strings and thus in the total phase Thus an inherentunbalance of around 05 or less is the final tolerance achieved in the capacitor bankstrings Regarding the phase unbalances this requirement is reported to be around

1Common Format for Transient Data Exchange

64Chapter 5 Evaluation of the Proposed and the Investigated Methods

1 [21] To validate algorithm performance the maximum allowable inherent unbalanceof 1 is simulated

Harmonic currents have been injected according to the limits set by the IEEE stan-dard 519 [47]Signal to Noise Ratio (SNR) of the output of currentpotential transformers are assumedto be 50 dB based on their rated secondary currentvoltage For the SCBs groundedthrough a capacitor the 50 dB SNR is simulated based on the nominal voltage acrossthe neutral capacitor

For evaluation under unbalanced voltages the balanced load is replaced with anunbalanced one Voltage unbalance of around 2 is considered which is the maximumacceptable value for the transmission level [48] The definition of voltage unbalance is aspercentage Voltage Unbalance Factor (VUF) defined in [49]

V UF =V2V1times 100 (51)

All of the voltage and current figures reported in this thesis are in primary values Tofacilitate interpretation of the fault location principle variations a demonstrative guideis provided in Fig 51 For the voltage based fault locations the plotted quantity would

Time Axis

Angle Zone

Magnitude Threshold

Element(s) FailureLocation determined k-factor gets updated

Counting Scheme Angle

Figure 51 Interpretation guide for fault location principle variations

be the SR and for the current based fault location it would be the compensated neutralcurrent Magnitude of the compensated neutral current will be plotted in percentage ofthe rated current of the SCB and angle of it is referenced to the corresponding phasecurrent Note that the magnitude threshold might not be shown on the principle variationfigures instead the tick marks on the magnitude axis are selected based on the thresholdThe intervals that have led to internal failure reports are also pointed in the figuresThe simulated internal failures include the following cases

bull Single element failure

bull Multiple element failure (simultaneous failures at one location)

51 Introduction 65

bull Consecutive failure (failure in the same location of a previous failure but with moretime interval in between compared to multiple element failures)

In the rest of the chapter first the angle zone margin and the counter setting are verifiedusing simulations and then the simulation case studies are presented according to variousSCB configurations

Blinder and Counter Settings

The angle zone in Fig 51 implies a tolerance band around zero for dependability toconsider currentvoltage transducer errors and security to exclude unbalances that donot originate from capacitor failures With 15 degrees safety margin an acceptable andreliable operation has been observed for the simulated scenarios Fig 52 demonstratesthe fault location principle variation for a single wye SCB with an element failure inphase B Harmonics voltage unbalance and arbitrary pre-existing inherent unbalance inthe SCB were simulated for this case As it can be seen in the absence of noise the

01 011 012 013 014 015 016 017minus180

180Phase A Superimposed Reactance

Angle Magnitude

01 011 012 013 014 015 016 017minus180

180Phase B Superimposed Reactance

01 011 012 013 014 015 016 017minus180

180Phase C Superimposed Reactance

Time (s)

Figure 52 Margin evaluation without measurement noise (fuseless wye SCB)

principle is securely far from the boundary and is right at the middle of the angle zoneThe measurement SNR of 50 dB with respect to the rated secondary voltage of 115

volts for the neutral PT of an ungrounded SCB implies noise magnitude of 288 timesgreater than even a 30 dB SNR with respect to the actual voltage at the secondary ofthe neutral PT The actual voltage at the secondary of the neutral PT has been found tobe in the range of 4 volts for internal failures This ensures that in practice the assumed

15 degrees margin will be more than satisfying in terms of reliability of the margin SeeFig 519 for comparison with the same case study with 50 dB measurement noise

Same performance has been validated for a double wye SCB Fig 53 demonstratesthe fault location principle for a fused double wye SCB that has been simulated for afailure in the left section of phase C Depending on the inherent pre-existing unbalanceinside the bank (which should be limited to 1 per phase as reported in [21]) the neutralcurrent is simulated to be less than 05 Amps Thus as the proposed algorithm showssatisfying performance for 50 dB SNR based on the 5 Amps rated current of the neutralCT secondary it will have the same successful operation for signal to noise ratios of evenless than 30 dB based on the actual neutral current in the neutral CT secondary

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

Angle Left Section Angle Right Section Magnitude

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

Figure 53 Margin evaluation without measurement noise (fused double wye SCB)

To demonstrate what we explained in Section 484 regarding the counter setting thefollowing simulations were performed The point is to clarify that although the faultlocation might be successful but the security could become a concern if we reduce thecounter limit Figs 54 and 55 illustrate simulation for single wye fused SCB Failure inphase A happens at 02 s and the failure in phase B happens on 022 s Figs 56 and 57illustrate the same issue for a fuseless double wye SCB Failure in phase A happens at 015s and the failure in phase B happens on 017 s To further demonstrate the consecutivefailures concept an illustrative simulation scenario is performed Six consecutive elementfailures are simulated the counter threshold is set on 30 and the time between failuresis 50 ms The failed elements location is A B C C B A chronologically The SCBis fuseless single wye grounded through a capacitor Figs 58 and 59 show successfuldetection of the failures with the counter setting of 30 Fig 510 illustrates the fact

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

Not a failure might compromise security

Figure 54 Fault location principle smaller counter settings for a single wye SCB

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

Figure 55 Successful detection of close internal failure [counter set on 10] single wyeSCB

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

Figure 56 Fault location principle smaller counter settings for a double wye SCB

01 015 02 025 03

Phase A Left Section Failed Elements

01 015 02 025 03

Phase B Left Section Failed Elements

01 015 02 025 03

Time (s)

Phase C Left Section Failed Elements

01 015 02 025 03

Phase A Right Section Failed Elements

01 015 02 025 03

Phase B Right Section Failed Elements

01 015 02 025 03

Phase C Right Section Failed Elements

Time(s)

Figure 57 Successful detection of close internal failure [counter set on 10] double wyeSCB

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

Figure 58 Counter setting and detection of close consecutive failures

01 02 03 04 05 06 070

Phase A Failed Elements

01 02 03 04 05 06 070

Phase B Failed Elements

01 02 03 04 05 06 070

Phase C Failed Elements

Time(s)

Figure 59 Fault location output for close consecutive failures

that for close failures to be distinguishable the consecutive failure has to happen afterthe reset of the principle ie after detection of the previous failure This is completelydependent on the counter threshold setting

01 02 03 04 05 06 070

Time (s)

Phase A Phase B Phase C

Figure 510 SR magnitude jump and reset for close consecutive failures

52 Single Wye Ungrounded

Simulation scenarios along with their corresponding fault location principle variations(track of change) and the fault location output are presentedCase 1-1 The very first scenario evaluates the case for balanced voltages and balancedSCB Measurement channel noise and harmonic distortion are considered An elementfails at 01 s in a fused SCB The increased magnitude of the superimposed reactanceand the angle for phase A which enters and remains in the angle boundary will result infailure detection in phase A at about 015 s in Fig 512Reset of the principle can be seen in Fig 511 as time passes the detection moment (015s) and the principle pattern changes as if no failure has took place The SEL methodexplained in Section 331 is also simulated for the same case This methodrsquos detectionangle variations is shown in Fig 513 in which each colored margin belongs to one phaseFig 514 shows that this method is also successful for this caseCase 1-2 Next case considers unbalanced load in the system and the resultant voltage

unbalance The rest of the scenario is the same as case 1-1The proposed method fault location principle (SR) its output the SEL method detectionangle and its output are plotted in the Figs 515 516 517 518 respectively Jumpsfrom 180 to -180 degree in Fig 517 are because it is the angle range defined in the SELmethod refer to Fig 32 As apparent from the results both the proposed method andthe SEL method have an acceptable performance under the introduced voltage unbalanceCase 1-3 As another consideration for single element failures pre-existing unbalance inphase capacitances is added to case 1-2 to evaluate the performance of the fault locationmethods The proposed methodrsquos fault location principle (SR) its output the SELmethod detection angle and its output are plotted in the Figs 519 520 521 522respectively

Again the compensation terms in detection principles make both methods successfulin dealing with cases with inherent unbalances

52 Single Wye Ungrounded 71

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

Figure 511 SR variations single failure in phase A Case 1-1

01 011 012 013 014 015 016 0170

Time(s)

Figure 512 Fault location output single failure in phase A Case 1-1

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

Figure 513 The SEL method detection angle single failure in phase A Case 1-1

01 011 012 013 014 015 016 0170

Time(s)

Figure 514 The SEL method fault location output single failure in phase A Case 1-1

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Phase B Failed ElementsN

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

Figure 520 The proposed fault location output single failure in phase A Case 1-3

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

Case 1-4 Until now the case studies were introducing different sources of unbalance stepby step From this point we will perform our evaluations for scenarios which include allof the unbalance sourcesFigs 523 and 524 demonstrate variations in the SR and the fault location output foran internally fused SCB respectively The following illustrative scenario includes eventsthat are successfully detected as reported in Fig 524 The satisfying performance ofthe proposed algorithm is validated under pre-existing unbalance voltage unbalanceharmonics and measurement noise

bull Single element failure in phase A at 02 s

bull Multiple element failure in phase B at 025 s

bull Consecutive failure in phase A at 03 s

bull Multiple element failure in phase C at 035 s

As it can be seen with the latching option and auto-update of the k-factors no maskingor unbalance cancellation (aka ambiguous failure) can affect the outputs of the proposedmethod The principle gets reset in order for the past failures not to impact detection ofsubsequent failures and each failure is detected and reported separately while the healthstate of the SCB is recorded In Fig 524 all of the phases have two failed elements after04 s which would have canceled each othersrsquo effect and result in ambiguous or missedfailure if the fault location havenrsquot had the calibrating factors updating propertyThe number of failures has been detected successfully according to the initial magnitude

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

Figure 523 SR variations Case 1-4

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

Figure 524 Fault location output Case 1-4

53 Single Wye Grounded Through a Capacitor 79

setting determined for the superimposed reactance see Table 51 for magnitude incre-mentsTable 52 shows the recorded k-factor values initial set and their first updated valueafter each of the failures in case 1-4 It is worthwhile noting that the initial values wouldhave been set to 100 if the simulated SCB havenrsquot included the inherent unbalance Notethat as per (421) and (422) k-factors of phase B and C are either reciprocal or ratioof the two phase A k-factors Thus they are not added to Table 52

Table 51 Increment in the magnitude of the superimposed reactance case 1-4Single Failure Double Failure

Magnitude () 0115 0228

Table 52 k-factor values for phase A case 1-4Initial 1st Failure 2nd Failure 3rd Failure 4th Failure

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

53 Single Wye Grounded Through a Capacitor

The proposed SR based fault location method is also validated for this configurationCase 2-1 A single element failure in phase A of an internally fused SCB takes place at025 s This scenario includes all of the unbalance sources as in Case 1-4

A closer look at the magnitude of the fault location principle is shown in Fig 527The figure demonstrates that a reliable magnitude threshold can be set smoothly as it isthe case for this worst case scenarioCase 2-2 The following illustrative scenario includes events that are successfully de-

tected as reported in Fig 529 The satisfying performance of the proposed algorithm isvalidated under pre-existing unbalance voltage unbalance harmonics and measurementnoise

bull Multiple element failure in phase A at 02 s

bull A first element failure in phase C at 025 s

bull Consecutive element failure in phase C at 045 s

The successful determination of fault locations in this illustrative scenario implies howupdating of k-factors addresses masking scenarios issue because having two phases withfailed elements has not lead to a false detection in the third phase (this is an ambiguousfailure scenario as shown in the first chapter) Fig 530 shows tracking of the changein counters of the three phases The counter threshold is 30 and it adds up another 30counts for a consecutive fault (adjustable setting)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

Figure 525 SR variations for a single element failure in phase A Case 2-1

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

015Superimposed Reactance Magnitude

Time (s)

Figure 527 Zoomed magnitude of the SR Case 2-1

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

Figure 530 Fault location counters Case 2-2

54 Single Wye Grounded via CT 83

54 Single Wye Grounded via CT

We will validate the properties and assumptions of the proposed SR based fault locationfor this configurationCase 3-1 The following illustrative scenario includes events that are successfully detectedas reported in Fig 533 The SCB is internally fused Track of the changes in the SR andthe counter are plotted in Figs 531 and 532 respectively The satisfying performanceof the proposed algorithm is validated under pre-existing unbalance voltage unbalanceharmonics and measurement noise

bull Single element failure at 02 s in phase C

bull Consecutive failure in phase C at 04 s

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

Figure 531 SR variations Case 3-1Case 3-2 To check whether keeping the reactance value constant does effect the con-secutive failure detection or not the results for the following scenario is presented hereThe SCB is fuseless

bull a unit fails at 022 s in phase A

bull a consecutive single element failure in phase A at 027 s

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

55 Y-Y Ungrounded with Neutral Current Unbalance 85

Figs 534 535 and 536 illustrate the successful evaluation It is worthwhile to notethat as apparent from precision limits an error in detection of number of failed elementsis expected when several elements fail simultaneously (failure of units) since error accu-mulation will be the consequence To minimize such an error in detection of number ofelements in presence of distracting signals (noise) the base magnitude has been set to 09of the expected superimposed reactance magnitude This makes the base value neithertoo much large to give less than the actual number of failed elements nor too much smallto give more than the actual number of failed elements For this illustrative scenario inthe simulated configuration each unit consists of 6 elements thus the detected number offailed elements matches its actual value a 6 element failure followed by a single elementfailure

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

55 Y-Y Ungrounded with Neutral Current Unbal-

For double wye SCBs as the fault location is based on another quantity we again demon-strate the results with scenarios that introduce the unbalance sources step by step andthen we will perform the rest of the cases with all of the unbalance sources involvedCase 4-1 Measurement noise and harmonic distortion are considered for this case Sys-tem voltages and the SCB are balanced Results are shown for a fuseless SCB A singleelement failure takes place in right section of phase B at 01 s The proposed methodrsquosfault location principle (compensated neutral current) its output the SEL method de-tection angle and its output are plotted in the Figs 537 512 513 514 respectivelyIn Fig 513 each colored band corresponds to one of the six possible locations for thefailed element

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

8Phase A Failed Elements

01 015 02 025 03 0350

8Phase B Failed Elements

01 015 02 025 03 0350

8Phase C Failed Elements

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

Figure 537 Compensated neutral current variations single failure in phase B rightsection Case 4-1

Case 4-2 After validation of case 4-1 the other sources of unbalance are added to thesimulation case The simulated scenario involves a single element failure at 01 s in rightsection of phase C of a fuseless SCBThe proposed methodrsquos fault location principle (compensated neutral current) its out-put the SEL method detection angle and its output are plotted in the Figs 541 520521 522 respectively In Fig 521 each colored band corresponds to one of the sixpossible locations for the failed element

As can be seen both methods demonstrate successful operation and compensationAfter validation of the proposed method for the cases that were comparable with theSEL fault location additional simulation scenarios were carried out to test the uniqueproperties of the proposed methodCase 4-3 The following illustrative scenario includes events that are successfully detectedas reported in Fig 546 The SCB is fuseless Track of the changes in the compensatedneutral current is plotted in Fig 545 The satisfying performance of the proposedalgorithm is validated under pre-existing unbalance voltage unbalance harmonics andmeasurement noise

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

Figure 538 The proposed fault location output single failure in phase B right sectionCase 4-1

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

Figure 539 The SEL method detection angle single failure in phase B right sectionCase 4-1

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

Figure 540 The SEL method fault location output single failure in phase B right sectionCase 4-1

The event sequence for case 4-3 is as follows

bull Single element failure at 01 s in left section of phase A

bull Consecutive failure in left section of phase A at 015 s

bull Multiple element failure in right section of phase B at 022 s

Table 53 shows the values calculated and set for detection of the number of failuresaccording to (463) for the fuseless SCB presented in Appendix B

Table 53 Increments in the magnitude of the compensated neutral current in percentof the rated current for single element failures

Left Section Reference Value Right Section Reference ValueMagnitude () 0071 0089

Case 4-4 Regarding the masking issue discussed in Fig 12 a case in which twophases experience left section failures and the other phase undergoes a failure in the rightsection can lead to incorrect fault location if an algorithm can not reset the constantsafter each failure Such a scenario has been simulated as an illustrative example for afused double wye SCB to demonstrate part of the validation process for the proposedmethod See Figs 547 and 548 Table 54 gives the values for K1 as per (456)initially and right after each failure detection for the described masking scenario

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

Figure 541 Compensated neutral current variations single failure in phase C rightsection Case 4-2

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

Figure 542 The proposed fault location output single failure in phase C right sectionCase 4-2

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

Figure 543 The SEL method detection angle single failure in phase C right sectionCase 4-2

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

Figure 544 The SEL method fault location output single failure in phase C rightsection Case 4-2

Table 54 K1 magnitude (pu) | phase (deg) sets for case 4-4Initial 1st failure 2nd failure 3rd failure

K1 00017|4951 00025|5247 00023|3527 00037|2201

It is worth mentioning that the initial magnitude for K1 approaches zero for a perfectlybalanced bank in a system with perfectly balanced voltages The non-zero set value forthe simulated scenario ensures compensation for the part of the neutral current that isnot caused by the internal failures (pre-existing unbalance)

56 Y-Y Grounded with Neutral Current Unbalance

Determining worst case scenarios is important for the proposed method evaluation Re-garding grounded double wye banks with neutral current unbalance and with referenceto what we discussed for the fault location principle in equation (467) the worst casescenario in terms of accumulation of unbalance terms is when the phase k-factors Kphave the same sign or in other words when left and right section mismatches are inthe same direction for all three phases We have considered this in the comprehensivescenario in case 5-1

56 Y-Y Grounded with Neutral Current Unbalance 93

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

Figure 545 Compensated neutral current variations Case 4-3

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

Figure 546 The proposed fault location output Case 4-3

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

Case 5-1 The illustrative scenario chosen to present includes the following events foran internally fused SCB

bull Single element failure in left section of phase C at 02 s

bull Multiple element failure in right section of phase A at 03 s

bull Consecutive element failure in left section of phase C at 04 s

Considering the maximum acceptable voltage unbalance in transmission systems andpre-existing unbalance in the SCB phase impedances Fig 549 shows measurementsfor zero sequence current and the differential neutral current for the described scenarioCancellation of unbalances that affect both wye sections equally can be seen in thedifferential quantity The compensated neutral current is shown in Figure 550Fault location principle and output are shown in Figs 550 and 551 respectively which

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

Figure 549 Zero sequence current and uncompensated differential neutral current Case5-1

demonstrate successful and reliable determination of the failures Notice resets in thecompensated fault location quantity (Figure 550) while uncompensated neutral currentis incrementally increasing (Figure 549)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

2Phase C Right Section Failed Elements

Time(s)

57 Case Studies with Additional Protection Elements 97

57 Case Studies with Additional Protection Elements

571 Y-Y Ungrounded with Neutral Voltage Unbalance-TiedNeutrals

In this section first the fact that left and right section failures will result in the sameamount of change in capacitance for the typical utility asymmetrical ungrounded doublewye bank Fig 410 is shown to validate the discussion in Section 472 and thena numerical example is given for the discussed neutral voltage estimation in the samesectionFor the SCB of Fig 410 the before failure and after failure phase capacitances for leftsection and right section failures are as follows respectively

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

The calculations are done using equations of Section 482 Values are in microF As aresult the change in the capacitance for both of the left and right section failure casesis 002microF And thus the neutral voltage would be the same for the left and the rightsection failures This confirms what we concluded in Section 472For the simulated SCB of Figure B4 the capacitance values are

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

which similarly give the same capacitance change of 000704microF and the simulation givesthe following neutral voltage for a simplified scenario of balanced voltages and no pre-existing unbalance with a failure simulated at 02 s Regardless of the section in whichthe failure takes place the neutral voltage is the same The voltage estimation is alsoevaluated as per (482) as followsThe phase capacitance in per-unit form and using IEEE Std C3799 is

Cp = 10015 pu (56)

Using Section 482 equations the rated phase capacitance is 5 microF while after the failurethe capacitance reaches 500704 thus the per-unit value would be 100141 which shows

01 012 014 016 018 02 022 024 026 028 030

Time(s)

Figure 552 The measured neutral voltage for rightleft section single element failures

negligible error in the standardrsquos estimation methodThe resultant neutral voltage would be

VN =CP minus 1

CP + 2= 52193times 10minus4 pu (57)

this corresponds to a peak of 98015V for the 230 kV system and matches the simulationresult shown in Fig 552

Simulation study for the configuration of Fig 48 is presented in this part The keydifference for this configuration is that due to additional measurements simultaneousfailures in different locations are detectable It is worthwhile to note that the providedSCB configuration is fuseless and therefore the tap is at the low voltage capacitorsThe LV capacitors are formed by parallel connection of fuseless capacitors As a resulta capacitor failure at the bottom section gives a tap voltage of zero and needs to betripped as no failures in the top section can be detected without a measurable tap voltageTherefore for fault location study we investigate various failures in the top sectionCase 7-1 The following event sequence is simulated

bull First element failure in left section of phase A at 02 s

bull Consecutive element failure in left section of phase A at 025 s

The figures for fault location principle (voltage differential) are plotted separately foreach phase Figs 553 to 558 demonstrate the successful determination of location andnumber of the failed elements

02 025 03 035 04 045minus180

Phase A [Left]

Top Section Bottom Section

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

Figure 553 Phase A fault location principle voltage differential protection

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

Figure 554 Phase B fault location principle voltage differential protection

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

Figure 555 Phase C fault location principle voltage differential protection

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Phase A Right Bottom

Time (s)

Figure 556 Phase A fault location output voltage differential protection

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Phase B Right Bottom

Time (s)

Figure 557 Phase B fault location output voltage differential protection

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Phase C Right Bottom

Time (s)

Figure 558 Phase C fault location output voltage differential protection

Case 7-2 To show the benefits of having separate differential voltage elements (func-tions) for left and right sections and also the additional left tap to right tap differentialfunction a sample simulation scenario is performed The case includes the followingfailures

bull Single element failure in each phase all at o2 s

bull Simultaneous failures in left and right section of phase A at 025 s

Simulation results Figs 559-562 demonstrate the reliable operation of the fault loca-tion for the first event which is an ambiguous (masking) scenario and the second eventwhich is a simultaneous left and right failure scenario

The 87-3 function principle and its resultant alarms are plotted in Figs 563-566

02 022 024 026 028 03minus180

Phase A 87minus1 [Left]

02 022 024 026 028 03minus180

Phase A 87minus2 [Right]

Time (s)

Figure 559 Phase A fault location principle simultaneous failures

Although the 87-1 and 87-2 functions locate the left and the right section simultaneouscapacitor failures the 87-3 function is only capable of locating one of them The doublearrow deltoid head in Fig 563 points out the discussed fact in Section 471 Whichstated that upon simultaneous failures in left and right sections the magnitude of theoperating function of 87-3 will be changed less than the expected increment for a singleleft section element failure

02 022 024 026 028 03minus180

Phase B 87minus1 [Left]

02 022 024 026 028 03minus180

Phase B 87minus2 [Right]

Time (s)

Figure 560 Phase B fault location principle simultaneous failures

02 022 024 026 028 03minus180

Phase C 87minus1 [Left]

02 022 024 026 028 03minus180

Phase C 87minus2 [Right]

Time (s)

Figure 561 Phase C fault location principle simultaneous failures

02 025 030123

Phase C Left Section

02 025 030123

Phase C Right Section

02 025 030123

Phase B Left Section

02 025 030123

Phase B Right Section

02 025 030123

Phase A Left Section

02 025 030123

Phase A Right Section

Time (s) Time (s)

Figure 562 Fault location output simultaneous failures

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

Right Section Alarm Left Section Alarm

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

Figure 563 87-3 fault location principle for three phases simultaneous failures

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

Figure 564 Phase A 87-3 fault location alarm simultaneous failures

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

Figure 565 Phase B 87-3 fault location alarm simultaneous failures

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

Figure 566 Phase C 87-3 fault location alarm simultaneous failures

573 Conclusion on the Results for Additional Protection Ele-ments

Results of a thorough fault location study was demonstrated for an actual double wyeSCB with three differential elements The successful determination of simultaneous fail-ures is due to fault location indicating quantities independence for each phase and sectionThis allows to reset each function without disturbing the detection of failed elements inthe rest of the phase and sections The auxiliary alarms of the tap to tap differentialelement were shown to be reliable (for example when needed in case of loss of bus VTs)In addition sensitivity analysis proved the possible malfunction of this auxiliary alarmfor simultaneous left and right section failures Finally neutral voltage estimation wasevaluated the mathematical proof and conclusion in the previous chapter regarding fail-ure of this quantity for discriminating between left and right section capacitor faults wasverified

58 The SEL Method for Y-Y Ungrounded with Iso-

lated Neutrals

According to the assumptions we investigated for the SEL fault location method for thisconfiguration that deploys neutral-to-neutral voltage unbalance protection performanceanalysis of the present method in the literature is required Therefore we simulated themethod introduced in Section 333 It is worthwhile to note that the evaluated (SEL)fault location method for this configuration only supports single element failuresCase 6-1 The single element failure takes place in the right bank of an internally fusedSCB at 022 s The affected phase is phase CAlong with the fault location principle of [27] the function outputs the differentialvoltage and the compensated quantity are plotted in Figs 567 568 and 569 Thenon-zero value for VNlNr in Fig 569 which exists before the internal failure occurrenceconfirms the need for the differential voltage quantity compensation Further illustrativescenarios would be presented in the external unbalance case evaluations

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

58 The SEL Method for Y-Y Ungrounded with Isolated Neutrals 107

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

Figure 568 The SEL method fault location output Case 6-1

01 015 02 025 03 035 040

Time (s)

Compensated QuantityDifferential Voltage

Figure 569 Measured and compensated differential voltage Split wye bank with isolatedneutrals

59 Further Investigation on Algorithms Reliability

591 Simultaneous Failures

Simultaneous failures with exactly the same occurrence time are unlikely compared tothe ones in the previously presented scenarios Since the proposed fault location meth-ods have single decision boundary for each phase and the superposition property is notapplicable to the internal failure impacts on the fault location principle it is expectedthat fault location methods fail in case failures become simultaneous or super-closeFig 570 presents this case for two elements that fail at the same time one in the rightsection of phase C and one in the left section of phase B in a fused double wye SCBAfter failures occurrence the phase angles reach constant values however the marginsto include these phase angles in the corresponding zero angle zone have to be so widewhich will make the fault location vulnerable in terms of loss of security For instance ablinder setting of 41 degrees in the presented scenario of Fig 570 is required to detect aphase B failure The situation would be worse for the discussed SEL method in Chapter33 as it is not phase segregated and thus the phase angle can only be compared withone margin for two simultaneous failures in different phasesFor single wye SCBs two simultaneous failures in phase A and B in a fuseless SCB aresimulated As can be seen in Fig 571 the voltage based method of fault location (SR)also fails

In short the variable range for the phase angle and also the number of involvedphases make the detection of failure location complex and non-practical in terms of therequired characteristic for detection of exactly simultaneous failures in different locations

592 Susceptibility to External Disturbances

Even though for a supplementary function like fault location the safe and straight forwardsolution for reliable operation would be blocking whenever a shunt or series power systemfault is detected but in order not to miss element failures during this transients weperform simulations to see if blocking is necessaryFor algorithm performance evaluation temporary faults (representing transients in ashunt branch with respect to the SCB) on the bus that the SCB is located and alsoat the remote sending bus is simulated The results are included depending on the newpoints that a scenario had brought up Furthermore single phase open pole trippingwith subsequent reclosing (representing transients in a series branch with respect to theSCB) is simulated and results are demonstrated here

59 Further Investigation on Algorithms Reliability 109

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

Figure 570 Compensated Neutral Current Fault location malfunction for simultaneousfailures

01 015 02 025 03 035 04minus180

X 03Y minus615

Phase A Superimposed Reactance

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

Phase B Superimposed Reactance

01 015 02 025 03 035 04 045minus180

Time (s)

Figure 571 Voltage based fault location malfunction for simultaneous failures

Single Wye Ungrounded

Case 8-1 A phase A to ground fault with fault resistance of 05 Ω and duration of 50 msis simulated Meanwhile an element fails in phase B of an internally fused SCB This is anillustrative scenario and simulation of other fault types validated the same performanceFigs 572 demonstrates the SR variations for this case Fig 573 illustrates severejumps in the magnitude of superimposed reactance note that the magnitude is in per-unit in this figure Fig574 shows the changes in the SR magnitude for the same scenarioas case 8-1 with the difference of fault resistance which was changed to 100 Ω Thiswas intentionally simulated to demonstrate that even high impedance faults change theSR much more than internal failures in a way that the magnitude is reliably far fromthe thresholds This would help to block the fault location when external disturbanceis suspected due to high level of magnitude in the fault location principle Fig 575illustrates the fault location output In both cases the proposed method has been ableto locate the failure once the external disturbance is cleared

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Detectionamp ResetFault

Clearance

FaultOccurance

Figure 572 Proposed method performance under power system fault Case 8-1

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

InternalFailureOccurance

Figure 573 Jumps in magnitude of the proposed principle under power system faultCase 8-1

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

Figure 574 Jumps in magnitude of the proposed principle under power system fault(Case 8-1 with high impedance fault)

01 015 02 025 03 035 04 0450

Time(s)

Figure 575 Proposed method dependability under power system fault Case 8-1

Case 8-2 Another illustrative scenario involves a single phase to ground fault in thesame phase that will undergo a capacitor failure during this ground fault Duration ofthe fault is set to 100 ms both the power system fault and the internal failure take placein phase C at 02 s and 022 s respectively Fault resistance is 25 ΩFig 576 demonstrates that during the ground fault higher magnitude of the SR or anyother supervisory source should be used for blocking

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

Must be blocked due to high magnitude

Figure 576 The proposed method fault location principle Case 8-2

Otherwise as it can be seen from Fig 577 the fault location method would havemistakenly picked up due to momentary angle criteria satisfaction in phase A As a resultof blocking and once the ground fault is cleared the SR method has been able to detectthe phase C internal failure see the arrow pointing to the detection interval in Fig 576and the counter reaching the threshold in Fig 577Case 8-3 A three phase to ground fault is simulated The SCB is fuseless and an in-

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

Figure 577 The proposed method fault location method counter Case 8-2

ternal failure takes place exactly at the same time that the power system fault initiatesResults for fault at the SCB bus in the middle of the connecting transmission line orat a far bus (with the transmission line in between) were the same Figs 578 and 579show dependable operation of the proposed method after disturbance clearanceCase 8-4 Single pole tripping is considered for evaluation the open pole time duration

is selected based on minimum de-ionisation time for fault arc at 230 kV [50] For aninternally fused SCB in the system shown in Fig B5 phase A of the connecting linegets open at 02 s and is re-closed at 056 s Meanwhile at 035 s an internal failureoccurs in the same phase Figs 580-582 illustrate the principle variations changes inthe counter and the fault location principle magnitude (zoomed out) for this scenariorespectively As can be seen in Fig 580 the fault location needs blocking during theopen pole However after the reclosure again the proposed method shows successfuldetection of the failure location Notice the suitability of a magnitude based blockingsignal as per Figs 581 and 582Simulation of other open pole scenarios also confirmed this conclusion

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

Fault amp elementfailure

Internal FailureDetection

Figure 578 Proposed method principle under power system fault Case 8-3

01 015 02 025 03 035 04 0450

Time(s)

Figure 579 Proposed method output under power system fault Case 8-3

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

Magnitude blockinghas to be applied

Figure 580 Plot of the SR Case 8-4

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

Figure 581 The proposed fault location counter during open pole Case 8-4

01 02 03 04 05 06 070

Time (s)

Phase APhase BPhase C

Figure 582 SR Magnitude jumps Case 8-4

We also simulated the SEL fault location method for the same scenarios to investigateits performance The SEL fault location principle and its output are shown for case 8-1in Figs 583 and 584 As can be seen once the system fault is cleared this methodalso detects the failure correctly This confirms a delay in fault location same as ourproposed method Same performance was verified for other scenarios as well

01 015 02 025 03 035 04 045minus180

minus120

minus60

Time (s)Figure 583 The SEL method fault location principle Case 8-1

01 015 02 025 03 035 04 0450

Time(s)

Figure 584 The SEL method output Case 8-1

Single Wye Grounded Through a Capacitor

Three of the simulated scenarios are brought here for validation purposeCase 9-1 For a fuseless bank at 02 s an element fails in phase B At 022 s a shuntpower system fault occurs at a remote bus on the same phase The fault is cleared at032 s Figs 585 and 586 illustrate the results From Fig586 it is concluded that thepower system fault makes the picked up counter get reset however with clearance of thefault the corresponding counter picks up again and the right location is determined bythe proposed methodCase 9-2 The simulation case number 8-2 for which the fault location algorithm forungrounded wye bank was evaluated was simulated again for the configuration of wyegrounded through a capacitor Simulations illustrate reliable determination of the failurelocation without the need for blocking The bank is internally fused for the simulatedcase of Figs 587 and 588 As it can be seen although the counter picks up mistakenlyfirst it resets as the principle does not remain in the boundary With clearance of thefault the counter picks up again and determines the right location for the failure Sameresults achieved for faults with other resistance location and duration both for the fusedand fuseless banksCase 9-3 A worst case scenario with long duration open pole 950 ms in the same phasethat the element will fail is selected as an illustrative scenario Figs 589 590 and 591present the proposed fault location principle the counter and the zoomed out per-unitmagnitude of the proposed principle As the figures present the proposed method stillis reliable for the external unbalance case Same results were verified for simultaneousfailures and open pole tripping

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

Figure 585 The proposed fault location principle for Case 9-1

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

Figure 586 The proposed fault location counter for Case 9-1

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Reclosure of phase C

Detection of failureOccurrence of failure

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

Figure 591 The proposed fault location principle magnitude for Case 9-3

Case 9-4 A fuseless bank is chosen to simulate a case in which at 022 s an internalfailure in Phase A and an open pole in the same phase occur simultaneously For thesake of clarity of the demonstrations a short dead-time has been considered for this singlephase auto-reclosure ie the event lasts 100 ms Figs 592 and 593 show the successfuldetermination of the failure once the external unbalance is cleared As explained beforeapplying a magnitude upper limit is not necessary for fault location of this configuration

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

Figure 592 The proposed SR variations Case 9-4 SCB grounded via capacitor

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

Figure 593 The proposed method output Case 9-4 SCB grounded via capacitor

Single Wye Grounded via CT

Case 10-1 An internal failure is simulated in phase B at 022 s while a network phaseto ground fault exists in the same phase from 02 s until 03 s Results are shown foran internally fused SCB Figs 594-596 demonstrate the results Simulations showthe reliability of the proposed method and the fact that a delay dependent on the faultclearance time is introduced in the fault location determinationCase 10-2 An open pole in phase A takes place at 02 s and lasts till 03 s An elementfailure in the same phase takes place at 022 s in an internally fused SCB Fig 597illustrates that during the severe transient caused by the open pole drastic changes inthe SR might render spurious failure detection in another phase although with phasere-closure ie after 03 s the right location is determinable Fig 598 demonstratesthat the SR magnitude jump is far more than the expected values for element failuresTherefore blocking by putting limits on the magnitude is included in the code Figs599 and 5100 show the successful results

Case 10-3 A special scenario is presented for this case All elements of a unit failin phase A at 02 s then at 026 s a phase to phase fault (A-C) with 50 ms duration issimulated At 03 s another single element failure takes place in phase A Fig 5101shows the SR variations along with the successful fault location output This scenarioalso confirms the discussed assumption in Section 44 ie larger failures do not compro-mise detection of future subsequent failures

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

Figure 596 The proposed fault location output for Case 10-1

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

Figure 598 The proposed fault location principle magnitude for the opened phase inCase 10-2

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

Figure 5101 Case 10-3 Unit failure and external unbalance case study SCB groundedvia CT (a) the proposed SR variations (b) output of the fault location

Conclusion for Single Wye Banks

Several simulations were performed to discover whether failures that occur during powersystem faults are detectable and countermeasures to maintain the required reliabilityof the proposed fault location methods were introduced Simulations show that depen-dent on the severity of the system faults the magnitude of the SR can change abruptlyto hundred times of its change for a single element failure Even when the entire unitfails the operating signal would change much less The exact values depend on num-ber of elements and unit construction ie number of seriesparallel connections Theneutral voltage and the ground current change drastically upon occurrence of systemdisturbances thus imposing unpredictable variations both in the angle and magnitudeof the operating principles Therefore fault location of ungrounded SCBs and groundedones via CT are susceptible to malfunction during the disturbance unless blocking isemployed In the fault location algorithms an upper limit is set for the SR magnitudeto ensure that the variations are suspect of element failures and to disable fault locationuntil the power system fault gets cleared In the actual implementations blocking thisfunction of capacitor protection relay [21] can be done via communication with a systemprotective relay or supervision from other protection elements within a multi-functionalnumerical capacitor bank relay In another approach reference [3] uses a restraint signalwhich is the magnitude of vectorial sum of neutral voltage and zero sequence voltage forits neutral voltage unbalance protection The susceptibility is much less for banks thatare grounded via a low voltage capacitor because the measured neutral point voltageis across the grounding capacitor and thus in normal operating conditions (no system

faults) it is much greater than the normally close to zero ground currentneutral voltageof the two other configurationsSome additional results are provided in Appendix C

Y-Y Ungrounded with Neutral Current Unbalance

Performance of the proposed enhanced neutral current compensated based fault locationwas tested under various system faults The following cases are presented as illustrativeexamplesCase 11-1 A phase A to phase C fault happens at 02 s meanwhile an internal failuretakes place in the right section of phase C at 022 s the power system fault is cleared at025 s The SCB is internally fused Figs 5102 and 5103 demonstrate the variationsin the proposed fault location principle and the modeled fault location relay output re-spectively

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

Figure 5102 Proposed method compensated neutral current Case 11-1

01 015 02 025 030

rPhase B Left Section Failed Elements

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

01 015 02 025 03012Phase C Right Section Failed Elements

Time(s)

Figure 5103 Proposed method output Case 11-1

To illustrate the counter pickup and latching after reaching a pre-set threshold Fig5104 is presented here This Figure shows changes in the fault location counterAs can be seen in Fig 5104 a failure is suspected in the left section of phase B becausethe principle has entered the corresponding margin however as the principle does notstay inside the margin till the counter reaches a threshold the counter starts countingdown and in fact it gets reset This is while for phase C in the right section the countercontinues to increase until it reaches the threshold and latches with a correct fault locationdetermination When interpreting the figures that show principlersquos angle variations oneshould note that the principle will continue to stay inside the detection boundary unlessit is reset ie detected by the algorithm or another consecutive failure takes place Falsecounter pickups are also not a concern as the counter threshold can be set high enough sothat only the correct counters can reach the threshold Fig 5105 illustrates variationsin the neutral current and the compensated neutral current Furthermore Fig 5106is provided to compare and observe the way the external unbalance has changed the

01 015 02 025 030

15304560

Phase A Left Section Counter

01 015 02 025 030

15304560

Phase B Left Section Counter

01 015 02 025 030

15304560

Time (s)

Phase C Left Section Counter

01 015 02 025 030

15304560

Phase A Right Section Counter

01 015 02 025 030

15304560

Phase B Right Section Counter

01 015 02 025 030

15304560

Phase C Right Section Counter

Time(s)

Figure 5104 Algorithm security considering counter pickup and count updown processCase 11-1

variations in the proposed principle magnitude

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Internal FailureOccurance

System FaultOccurance Fault

Clearance

DetectionandReset

Figure 5105 Variations in the proposed principle magnitude under power system fault

01 015 02 025 030

Time (s)

Compensated IN IN

Figure 5106 Variations in the proposed principle magnitude without power systemfault

Case 11-2 A phase B to ground fault happens simultaneously with an internal failurein the left section of phase B both at 022 s The SCB is fuseless Figs 5107 and 5108demonstrate the successful fault location results for the proposed methodCase 11-3 For a 100 ms open pole in phase B an internal failure in right section of phase

C takes place at the middle of the dead-time The SCB is fuseless Figs 5109- 5111demonstrate the proposed fault location method reliable performance It is worthwhileto note that higher pick up delays further guarantee the discrimination between faultyphase and other phases and the illustrative scenarios provided here assume minimumpick up delays for reliable operation

Simulations also showed successful performance for the same scenario with the openpole interval aka dead-time increased to 360 ms and also for the scenarios of cases8-2 and 8-4

For further evaluation in the next illustrative scenario we have increased the dead-time of the open pole Because it is a common setting that bank undervoltage protectiontrips the SCB in a second when the bus voltage reaches 07 pu [3] an open pole of lessthan a second is considered for worst case simulationsCase 11-4 An open pole tripping for phase B is simulated at 02 s internal failure inright section of phase C occurs at the same time in the fuseless SCB the line reclosuretakes place after 950 ms

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Internal Failure Detection

Fault Clearance

Fault amp Failure Occurance

Figure 5107 Proposed compensated neutral current Case 11-2

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

Fig 5112 shows the proposed principle for the first 40 ms of the simulation It showsthe principle reaching the corresponding fault location boundary and the reset followedby fault location determination without any interference from the open pole of the otherphaseFigs 5113 and 5114 demonstrate the counter and output of the fault location functionfor Case 11-4 respectively

Case 11-5 Phase B is opened at 02 s and reclosure takes place 950 ms later meanwhilean internal failure in the same phase happens for the internally fused SCB at 05 s in theleft bank Simulations show that the fast detection of the failure depends on whetherthe open pole is in the same phase as the failure or not In case that failure is in adifferent phase then the proposed method can detect the failure faster Figs 51155116 and 5117 illustrate the proposed fault location principle the counter and theoutput respectively

As can be seen in Fig 5117 the failure is detected within about 600 ms The reasonfor this delay is demonstrated in Fig 5115 The open pole in the same phase as theinternal failure has made the jump in the principle magnitude to be lower than theexpected value This happens while the angle criteria is within the margin of detectionWith the closure of the opened breaker pole the magnitude also satisfies the detectioncriteria and the failure location is determined successfully

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

Figure 5109 The proposed fault location principle Case 11-3

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

Negative effect of open pole on the principle magnitude

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

The SEL method also was tested for reliability under external unbalances Figs5118 and 5119 demonstrate the SEL method performance for case 11-1 Each coloredzone belongs to one of the six possible locations As can be seen the SEL method

01 015 02 025 03minus180

minus120

minus60

Time (s)

Figure 5118 The SEL method principle for Case 11-1

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

Figure 5119 The SEL method output for Case 11-1

also performs well In addition for simultaneous shunt fault and internal failures sameperformance was validated

For the case 11-3 the SEL method evaluation is presented in Figs 5120 and 5121As can be seen the SEL method also determines the location of the failure successfully

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

Figure 5120 The SEL method principle Case 11-3

The SEL method assessed performance for case 11-4 is also selected for illustration hereFigs 5122 and 5123 show the fault location criteria and its output respectively Ascan be seen although the SEL method can detect the failure however it seems to takemuch longer time than our proposed method for fault location determination The rea-son is that during the open pole the magnitude of the negative sequence current becomescomparable to the positive sequence current therefore the assumption that the phasecurrent magnitude is only influenced by the positive sequence current magnitude is nolonger valid unless the negative sequence current magnitude reduces ie the line reclosuretakes place (at 115 s) This fact is presented in Fig 5124 Note that the longer it takesfor a failure location to be determined the more the chances of occurrence of consecutiveevents thus the subsequent failures will be missed unless a k-factor auto-set is performed

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

Figure 5124 Positive sequence and negative sequence line currents Case 11-4

Case 11-5 for the SEL method is selected to present here as it demonstrates the im-portant role of magnitude threshold Figs 5125 and 5126 are plots of the simulationresults and output respectively From the fault location output it seems that the SELmethod has lost its security because of a failure detection in phase A during the veryfirst moment after the open pole operation Fig 5127 shows the compensated neutralcurrent of this method In [31] the magnitude threshold is not disclosed in detail how-ever having this case study the importance of this criterion is shown

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

The magnitude which hasled to correct fault location

The magnitude which hasled to false fault location

Figure 5127 The SEL method compensated neutral current magnitude Case 11-5

Y-Y Grounded with Neutral Current Unbalance

For double wye grounded banks with neutral current unbalance protection particularlywe should refer to (467) and (466) where the uncompensated term in the neutral differ-ential current depends on the mismatch between the right and the left section reactancesand the level of unbalance that affects I0 Therefore solid ground faults (bolted faults)for SCBs with same sign mismatches for all three phases are worst case scenarios forexternal unbalance susceptibility evaluationCase 12-1 Simultaneous shunt ground fault and element failure happen for phase Bat 02 s The fault clearance time is 100 ms and the failure is in the right bank of afuseless SCB The residual current and the measured differential current are shown inFig 5128 The fuseless bank rated current peak is 354 A which signifies the incrementin the differential neutral current to be around 1 percent The proposed fault locationprinciple compensated neutral current and the output counter are shown in Figs 5129and 5130

01 015 02 025 03 035 040

I Diff

Time(s)

Figure 5128 Case 12-1 (a) Zero sequence current (b) uncompensated differentialneutral current

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Fault ampfailure occurrence

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

Figure 5130 Counter of the proposed fault location method Case 12-1

As can be seen the fault location is determined with a delay that is directly dependenton the fault clearance time However more important is that the detected fault locationis still reliable regardless of the severity of the shunt fault Fig 5128 shows that thedifferential neutral current magnitude is not affected by the zero sequence current levelwhich is present due to the external unbalanceSame results were confirmed for single phase to ground fault in the other phase and alsofor double phase to ground and three phase to ground faultsCase 12-2 For the same SCB same internal failure takes place but this time the externalfault instead of shunt fault is an open pole in the same phase The open pole lastsfor 360 ms The residual current and the measured differential current are shown inFig 5131 The proposed fault location principle compensated neutral current andthe output counter are shown in Figs 5132 and 5133 Further simulation cases also

01 02 03 04 05 06 070

I Diff

Time(s)

showed that same detection delays do exist even if the open pole does not happen forthe same phase as the internal failureCase 12-3 The illustrative scenario is as follows for a selected SCB which is fuseless

bull A phase A to ground fault takes place at the SCB bus at 02 s the fault gets clearedat 03 s

bull An internal failure in right section of phase A is simulated at 022 s

bull Two elements fail in the left section of phase C at 036 s

bull A single phase tripping takes place in phase C of the connecting transmission lineat 038 s and a successful reclosure happens at 048 s

The fault location principle is demonstrated in Fig 5134 As can be seen in the faultlocation report presented in Fig 5135 the external failures do not render spuriousreports although they introduce detection delays

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

ReclosureElement failure amp openpole occurrence

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

Left Section Right Section

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

The SEL Method for Y-Y Ungrounded with Isolated Neutrals

To complete investigation of susceptibility to external unbalances we performed simula-tions for this configuration that deploys neutral to neutral voltage unbalance protectionPresented studies are under scenarios that might cause assumption violation see Section333Case 13-1 A failure in the left section of phase B of a fuseless SCB takes place at 022s An external solid fault phase C to ground is simulated to disturb the principle from02 s until 03 s Figs 5136- 5138 demonstrate the results

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

Figure 5136 The SEL method referenced angle for fault location under external unbal-ance Case 13-1

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

An internal failure takesplace

A fault exists in thepowersystem

Figure 5138 Measured and compensated differential voltage under external unbalanceCase 13-1

As it can be interpreted from these figures the SEL fault location method seem tolose security during the fault presence in the network shown by red output in Fig 5137However upon clearance of the fault the fault location shows dependability and doesnot miss the past internal failure A solution could be blocking the fault location withdetection of power system faults The reason behind this loss of reliability is in fact theincrease in the voltage unbalance during the fault see Fig 5139 Note that havingconsiderable voltage unbalance violates the assumption of negligibility of the negativeand the zero sequence voltages effect on the fault location principle phase angle

As it was explained in Section 333 the SEL method seems to have the assumptionthat ang(Vp minus VNl) = angV +

p where Vp denotes the phase that has the failed element thusa case study was developed to demonstrate a scenario in which by occurrence of a phaseto ground fault the assumption is violated during the presence of the faultCase 13-2 Fig 5140 illustrates the simulation results in which an element failure in

right section of phase C happens simultaneously with a shunt fault of phase C to groundThe SCB is internally fused with nonidentical section reactances that also include pre-existing unbalance The fault is cleared after 100 ms As can be seen in this figureduring the fault the assumption violation keeps the phase angle out of the fault locationboundary

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

Figure 5139 Voltage unbalance during power system fault Case 13-1

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

Figure 5140 Case 13-2 Referenced angle for the SEL method under ground-fault ofthe phase with failed elements

Y-Y with Voltage Differential

For the utility configuration of Fig 48 both series and shunt external unbalances weresimulated An illustrative scenario is provided here to demonstrate their impact on thefault location reliabilityCase 14-1 The scenario includes both shunt and series disturbances as follows

bull a phase B to ground fault happens at 02 s which is cleared at 03 s

bull a capacitor element fails in the left section of phase B at 022 s

bull at 042 s another element fails this time in phase C right section

bull at 044 s an open pole takes place for phase C which lasts for 100 ms

Simulations show reliable operation of the described fault location in Section 471 Thefault location principle for the first failure involved phase based on the differential ele-ment is provided in 5141 and Fig 5142 shows the tap to tap differential element forall of the phases Same applies to Figs 5143 and 5144 for the second failure Note thetime axis intervals for these eight figures the simulation time is divided in two parts forthe sake of the principle plots clarity

The fault location outputs for each phase and the output alarms of the third differ-ential element are plotted in Figs 5145 5146 5147 and 5148 respectively As itcan be seen the third element even detects the failures faster for this special case Thiswas likely to happen as the sensitivity and magnitude thresholds are different for thiselement

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

Figure 5141 Phase B fault location principle Case 14-1 first failure

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

Figure 5142 87-3 fault location principle for three phases Case 14-1 first failure

045 05 055 06 065 07minus180

Time (s)

Figure 5143 Phase C fault location principle Case 14-1 second failure

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

Figure 5144 87-3 fault location principle for three phases Case 14-1 second failure

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

Figure 5145 Phase A fault location output Case 14-1

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

Figure 5146 Phase B fault location output Case 14-1

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

Figure 5147 Phase C fault location output Case 14-1

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

Figure 5148 Third (87-3) differential element alarms Case 14-1

Track of the changes in the counters of this element are shown in Fig 5149 seehow the open pole occurrence prevents the first counter pickup of phase C from reachingthe alarm level Although with reclosure the second time that the counter picks up itreaches the corresponding alarm level successfully

02 04 060

Phase A Left Section (87minus3)

02 04 060

Phase A Right Section (87minus3)

02 04 060

Phase B Left Section (87minus3)

02 04 060

Phase B Right Section (87minus3)

02 04 060

Phase C Left Section (87minus3)

Time (s)02 04 06

Phase C Right Section (87minus3)

Time (s)

Figure 5149 Third (87-3) differential element counters Case 14-1

Conclusion for Double Wye Banks

A comprehensive investigation on fault location in double wye shunt capacitor bankswith different unbalance protections was performed The investigation covers both un-grounded and grounded banks with either of the internally fused or fuseless technologiesBoth the proposed methods and the investigated methods of the literature were evalu-ated Because for double wye shunt capacitor banks system (external) unbalance affectsboth wye sections equally it is not necessary to block the fault location function undersuch a condition However simulations demonstrated that for double wye banks withisolated neutrals (neutral to neutral voltage unbalance protection) the SEL fault locationmethod present in the literature seemed to require blocking during external disturbanceApart from reliable performance of the evaluated methods simulations showed that de-lays may be introduced in the detection depending on the type and phase of the externalfailure whether it involves the same phase as the capacitor failure or it involves anotherphase of the system See Appendix C for some more additional results

593 Regular Updating of the k-factors

To demonstrate the k-factors regular updating importance and how it mitigates thegradual changes effect in reactance caused by weather conditions partial shading or agingillustrative simulations are performed A linear change in one of the phase capacitancesis assumed The change starts at 02 s and its upward ramp ends after about 50 msAlgorithm setting for regular updates is set faster than the linear change rate and triggersonce every fifteen protection passes (an arbitrary setting for this illustrative example)As a worst case scenario it is assumed that the other phasesections of the SCB do notexperience the linear capacitance change so that the event can mimic an internal failureNote that for the sake of simplicity and clarity of the plot the rate of change is muchfaster than what we explained in Section 481 Figs 5150 and 5151 present the faultlocation principle variations They illustrate the reactance change in the phase B of afuseless single wye SCB and in the left section of phase A of a fused double wye SCBrespectively The moments of regular reset are signified by arrows As it can be seenwithout a regular update such a condition can lead to a false failure report as bothmagnitude and angle criterion can satisfy the fault location conditions

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

Figure 5150 K-factors regular updates impact on the security of SR based fault locationmethod

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Figure 5151 K-factor regular updates impact on the security of enhanced neutral currentbased fault location method

510 Proposed Methods Verification for an Existing

Utility System

In the previous subsections of this chapter the fault location methods were evaluatedon either adapted bank constructions from industrial publicationsstandards or actualbanks To further verify the proposed methods a power system model representing anactual utility was provided Fig B6 in the Appendix B shows the single line diagramof the system and Table B3 in the Appendix B provides details on the ungroundedfuseless bank connected to this system Both the proposed methods for ungroundeddouble wye banks and the ungrounded single wye banks will be verified in this sectionfor fault location determination It is worth noting that this double wye bank has onceassumed to have neutral current unbalance protection and once as a single wye bankneutral voltage unbalance protection

Case 15-1 Simulation includes the following internal failures

bull a capacitor element fails in phase B at 02 s

bull three capacitor elements fail at 03 s in the same phase

Figs 5152-5154 illustrate the operating principle the security counters and the outputof the fault location As can be seen the proposed SR method determines the failuressuccessfully Simulation of shunt faults at the bus showed successful detection of thefailure If the shunt fault involves the same phase as where the element fails the detectionwill be delayed until the fault is cleared

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

Figure 5152 The proposed SR fault location principle for Case 15-1

510 Proposed Methods Verification for an Existing Utility System 161

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

Figure 5153 The proposed SR fault location counter for Case 15-1

01 015 02 025 03 03501234

Time(s)

Figure 5154 The proposed SR fault location output for Case 15-1

The following scenario is selected for demonstration of the resultsCase 15-2 The scenario includes the following events

bull a phase B to ground fault happens at 02 s and is cleared at 035 s

bull an element fails in the same phase at 025 s

Figs 5155-5157 illustrate the operating principle the security counters and the outputof the fault location As can be seen the proposed SR method determines the failuressuccessfully note that this is a result of utilizing angle criterion magnitude criterionand pickup counters

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

The same power system is simulated for verification of the enhanced fault locationmethod for double wye banks A complete illustrative scenario is chosen for demonstra-tion of the resultsCase 15-3 The scenario includes the following events

bull an element fails in phase A of the right section at 02 s

bull a phase A to ground fault happens at the Bus at 03 s and is cleared at 045 s

bull another element fails in phase A of the right section at 035 s

bull an element fails in the left section of phase C at 05 s

Figs 5158-5160 illustrate the operating principle the security counters and the outputof the fault location As can be seen the proposed enhanced method determines thefailures successfully It is worthwhile to note that the two consecutive failures happenedduring the shunt fault are not distinguishable in terms of occurrence time but the methodsuccessfully determined that there were two failures This is because the algorithm issomehow blind during the external faults as it was concluded before

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

60Phase C Right Section Counter

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

This chapter presented a comprehensive method validation Both the proposed methodsand the literature methods that were investigated in terms of assumptions in the previouschapter were evaluated Beside the evaluations under normal system conditions externalunbalances were also deployed in the simulations to check the fault location algorithmsreliability Simulations included measurement noise harmonics and steady state voltageunbalances Results validate reliability of the methods although in some configurationsblocking was applied to prevent from loss of algorithm security

Chapter 6

Proposed Methods Applications andOnline Monitoring

61 Introduction

In this chapter the proposed methodsrsquo properties are further compared and discussed todemonstrate their advantages and applications A commercial shunt capacitor bank relayis tested to present the shortcomings of conventional unbalance relaying Features of theproposed methods make them online monitoring methods rather than only fault locationmethods In this regard applications such as fuse saving for externally fused SCBsis perceived and verified using an illustrative scenario also the existing fault locationmethods are compared with regard to required features for online monitoring application

62 Online Monitoring vs Fault Location

The proposed methods can be viewed as rather online monitoring methods [51] thanfault location only methods This originates from their self-tuning property Dynamiccalibration of the operating quantity enables generating internal failure reports with thefollowing applications

bull Providing time stamped event records for postmortem and root cause analysis

bull Quantifying the unbalance level to arrange preventive maintenance during plannedoutages

bull Localizing the fault location problem down to 16 (Double Banks) or 13 (SingleBanks) of the search space for internally fused and fuseless HV-SCBs

bull Fuse saving for externally fused SCBs

The proposed methods features are summarized for the sake of comparison in the twonext subsections

62 Online Monitoring vs Fault Location 167

621 Failurersquos Involved Phase Determination Methods

Table 61 summarizes the proposed method online monitoring features vs the existingfault location methods The following explain each row of Table 61

Table 61 Method Comparison for Internal FailuresOnline Monitoring (Ungrounded Wye Banks)Proposed Calibrated SEL Method Discussed

Method of [36]SR Method in [26273435]

XDetermining theX X

involved phaseXAddressing

7 Disclaimer 1 7 Disclaimer 2

ambiguous failures

XDeterminingMentions manual

7 Disclaimer 2

consecutive failuresre-set [27 35](no demonstration)

XDynamic report of7 7

number of failed capacitorsXFuse saving for Mentioned in [35]externally fused SCBs (no demonstration)

XAdapted for banks7 Disclaimer 3grounded via CT Capacitor

(Neutral Unbalance Protection)Disclaimer 1 The method seems to apply a manual reset therefore it seems to be vulnerable

to offsetting failuresDisclaimer 2 The method compensates for pre-existing imbalance based on when the bank is

commissioned (undamaged) only therefore it seems that it does not consider consecutive

failures and their offsetting effectDisclaimer 3 The method is not dependent on neutral measurement Therefore grounding

impedance or measured quantity is not discussed

The first row shows the common feature of the methods which is determining theinvolved phase for a single event of capacitor element failures

The second row points out to the fact that failures in different phases can offsetagainst each other When the algorithm does not automatically record the determinedfailures or is not able to determine subsequent failures or has a high pickup delay due toalgorithm security or safety margin such failures will result in ambiguous alarms or noalarms

The third row points out the ability to reset the operating quantity and to forgetprevious failures in order to determine any consecutive failure If the algorithm cannot forget the past failures it wonrsquot be able to determine consecutive failures becausepre-existing unbalance has impact on the operating quantity

The forth row highlights the online monitoring feature of dynamic reporting of numberof failures Although magnitude of operating quantities are proportional to the unbal-

168 Chapter 6 Proposed Methods Applications and Online Monitoring

ance however quantizing the level and following failures is an online monitoring featurethat conventional unbalance protection methods do not provide

The fifth row shows the application of the monitoring method for fuse saving forexternally fused SCBs which is a direct result of online monitoring The method in [35]only points out to such an application but does not elaborate on this or provide anydemonstration

The sixth row presents the adapted SR feature that is proposing online monitoringfor two other grounding arrangements from IEEE Std C3799 SCBs grounded via CTand grounded via a low voltage capacitor (at the common neutral point) The methodof [36] does not need neutral measurement instead requires three phase currents inaddition to the bus voltages and therefore is applicable to ungrounded and groundedbanks However we wish to note that measuring a corresponding neutral quantity is thecommon practice for unbalance protection of ungrounded banks and for solidly groundedbanks the common practice is deploying voltage differential (tap voltages are provided)

Both of the methodsrsquo details are not disclosed in readily available literature Howeverthe SEL method discussed in [26273435] was simulated based on the available resourcesDetails such as magnitude criteria algorithm pick up and drop out conditions were notavailable Therefore except for the rudimentary simulation cases that determine involvedphase of single failures we didnrsquot include particular simulation results of that method inthe previous chapter

The investigated scenario is

Fig 61 shows successful pick up of a first failure (pointed out by the arrow) but as itcan be seen from Fig 63 this method seem not to be able to pick up for the secondfailure please refer to Section 33 for details of the detection zones marked in gray inthis figure Even with occurrence of the second failure the first failurersquos operand willdrop out if the pickup delay is not short enough The offsetting effect is apparent in themagnitude shown in Fig 62In comparison Fig 64 shows the proposed methodrsquos successful determination of eachof the failures which is a result of calibration and reset of the SR followed by each failuredetection and record

622 Failurersquos Involved Phase and Section Determination Meth-ods

Table 62 summarizes the proposed method online monitoring features vs the existingfault location methodsThe SEL method was simulated using the basic information in the literature

02 025 03 035 04minus180

minus120

minus60

Time (s)

Figure 61 Involved phase determination criterion for the SEL method-each colored zonerepresents one phase

02 025 03 035 040

Time (s)

Figure 62 Magnitude of the operating function of the SEL method note the impact ofoffsetting against the previous failures

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

Figure 63 Assertion and de-assertion of the output operand for the SEL method

Table 62 Method Comparison for Internal FailuresOnline Monitoring (Ungrounded Y-Y Banks)Proposed Enhanced SEL Method Discussed

Method of [37]Current-based Method in [26273435]

XDetermining theX X

7 Disclaimer 1 Disclaimer 2ambiguous failures

Disclaimer 2consecutive failures

re-set [27 35](no demonstration)

XDynamic report of7

Via lookup tablenumber of failed capacitors (not calibrated)XFuse saving for Mentioned in [35]externally fused SCBs (no demonstration)

XAdapted for grounded banks7 Disclaimer 3

(Neutral Unbalance Protection)XLess detection delay under

Disclaimer 4 Disclaimer 3external disturbance

Disclaimer 1 The method seems to apply a manual reset therefore it seems to be vulnerable to

offsetting failuresDisclaimer 2 Method works based on angle of step change for a single quantity based on one

of the phases (see literature review) Preliminary simulations show that this angle seems

to be close to zero for subsequent unbalance current measurements thus it can not identify

consecutive failures or compensate for pre-existing unbalanceDisclaimer 3 Details of the method is not disclosed in the readily available literature comparison

simulations not availableDisclaimer 4 According to our simulations this method seems to have more delay in some cases

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

Figure 64 Online monitoring Application for Involved Phase Determination

An offsetting scenario was considered to demonstrate the shortcomings that SEL methodseem to have It is worthwhile to recall that in the previous chapter the delay issue ofthis method was verified under the external unbalances due to presence of a considerableneglected negative sequence current The illustrative offsetting scenario to be comparedhere is

bull Single element failure in phase B left section at 02

bull Consecutive failure in phase B right section at 025

bull Single element failure in phase C left section at 03

bull Consecutive failure in phase C right section at 035

In Figure 65 successful determination of the first failure by the SEL method is shownby an arrow however as pointed by the circle the consecutive failure in that phase ismissed The third failure is also determined successfully but its consecutive failure isagain missed Figure 66 demonstrates the offsetting effect of the consecutive failuresThe magnitude goes back to zero once a subsequent failure balances the previous oneThe output operand of the SEL method is shown in Figure 67 In comparison withthe SEL method Figure 68 shows successful monitoring of all of the four failures bythe proposed method Figure 69 depicts the resultant outputs from the proposed onlinemonitoring method

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

Figure 65 Involved phase and section determination criterion for the SEL method-eachcolored zone represents one phasesection

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Figure 66 Drop out and masking apparent in the SEL operating function magnitude

02 03 04

Phase A Left Section Alarm

02 03 04

Phase B Left Section Alarm

02 03 04

Time (s)

Phase C Left Section Alarm

02 03 04

Phase A Right Section Alarm

02 03 04

Phase B Right Section Alarm

02 03 04

Phase C Right Section Alarm

Time(s)S

Figure 67 Missing consecutive failures for the SEL method

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

Figure 68 Online monitoring Application for Involved Phase and Section DeterminationDecision Criteria

02 03 0401234

Time(s)

02 03 0401234

Time(s)

Figure 69 Online monitoring Application for Involved Phase and Section DeterminationOutputs

63 Demonstrating Fuse Saving for Externally Fused

Developing fault location methods is not meaningful for externally fused SCBs sincethey have failed units visual indication However because it is more common for themto experience cascading element failures [52] there is a perceived application of internalfailure monitoring for fuse saving in this type of capacitor unit design [35] This meansproviding advance alarms before the unbalance leads to fuse operation Similar to fuselessSCBs the failed elements remain as short circuits thus verified fault location methodsfor fuseless SCBs are considered verified for externally fused SCBs as well This is due tothe same PSCAD model and MATLAB algorithm for these two unit design philosophiesAs an illustrative case study for an ungrounded externally fused bank the following eventswere simulated Details of the bank and the utility system are covered in Appendix BTable B4 and Fig B6 respectively

bull Double element failure in phase C at 025 s

bull Consecutive element failure in phase A at 035 s

The variations in the SR along with the successful outcome of the proposed faultlocation method are presented in Fig 610

63 Demonstrating Fuse Saving for Externally Fused SCBs 175

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

Figure 610 Fault location report for externally fused SCBs (a) the proposed SR mag-nitude and angle variations (b) involved phase and number of shorted parallel elementgroups

64 Comparing Conventional Unbalance Relaying of

a Commercial Relay

Conventional unbalance relaying is dedicated to internal failures detection and to tripthe bank when the unbalance level can cause cascading failure and damage to the bankTherefore failure information such as the involved phase or auto re-calibration of theoperating quantity are not considered for such a protective function Here we demonstratewhat are the operand states for the mentioned illustrative scenarios and what they lackin terms of online monitoring information

641 The open loop test set-up

In order to test a commercial multi-functional capacitor bank relay LabVIEW softwarewas used for play back of PSCAD COMTRADE records The hardware platform is NIcDAQ 9178 with NI 9264 analog output module The commercial relays available in ourresearch laboratory accept low level inputs and the step down ratio is compensated bythe relay in order to process the same signals as the PSCAD time domain simulations bythe protective functions The corresponding step down scales are calculated separatelyfor voltages and currents as follows

VoutVin

212times 115radic3timesradic

IoutIin

23times 5timesradic

In which the outputs are limited to 5 Vpminusp and the rms value of the rated secondary ofthe VTs and CTs are 115 L-L and 5 A respectively A safety margin factor in pu of thissecondary value is also considered for system transients

642 Relay outputs analysis

To further demonstrate the proposed method advantages a commercial relay was testedusing PSCAD COMTRADE records To test the voltage based unbalance protectionsame event sequence as the scenario in Fig 64 was played back for the relay For thesake of comparison the relay pickup and dropout delays have been adjusted similar to theproposed method however it is common practice to apply a delay of 10-30 s for the mostsensitive stage of the conventional unbalance protection STG1 in Fig 611 and a shortdropout delay of 025 s for all of the stages The relay oscillography records are depictedin Fig 611 where the arrows show the assumed short pickup delays In comparisonwith the demonstrated report of number and location of element failures by the proposedmethod in Fig 64 the following points can be seen for the tested conventional unbalanceprotection

bull At instant 1 STG 1 has picked up however the involved phase is unknown

64 Comparing Conventional Unbalance Relaying of a Commercial Relay 177

bull At instant 2 STG 2 has picked up however there is not enough information regard-ing the current and the former event (Phase A one failure Phase B two failures)This is considered as an ambiguous alarm

bull At instant 3 a consecutive failure happens in phase A but no change can be foundin the relay operands This shows missing an event The operating quantityrsquosmagnitude is not proportional to the level of unbalance when consecutive failureshappen in different phases

bull At instant 4 all of the phases have two failed elements this is an offsetting scenarioand as it can be seen the operating quantity jumps to the pre-existing unbalancevalue and the picked up functions are reset

Furthermore if the pickup delays had been set to their typical value even the first pickedup stage would have been dropped out before it can operate the function output resultingin missing all of the internal failures The mentioned points demonstrate the importanceof a per-phase indicating quantity with automatic re-calibration upon determining eachfailure for the purpose of online monitoring

Figure 611 Relay oscillography records for voltage based unbalance protection

To test the current-based unbalance protection methods for comparison with theproposed involved phase and section determination methods the scenario of Figure 69

was played back for the relay After adjusting each stagersquos pick up value the followingpoints can be seen in the resultant relay oscillography records Figure 612 The top plotshows the operating quantity which is magnitude of a neutral current based signal

Figure 612 Relay oscillography records for current based unbalance protection

bull At instant 1 STG 1 has picked up however the involved phasesection is unknown

bull At instant 2 the offsetting effect resets the operating quantity the consecutivefailure is missed and even the previous failure is determinable only when the dropout delay is high or operand has a latched setting

bull At instant 3 again STG 1 picks up but without involved phasesection information

bull At instant 4 again offsetting resets the operating quantity resulting in missing theevents

65 Summary 179

65 Summary

In this chapter applications of the proposed fault location methods were demonstratedFuse saving for externally fused banks and online monitoring of internal failures can re-sult in preventive maintenance for SCBs By determining ambiguous failure scenariosthe proposed reliable monitoring methods can reduce the outages due to cascading fail-ures This property was highlighted by comparison with a commercial relay unbalanceprotection operands for the simulated illustrative scenarios

Chapter 7

Summary Conclusions and FutureWorks

High Voltage Shunt Capacitor Banks (HV-SCBs) are manufactured with series and par-allel connection of capacitor units Each capacitor unit itself is comprised of tens ofcapacitor elements Internal element failure is a common source of unbalance in SCBsas a result of dielectric failure After certain number of element failures tripping shouldtake place which prevents from cascading failures or further voltage stress on the remain-ing elements As an online monitoring tool which assists decision making and front linecrews to spend less time on maintenance service fault location of HV-SCBs is an assetfor a capacitor bank protection and control relay It helps to determine the location ofthose failed elements that have led to tripping Fault location data is also useful forplanning maintenance schedules before an unplanned trip takes place

71 Summary and Conclusions

The challenges for fault location determination and the motivation for the project wasexplained first One of the challenges for locating internal failures is the number of avail-able measurement points or equivalently the number of transducers that measure volt-agescurrents of the SCB This limits the fault location to determining the phase andsection in which the element has failed Because it is seldom economic to add voltageor current transducers for solely fault location the thesis has aimed to propose methodsbased on the already available measurements that are practically available from utilitiesrsquoexisting monitoring programs The other challenge is cascading failures and failuresthat become ambiguous because of the impact of subsequent failures This challenge wasaddressed in the thesis by determining consecutive failures location and resetting thealgorithm principle The proposed principles also include inherent compensation termsand updating routines not to operate for other sources of unbalance than internal fail-ures such as system unbalance inherent unbalance due to manufacturing tolerancesgradual changes in capacitance due to weather conditions partial shading and aging ofthe cansThe theory of unbalance protection methods as the sensitive relaying scheme to internal

71 Summary and Conclusions 181

failures in SCBs was discussed in a separate introductory chapter Application of theknown relationships among the measured voltagescurrents taken around the SCB forderiving unbalance operation functions was presented The fundamentals of compensat-ing terms in unbalance relaying were explained as the basis for devising fault locationmethodsAn extensive literature survey was carried out because the subject was covered undervarious titles in patents and industrial conferences rather than common academic liter-ature The literature survey was further elaborated by investigating the approaches toderiving the final decision making equations of a relevant fault location method in theliterature The literature survey chapter also gave an idea of different connections inSCBs and the most commonly available measurementsThe main chapter of the thesis describes the proposed methods The proposed methodsare divided into two categories those based on a new indicating quantity derived byestimation of the change in each phase reactance namely the rdquoSuperimposed Reactance(SR) basedrdquo methods which are actually voltage-based and the ones that are enhancedversions of current-based unbalance protection Apart from the main case study of SCBsthat were adapted from the literature data particular existing utility configurationswere also discussed for fault location in regard to additional measurements Beside eachmethodrsquos decision criteria derivation the dynamic unbalance compensation detection ofnumber of failed elements and other detailed settings of the methods such as blindersand counting schemes were presentedSimilar to many other protection applications evaluation of the proposed methods underfault and no-fault conditions was required With a difference that the detection time isnot critical for the present monitoring scheme The evaluations also included the inves-tigated methods of the literatureThe presented results validated reliability of the proposed methods for double wye SCBsunder external unbalances This was explained to be due to equal impact of system un-balances for both of the wye sections Simulations showed that depending on the type ofexternal unbalance delays might impact the fault location determination For single wyeSCBs results demonstrated that for ungrounded banks and banks grounded via CTs theoutput of fault location should be blocked in case of system faults Magnitude limits andother protection functionsrsquo output signals were suggested for this blocking Dependabilityand security of all of the methods were successfully verified with simulations consideringpre-existing inherent unbalance in the bank measurement noise harmonics and systemvoltage unbalanceThe auto calibration property of the proposed methods enables generating internal fail-ure reports that are further than a fault location report in terms of detecting subsequentfailures and live reporting of number of failed capacitor elements and could be referred toas online monitoring system outputs To demonstrate this advantage comparison basedon open loop testing of a commercial relay was provided Fuse saving for externally fusedSCBs was also validated as another advantage of the proposed methodsThe following terms summarize the contributions of the present research work

bull Assumptions of relevant methods of the literature were investigated and their per-formance analysis under external disturbances was presented which demonstrated

182 Chapter 7 Summary Conclusions and Future Works

issues such as detection delays due to external disturbances or importance of mag-nitude criterion

bull A novel technique was developed for estimation of the change in reactance usingavailable measurements for unbalance relays The method was notified as Superim-posed Reactance (SR) and a fault location technique based on this was proposedand verified for SCBs protected with neutral voltage unbalance The proposedSR adopts calibrating factors for element failures online monitoring and inherentwithin its definition presents a straightforward solution to set reference indexes forestimating number of failed capacitor elements

bull The concept of Superimposed Reactance was expanded for fault location of SCBsthat use ground current unbalance or grounding capacitor voltage monitoring forunbalance protection

bull An enhanced fault location technique was developed for SCBs protected with neu-tral current unbalance (both grounded and ungrounded) The algorithm enablesonline monitoring properties and detection of ambiguous failures

bull A complete fault location method was developed and verified for an actual andcommon design of double wye SCBs protected with tapped voltage differential forboth sections

bull Based on IEEE C3799 formulas for deriving the perunit magnitude of unbalancequantities for protection purposes neutral voltage estimation was investigated forasymmetrical double wye SCBs fault location Results demonstrated that a faultlocation based on this quantity (measurement and estimation) is not capable ofdistinguishing between the faulted and healthy sections for the intended configura-tion

bull An open loop testing scheme was developed to demonstrate shortcomings of con-ventional unbalance relaying with respect to online monitoring Advantages of theproposed methods were also demonstrated and compared in this respect

All of the developed fault location methods have the following properties which presentcomprehensive capabilities for a fault location algorithm

bull Make the best out of the available measurements and can be embedded in unbalancerelaying functions

bull Deploy k-factor auto-setting and self-tuning concept

bull Compensate for pre-existing unbalance in the SCB (manufacturing tolerances) andsystem unbalance

bull Compensate for gradual changes in the capacitance (aging temperature impacts)

bull Determine consecutive failures location

72 Future Works 183

bull Overcome ambiguous failures issue

bull Determine number of failed elements (live report)

72 Future Works

There exists potential research topic on application of current sensors with wireless ac-quisition and transmission modules for direct monitoring of power system equipmentsincluding individual capacitor unit monitoring Challenges for these monitoring systemsincludes the following but is not limited to them selection of the appropriate currentsensor power supply of the modules safety of the power supply during transients syn-chronous acquisition and the confined space for extra installations Although commer-cialization of such an approach is uncertain however with the prospective of smart gridsthe future for such methods could become bright

In case of access to high voltage laboratories and power capacitors break down dis-charge can be analyzed to investigate more applications for monitoring of different typeof power capacitors The breakdown analysis result can be an asset for development ofreal-time supervision schemes of HV-SCBs

With integration of intermittent renewable generations today advanced control sys-tems as mitigation measures for correspondent overvoltage issues are being developedhowever performing research on impact of these integrations on capacitor failures andoutage times is also a perceived research area Such a study would involve both capacitorovervoltage protection functions and unbalance protection functions

Sensitivity analysis for the proposed methods considering inrush current limiting re-actors and investigating fault location for harmonic filter banks could be a potential areafor future research

Bibliography

[1] M Dhillon and D Tziouvaras ldquoProtection of fuseless shunt capacitor banks usingdigital relaysrdquo in 26th Annual Western Protective Relay Conference October 1999

[2] ldquoIEEE Guide for the Protection of Shunt Capacitor Banksrdquo IEEE Std C3799-2012(Revision of IEEE Std C3799-2000) pp 1ndash151 March 2013

[3] C70 Capacitor Bank Protection and Control System UR Series Instruction ManualGE Digital Energy August 2013

[4] E Price and R Wolsey ldquoString current unbalance protection and faulted stringidentification for grounded-wye fuseless capacitor banksrdquo in 65th Annual GeorgiaTech Protective Relaying Conference May 2011

[5] SampC Potential Devices 15-Volt-Ampere Models Instruction Sheet 581-510 S amp CElectric Company March 2003

[6] B Kasztenny J Schaefer and E Clark ldquoFundamentals of adaptive protection oflarge capacitor banks - accurate methods for canceling inherent bank unbalancesrdquoin Protective Relay Engineers 2007 60th Annual Conference for March 2007 pp126ndash157

[7] P Danfors N Fahlen and O Nerf ldquoProtective device for capacitor bankrdquo USPatent 4 219 856 August 1980

[8] P G Hjertberg and P Skogby ldquoRelay protection for capacitor banksrdquo US Patent3 143 687 August 1964

[9] J A Zulaski ldquoShunt capacitor bank protection methodsrdquo Power Apparatus andSystems IEEE Transactions on vol PAS-101 no 6 pp 1305ndash1312 June 1982

[10] M Becker and K Renz ldquoDevice for locating internal faults in a high-voltage capac-itor batteryrdquo US Patent 4 956 739 September 1990

[11] H Santos J Paulino W Boaventura L Baccarini and M Murta ldquoHarmonic dis-tortion influence on grounded wye shunt capacitor banks protection Experimentalresultsrdquo Power Delivery IEEE Transactions on vol 28 no 3 pp 1289ndash1296 July2013

BIBLIOGRAPHY 185

[12] N Hejazi ldquoEffect of induction on controlsignal cables on shunt capacitor bankprotective schemesrdquo Masterrsquos thesis The University of Western Ontario 2009

[13] J-U Lim and T Runolfsson ldquoImprovement of the voltage difference method todetect arcing faults within unfused grounded-wye 229-kv shunt capacitor bankrdquoPower Delivery IEEE Transactions on vol 22 no 1 pp 95ndash100 Jan 2007

[14] M Bishop T Day and A Chaudhary ldquoA primer on capacitor bank protectionrdquoIndustry Applications IEEE Transactions on vol 37 no 4 pp 1174ndash1179 Jul2001

[15] H Jouybari-Moghaddam and T S Sidhu ldquoA study of capacitor element failures inhigh voltage capacitor banksrdquo in IEEE CCECE 2017 May 2017

[16] Power Capacitors and harmonic filters buyerrsquos guide ABB Document No 1HSM9543 32-00en September 2013

[17] Distribution Automation Handbook Section 810 protection of capacitor banks ABBDocument No 1MRS757290 March 2011

[18] K C Agrawal Industrial Power Engineering and Applications Handbook MAUSA Butterworth-Heinemann 2001

[19] R Moxley J Pope and J Allen ldquoCapacitor bank protection for simple and complexconfigurationsrdquo in Protective Relay Engineers 2012 65th Annual Conference forApril 2012 pp 436ndash441

[20] S R McCormick K Hur S Santoso A Maitra and A Sundaram ldquoCapacitorbank predictive maintenance and problem identification using conventional powerquality monitoring systemsrdquo in Power Engineering Society General Meeting 2004IEEE June 2004 pp 1846ndash1850 Vol2

[21] M Ellis D Meisner and M Thakur ldquoInnovative protection schemes for h con-figuration fuseless grounded shunt capacitor banksrdquo in Protective Relay Engineers2012 65th Annual Conference for April 2012 pp 449ndash458

[22] Forced outage performance of transmission equipment for the period Jan 1st 1998-31 Dec 2002 Canadian Electricity Association 2004

[23] Near-Term Measures for the Return-to-Service of two units at Bruce A NGS InstallSeven 230kV Capacitor Banks in South-Western Ontario IESO REP 0490 IESO2009

[24] Richview SC22 Incident- January 30 2007 IESO REP 0386 IESO 2007

[25] L Fendrick T Day K Fender J McCall and A Chaudhary ldquoComplete relayprotection of multi-string fuseless capacitor banksrdquo in Pulp and Paper IndustryTechnical Conference 2002 Conference Record of the 2002 Annual June 2002 pp194ndash198

186 BIBLIOGRAPHY

[26] S Samineni C Labuschagne and J Pope ldquoPrinciples of shunt capacitor bank appli-cation and protectionrdquo in Protective Relay Engineers 2010 63rd Annual Conferencefor March 2010 pp 1ndash14

[27] J Schaefer S Samineni C Labuschagne S Chase and D Hawaz ldquoMinimizingcapacitor bank outage time through fault locationrdquo in Protective Relay Engineers2014 67th Annual Conference for March 2014 pp 72ndash83

[28] J A Zulaski ldquoDevice for detecting unbalanced conditions in a polyphase equipmentbankrdquo US Patent 4 104 687 August 1978

[29] N R Clark and S B Farnham ldquoConnection arrangements and protective practicesfor shunt capacitor banksrdquo American Institute of Electrical Engineers Transactionsof the vol 68 no 2 pp 1226ndash1231 July 1949

[30] M Becker and K Renz ldquoMonitoring device for detecting faults in an electricaldevice particularly in an lc filter circuit in an ac voltage networkrdquo US Patent4 713 604 December 1987

[31] S Samineni and C A Labuschagne ldquoApparatus and method for identifying afaulted phase in a shunt capacitor bankrdquo US Patent 8 575 941 November 2013

[32] T R Day and D P Roth ldquoDevice protection using temperature compensationrdquoUS Patent 7 990 668 August 2011

[33] A Chaudhary T Day K Fender L Fendrick and J McCall ldquoPull a few strings[complete protection of multistring fuseless capacitor banks]rdquo Industry ApplicationsMagazine IEEE vol 9 no 6 pp 34ndash39 Nov 2003

[34] S Samineni C Labuschagne J Pope and B Kasztenny ldquoFault location in shuntcapacitor banksrdquo in Developments in Power System Protection (DPSP 2010) Man-aging the Change 10th IET International Conference on March 2010 pp 1ndash5

[35] S Samineni C Labuschagne S Chase and J Hawaz ldquoFault location in capaci-tor bankshow to identify faulty units quickly and restore the bank to servicerdquo inCIGRE 21 rue dArtois F-75008 Paris France 2014 pp B3ndash212

[36] A Kalyuzhny J C Mccall and T R Day ldquoCorrective device protectionrdquo USPatent 7 973 537 July 2011

[37] Z Gajic M Ibrahim and J Wang ldquoMethod and arrangement for an internal failuredetection in a y-y connected capacitor bankrdquo US Patent 20 130 328 569 December2013

[38] B Kasztenny D McGinn and I Voloh ldquoEnhanced adaptive protection method forcapacitor banksrdquo in Developments in Power System Protection 2008 DPSP 2008IET 9th International Conference on March 2008 pp 269ndash274

BIBLIOGRAPHY 187

[39] H Jouybari-Moghaddam T S Sidhu and P Parikh ldquoA study of fault locationmethod in double wye shunt capacitor banksrdquo in CIGRE Canada VancouverCanada October 2016

[40] Home Guides ldquoThe difference between air temperature in shade andin sunrdquo SFGATE [Online] Available httphomeguidessfgatecomdifference-between-air-temperature-shade-sun-92497html

[41] ldquoIEEE Standard for Shunt Power Capacitorsrdquo IEEE Std 18-2012 (Revision of IEEEStd 18-2002) pp 1ndash39 Feb 2013

[42] N D Sadanandan F A Deviney L Hollomon and M Sendaula ldquoMicroprocessor-based capacitor bank control and protection systemrdquo IEEE Transactions on PowerDelivery vol 4 no 1 pp 241ndash247 Jan 1989

[43] H Jouybari-Moghaddam T S Sidhu M R Zadeh and P Parikh ldquoEnhancedfault location scheme for double wye shunt capacitor banksrdquo IEEE Transactions onPower Delivery vol 32 no 4 pp 1872ndash1880 August 2017

[44] H Jouybari-Moghaddam T S Sidhu P Parikh and I Voloh ldquoEnhanced fault lo-cation method for shunt capacitor banksrdquo in 2017 Texas A amp M Protective RelayingConference April 2017

[45] SEL-487V Relay Capacitor bank protection automation and control- instructionmanual Schweitzer Engineering Laboratories INC August 2012

[46] G Scheer ldquoRoles of annunciators in modern electrical substationsrdquo in 13th AnnualWestern Power Delivery Automation Conference Spokane Washington March2011

[47] ldquoIEEE Recommended Practice and Requirements for Harmonic Control in ElectricPower Systemsrdquo IEEE Std 519-2014 (Revision of IEEE Std 519-1992) pp 1ndash29June 2014

[48] GridSense Inc ldquoVoltage and current unbalancerdquo Application Note [On-line] Available httpwwwgridsensecomwpwp-contentuploads201309App-Note-PM-VoltageCurrent-Imbalancepdf

[49] P Pillay and M Manyage ldquoDefinitions of voltage unbalancerdquo Power EngineeringReview IEEE vol 21 no 5 pp 49ndash51 May 2001

[50] Network Protection amp Automation Guide Levallois-Perret France Alstom 2002

[51] H Jouybari-Moghaddam T S Sidhu M R Zadeh and P Parikh ldquoShunt capacitorbanks online monitoring using a superimposed reactance methodrdquo to be publishedin IEEE Transactions on Smart Grid 2017

[52] T Ernst ldquoFuseless capacitor bank protectionrdquo in Proc of Minnesota Power SystemsConf 1999 pp 77ndash83

188 BIBLIOGRAPHY

[53] U Khan ldquoModeling and protection of phase shifting transformersrdquo PhD disserta-tion The University of Western Ontario 2013

[54] PSCADEMTDC V 452 Manitoba HVDC Research Center Winnipeg MBCanada

[55] ldquoIEEE Guide for the Application of Shunt Power Capacitorsrdquo IEEE Std 1036-2010(Revision of IEEE Std 1036-1992) pp 1ndash88 Jan 2011

[56] ABB Application Guide for Instrument Transformers ABB Feb 2015

[57] Nokian Capacitors ldquoUnbalance protection current relay NUR-36rdquo Product Flyer[Online] Available httpwwwnokiancapacitorsru

[58] T Longland T W Hunt and W A Brecknell Power Capacitor Handbook UKButterworths 1984

Appendix A

Simulation Settings

The solution time step was 10micros and the COMTRADE recording time step was selectedto be 50micros [53] therefore PSCAD applies interpolation for synchronization between thetwo [micros] [54] The recorderrsquos low pass filter was not used instead anti-aliasing filterswere considered in PSCAD simulation before recording the signals The filters were forthorder butter-worth low pass filters with cut off frequency of 1536 HzAs the time step for recording in PSCAD can only be an integer a MATLAB function(linear interpolation or resample) must be applied in the processing code to synchronizethe resampled data with the original records Accordingly the mentioned time steps cannot be adjusted to be an integer multiple of the final 64times 60 data sampling rate As theresample function in MATLAB again requires a rational fraction between the recordingrate and the resampling rate for the relay model the interp1 function (linear interpola-tion) was used instead

Appendix B

Simulated System and Specificationsof the SCBs

Figs B1 and B2 illustrate both the bank and unit construction for ungrounded singlewye SCBs they are adapted from [55] and [34] respectively Figs B3 and B4 illustrate

S=6P=2

Ce=136F

Figure B1 230 kV internally fused ungrounded single wye SCB

both the bank and unit construction for ungrounded double wye SCBs they are adaptedfrom [27] and [34] respectively For double wye grounded banks the right sectionreactance would be the same as the left sectionFor double wye banks with isolated neutrals if the bank sections are configured identicalthey are the same as the grounded double wye configurations If they are configurednon-identical they will be configured as the ungrounded double wye configurationThe schematic of the simulated power system is presented in Fig B5 The componentparameters and their values are shown in Table B1 For the existing utility configurationof Section 47 a source impedance of Z1 = 667ang8428Ω and Z0 = 1334ang70Ω was usedfor the simulation The extracted application settings for Fig 48 and Fig 410 are asfollows in Table B2

Ce=608F

Figure B2 230 kV fuseless ungrounded single wye SCB

Ce=1microF

Figure B3 230 kV internally fused ungrounded double wye SCB with single string perphase for each section

Ce=36microF

Figure B4 230 kV fuseless ungrounded double wye SCB

192 Chapter B Simulated System and Specifications of the SCBs

100 MVA

230 KV

50 km 50 km

Figure B5 Schematic of the simulated power system

Table B1 System ParametersParameter Value

Source ImpedanceZ1 = 15 + j10Z0 = 15 + j30

External Impedance 5 + j50

Balanced LoadAbout 40 MW per phase (dependent on the SCB capacity)

at 09 power factor lagging

Transmission LinesZ1 = 2545 Ωang859 degZ0 = 6876 Ωang746 deg

Table B2 Utility Banks Construction DataSCB Su N P S Pst-L Pst-R

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

The existing utility system discussed in Section 510 and the corresponding SCBconstruction data are shown in FigB6 and Table B3 respectively as follows

Figure B6 Single line diagram of the existing utility system

Table B3 Construction data for single wye SCB and each bank of the double wye SCBProtection Element Ce Su N S Pst

Neutral Voltage Unbalance 58936 6 1 6 2

Neutral Current Unbalance 58936 6 1 6 1

Table B4 shows the bank construction data for the externally fused SCB this hasbeen adapted from provided data in [1 2]

Table B4 Construction data for the single wye SCB with externally fused unitsCe Su N S P

3316 8 3 5 14

Appendix C

Plot of Additional Signals DuringExternal Unbalance

Residual and Neutral Voltage for Single Wye SCB

To demonstrate the changes in residual and neutral voltages upon internal and externalfailures the following scenarios are selected An internal failure taking place at 025 sec-ond in the phase C of a fuseless wye SCB is simulated under three conditions Firstwhen we have the failure only second when we have the failure and a shunt power systemfault in the middle of the transmission line with 100 ms clearing time and last when wehave the failure happening while the same phase is open in a 360 ms open pole trippingand a subsequent reclosure scenarioAs per equations (416)-(424) in the SR based proposed method in addition to phasevoltages the neutral voltage and zero sequence voltage are contributing in the faultlocation principle definition therefore the plots of these two variables in the three afore-mentioned case studies are presented here Figs C1-C3 illustrate the comparison forthe three aforestated scenarios respectively Simulations include presence of pre-existingSCB unbalance harmonics measurement noise and voltage unbalanceThe effect of internal failure on neutral voltage can be seen in Fig C1 In case ofexternal disturbance the results will be different Affecting both neutral voltage and thezero sequence voltage

Neutral Current and Compensated Neutral Current for Double Wye SCB

To demonstrate the changes in compensated and uncompensated neutral measurementsupon internal and external failures the following scenarios are selected to illustrate thesignal variations An internal failure taking place at 025 second in the phase A of afused double wye SCB is simulated under three conditionsFirst when we have the failure only second when we have the failure and a shunt powersystem fault in the middle of the transmission line with 100 ms clearing time (includesboth phase to phase and phase to ground fault (once phase A another scenario phaseB) with 20Ω fault resistance) and last when we have the failure happening while thesame phase is open in a 360 ms open pole tripping and a subsequence reclosure scenario

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

Internal failureoccurs

Figure C1 Neutral voltage and zero sequence voltage internal failure only (the bankand system have pre-existing unbalance too)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

Power system fault clearance

Internal failure and power system faultoccurrence

Figure C2 Neutral voltage and zero sequence voltage simultaneous internal failure andshunt power system fault

196Chapter C Plot of Additional Signals During External Unbalance

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Reminusclosuremoment

Open polemoment

Figure C3 Neutral voltage and zero sequence voltage internal failure in one phase ofthe SCB while the same phase of the line is open

Figs C4-C13 demonstrate the compensated neutral current neutral current and neu-tral voltage along-with the fault location counter for each of the afore-stated scenariosrespectively

With reference to Fig C5 the internal failure location is determined in less than 50ms In addition Fig C4 presents the fact that neutral voltage phase angle variationin case of failure is minimal in double wye SCBs As can be seen it takes more than50 ms to determine the failure location Also again the necessity of compensation isapparent in the phase angle plot as the neutral current and voltage phase angles do notfollow any special patterns to differentiate an internal failure Successful fault locationdetermination in various fault resistance and fault clearance times had been validatedbefore here again we see same results The only change from the previous scenario is thehigher magnitude jump in the neutral voltage From the figures of both shunt powersystem faults and open poles that involve the same phase as the one that includes theinternal failure we conclude that the magnitude of the compensated neutral current doesnot jump as much as it is expected unless the fault is cleared or the open pole is reclosedHowever for double wye banks in the event of an open pole the fault location still isreliable and there isnrsquot any need for blocking the fault location functionFor grounded bank simulations show that there is no need for restraint supervision forfault location Fault location is not susceptible to external unbalance except for theintroduced detection delays

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

Compensated Neutral Current Neutral Current Neutral Voltage

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

Internal failure takes place

Figure C4 Neutral measurements for a scenario including an internal failure occurrence

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

Figure C5 The proposed fault location counter for an internal failure occurrence

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

Powersystemfaultinterval

Figure C6 Neutral measurements for a scenario including an internal failure occurrenceduring a power system phase to phase fault

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

Figure C7 The proposed fault location counter for the scenario of Fig C6

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

Figure C8 Neutral measurements for a scenario including an internal failure occurrenceduring a power system phase to ground fault for the same phase

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

Figure C9 The proposed fault location counter for the scenario of figure C8

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

Internal failure takesplace

Figure C10 Neutral measurements for a scenario including an internal failure occurrenceduring a power system phase to ground fault in another phase

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

Figure C12 Neutral measurements for a scenario including an internal failure occurrenceduring an open pole in the same phase

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

Figs C14 and C15 show the way that same phase shunt fault and other phase shuntfaults respectively affect both the fault location principle (compensated value) and theuncompensated measurement

As can be seen in Figs C15 and C14 unlike the ungrounded bank Figs C8 andC10 the effect of same phase faults and the faults that do not involve the phase that hasthe failed element are the same for grounded banks and that is why both of the scenariosfor grounded banks result in detection delay

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

(A)Internalfailuretakesplace

failure isdetectedandprinciplegets reset

Figure C14 Compensated and uncompensated neutral current for fault in phase B andinternal failure in phase B

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

(A)Powersystemfaultinterval

Internalfailuretakesplace

failure isdetectedandprinciplegetsreset

Figure C15 Compensated and uncompensated neutral current for fault in phase A andinternal failure in phase B

Appendix D

Additional Simulation Results onMeasurement Accuracy

In this appendix some simulation results which demonstrate the successful performanceof the proposed fault location methods considering instrumentation errors system un-balance and harmonic rich scenarios are presentedImpact of system unbalance capacitor inherent unbalance and both of these unbalanceson the estimated superimposed reactance quantity is shown in Figure D1 The simulatedfailures have been

bull Double element failure in phase B at 025 s

01 015 02 025 03 035 04 0450

minus3

Time(s)

Case ICase IICase III

Figure D1 Superimposed Reactance Magnitude case I system unbalance and capacitorunbalance case II capacitor unbalance only case III system unbalance only

204Chapter D Additional Simulation Results on Measurement Accuracy

Simulations have verified the successful fault location report for the simulated casesThis is due to the fact that irrespective of the level of unbalance between three phasephasors each phasersquos estimated voltage phasor is accurate Also the calibrating factorseffectiveness ensure reliable online monitoring of the capacitor failures Our simulationshave also validated the performance of the proposed methods for system unbalances of8 In practice voltage unbalance in transmission systems is required to be kept as lowas 2 or less

With regard to CTPT errors we should point out that the proposed methods havedifferential property and apart from the initial compensation that negates any pre-existing unbalance measured due to errors they apply thresholds and zones to accountfor the remainder of error consequencesIn general by deploying magnitude zones ie upper and lower limits for magnitudethresholds or blocking by means of time delays or supervision from other protectivefunctions of a capacitor bank multi-functional numerical relay the proposed method se-curity during system faults is also taken care of We do block the monitoring functionbecause we do not deal with system faults This is due to the fact that the monitoringfunction is dedicated to internal failures that impose minor changes on the measurementchannels As verified in Chapter 5 even in worst case scenarios upon clearance of thedisturbance the transient error will vanish and even an internal failure event that mightoccur during these severe transients will be eventually monitored and recorded in capac-itor element failure reports

Based on reference [56] the errors of a CVT and inductive voltage transformer changevery little for voltage variations and the voltage dependence can for all practical appli-cations be neglected To investigate ratio errors a maximum ratio error of 6 fromrated values in voltage transformers and CVTs [56] was simulated Figure D2 shows theimpact of the ratio error on the superimposed reactance In this figure no measurementnoise case 50 dB SNR case and 50 dB SNR plus 6 ratio error are shown for onlinemonitoring of the selected scenario earlier mentioned in this appendix Simulations haveverified successful fault location for these scenarios

01 015 02 025 03 035 040

minus3

Time(s)

No NoiseWith NoiseWith Noise and Ratio Error

Figure D2 Superimposed Reactance Magnitude case I no measurement noise case II50 dB SNR case III 50 dB SNR and 6 ratio error

For CT errors we assumed a high ratio error of 10 [56] for another illustrativescenario under system fault for a SCB grounded through CT The simulation scenarioincludes the following events

bull A Phase B to Ground Fault at 02 s which lasts for 100 ms

bull Two elements failure in phase B of the capacitor bank at 025 s

As can be seen in Figure D3 the change in the SR has been negligible This figurehas been zoomed to the time interval in which the decision criteria has been satisfied andthe internal failure is detectedApplying different potential transformer characteristics (B-H curves) or different PSCADCT models have also verified successful performance of the proposed methods

035 04 045 050

Time (s)

Rated Ratio10 Ratio Error

Figure D3 A closer look at the SR considering Neutral CT ratio error

As explained our studies have considered non-ideal scenarios Power system har-monics and measurement noise are other factors we have considered The reason theproposed methods are robust against such factors is the fact that

bull The proposed method does not rely on any new measurement and only requires theactual measurements present in the HV substations today

bull The relay model for the proposed methods deploys the filters that numerical relaysdeploy in practice and is therefore reliable under non-ideal conditions These filtersinclude Anti-Aliasing filter CVT Transient filter Decaying DC Removal andDFT filter (fundamental frequency phasor estimation)

A low pass analog filter is part of the hardware acquisition in commercial numerical SCBprotection and control relays [45] Further digital filters with half power points of 640

Hz in product [45] or 100 Hz in product [57] are part of the input processing before thephasor calculation is performed

In our simulations DFT is applied for fundamental frequency phasor estimationDFT is a long window phasor estimation algorithm which is generally considered to beimmune to noise and harmonics to an acceptable extent Frequency response of real andimaginary filter of the applied full cycle DFT with 64 samples per power system periodare shown in Fig D4 The attenuation level for harmonics is effective while the 64samples per cycle is one that is actually deployed in some commercial relays [3]

0 60 120 180 240 300 360 420 480 540 600 6600

15Real Filter minus DFT

0 60 120 180 240 300 360 420 480 540 600 6600

15Imaginay Filter minus DFT

Frequency (Hz)

Figure D4 Full cycle DFT frequency response

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

Figure D5 Frequency response of the applied anti aliasing filter

Neutral current waveform of a sample scenario in which a single element fails in one ofthe six possible locations of a double wye bank is selected to show the effectiveness of thelow pass filter and the applied DFT filter see Fig D6 Note that the uncompensatedneutral current is depicted in this figure ie the signal also carries the system unbalanceand pre-existing internal unbalance of the bank besides the noise and harmonics Thisdemonstrates that the algorithm has been robust and able to extract the fundamentalfrequency phasor with an acceptable capability To further validate the proposed methodperformance we made the harmonic injections 10 times richer and results verified samesuccessful determination of the fault location The reason is that the fundamental fre-quency phasor of the phase and neutral currents are estimated accurately FigD7 shows

the neutral current waveform and the estimated fundamental frequency phasor for thisscenario

0 005 01 015 02 025 03 035 04minus05

05Neutral Current Waveform Before Low Pass Filter

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

Neutral Current Waveform After Low Pass Filter

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

Magnitude of the Estimated Fundamental Frequency Phasor for Neutral Current

Before Failure After Failure

Figure D6 Low pass filter and DFT filter application on the measured signal

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Figure D7 Low pass filter and DFT filter application on the measured signal for systemwith ten times richer harmonic sources

Appendix E

Further on SCBrsquos Protection andInternal Failures

During this study some useful information from utility practice was learned and here isa summary of the main parts

E1 Other protection functions for SCBs

Apart from fusing which is the first line of protection against over-current and unbal-ance relaying which is the subject of the present thesis and helps to disconnect the SCBto prevent from cascading failures inside the SCB HV shunt capacitor banks are pro-tected in various ways by different utilities Common protection elements include thefollowings Applicability of these functions depends on which CTs or VTs are availableand the protection philosophy of the utility

No Volt Protection On supply failure SCBs should be disconnected and lockedout to prevent from automatic switch-on upon resumption of grid supply Reclosing isonly allowed after passing the capacitorrsquos expected safe discharge time Even suddenvoltage dips may cause the charged capacitors discharge into the terminal equipmentand damage them [18]

Line and Overvoltage Protection The overall cover for the complete capacitorbank and any ancillary equipment including cabling busbars and other external con-nections is line and over voltage protection [58] In particular this would be overcurrentfunction sensitive to true rms current and overvoltage protection for prolonged exceedingin the voltage over 11 pu Principally the unbalance protection is intended to detectfailed elements inside the SCB and prevent from cascading failures by tripping the bankbefore the stressed elements fail However in a healthy bank external problems can stillmake elements overstressed Protection from system overvoltages that might cause thisoverstress is done via overvoltage protection [3]

E2 Resistive Potential Devices (RPDs) 209

Overcurrent Protection In order to detect line-to-line faults or bus ground faultsoutside the shunt capacitor banks overcurrent relays (OCRs) are applied in connectionwith current transformers (CTs) [13]

E2 Resistive Potential Devices (RPDs)

Some utilities employ resistance type voltage sensing devices for voltage monitoring ofshunt capacitor banks A commercial product of this type is SampC 15 Volt AmperePotential [5] The 15 VA Resistive Potential Device (RPD) is applicable to neutralto ground connection of ungrounded wye connected SCBs For intermediate tap pointto ground connections on grounded wye SCBs and for line to ground connections inall other applications 30 VA RPDs are applicable The RPDs have constant currentoutput like CTs An adjustable burden resistor is connected across the output terminalsand produces an output voltage directly proportional to the voltage applied to the lineterminalParticularly the superiority of the 15 VA devices are first that they do not possessresonant characteristics and are immune to ferroresonance unlike CVTs Their limitedfrequency response makes them ideal for locations with high frequency transients Secondunlike VTs they do not saturate when subjected to switching overvoltages As the 15 VARPDs are immune to these voltage surges they are suitable for neutral voltage monitoringfor increased sensitivity since they can be applied in ratings below the system nominalvoltage The output of RPDs has minimal phase shift and excellent linearity at lowvoltages Figure E1 illustrates a simplified diagram for a RPD connected across a lowvoltage capacitor Figure E2 depicts a more detailed schematic for the 15 VA SampCpotential device The high voltage resistor in Figure E2 is in the range of tens of MΩ

E3 Rack bonding

Substation capacitor units are typically mounted in racks that are insulated from theground One side of a parallel set of capacitors is connected to the line side of thesystem The other side of the capacitors is typically either connected directly to theframe (if aluminum) or to an aluminum bus directly connected to the frame All rackvoltages are anchored at the voltage potentials of some particular capacitor unit terminalsby rack bonding ie the rack must be tied to a fixed potential otherwise the voltagethe capacitor bushing will be subjected to cannot be determined

210 Chapter E Further on SCBrsquos Protection and Internal Failures

Figure E1 Resistive divider for voltage sensing in SCBs [1]

Figure E2 SampC 15 VA Potential Device Schematic [5]

Curriculum Vitae

Name Hessamoddin Jouybari Moghaddam

Education University of Western OntarioLondon ON2013 - 2017 PhD ECEGPA 916

Tehran Polytechnic (Amirkabir University of Technology)Tehran Iran2010 - 2012 MSc ECEGPA 180220

Ferdowsi University of MashhadMashhad Iran2006 - 2010 BSc ECE[Ranked first amongst the power group students]

Honours and Western ECE Graduate Student Award for Excellence in ResearchAwards 2017

Ferdowsi University Academic Foundation Award2010

Publications

Journal papers

bull H Jouybari-Moghaddam T S Sidhu M R Dadash Zadeh P Parikh Shunt Ca-pacitor Banks Online Monitoring Using a Superimposed Reactance Method Ac-cepted for IEEE Transactions on Smart Gridshttpdxdoiorg101109TSG20172690643

bull H Jouybari-Moghaddam T S Sidhu M R Dadash Zadeh P Parikh EnhancedFault Location Scheme for double wye shunt capacitor banks IEEE Transactionson Power Delivery vol32 no4 pp 1872 -1880 Aug 2017

bull H Jouybari-Moghaddam SH Hosseinian B Vahidi Grid reconnection detec-tion for synchronous distributed generators in stand-alone operation InternationalTransactions on Electrical Energy Systems (formerly ETEP) John Wiley amp Sonsvol25 no1 pp 138 -154 Jan 2015

bull H Jouybari-Moghaddam B Vahidi SH Hosseinian Rotational Invariance Tech-nique for Evaluation of Perturbed Lightning Impulses IEEE Transactions on PowerDelivery vol 28 no 1 pp 531-533 Jan 2013

bull H Jouybari-Moghaddam A Alimardani SH Hosseinian Influence of ElectricVehicle Charging Rates on Transformer Derating in Harmonic-rich Battery ChargerApplications Archives of Electrical Engineering Polish Academy of Sciences vol61 no 4 pp 483-497 Dec 2012

bull H Jouybari-Moghaddam G B Gharehpetian SH Hosseinian Performance ofpower-line-signaling based detection algorithms for islanding protection of dis-tributed generators in interharmonic polluted systems Renewable Energy amp PowerQuality Journal Paper 272 No 10 Apr 2012

Conference Papers

bull H Jouybari-Moghaddam T S Sidhu I Voloh M R Dadash Zadeh rdquoNew Methodof Capacitors Failure Detection and Location in Shunt Capacitor Banksrdquo Acceptedfor 2017 Western Protective Relay Conference Spokane WA USA October 17-192017

bull H Jouybari-Moghaddam T S Sidhu rdquoA Study of Capacitor Element Failures inHigh Voltage Capacitor Banksrdquo IEEE CCECE 2017 Windsor ON Canada 30April-3 May 2017

bull H Jouybari-Moghaddam T S Sidhu P Parikh I Voloh rdquoEnhanced Fault Loca-tion Method for Shunt Capacitor Banksrdquo Texas AampM 70th Annual Conference forProtective Relay Engineers College Station TX USA April 3-6 2017

bull H Jouybari-Moghaddam T S Sidhu P Parikh rdquoA Study of Fault LocationMethod in Double Wye Shunt Capacitor Banksrdquo CIGRE Canada Conference Van-couver Canada October 17-19 2016

bull H Jouybari-Moghaddam SH Hosseinian B Vahidi Active distribution networksislanding issues An introduction in proc 11th International Conference on Envi-ronment and Electrical Engineering EEEIC12 Venice Italy 18-25 May 2012

bull H Jouybari-Moghaddam SH Hosseinian B Vahidi Automatic Local State De-tection for Synchronous Distributed Generators in proc 11th International Con-ference on Environment and Electrical Engineering EEEIC12 Venice Italy 18-25May 2012

bull H Jouybari-Moghaddam SH Hosseinian A Alimardani Application of a Proba-bilistic Approach to Distribution Transformer Derating Calculation in proc 17thElectric Power Distribution Conference EPDC12 Tehran Iran May 1-2 2012

bull H Jouybari-Moghaddam SH Hosseinian B Vahidi M Ghiasi Rad Smart Con-trol Mode Selection for proper operation of Synchronous Distributed Generators2nd Iranian Conference on Smart Grids (ICSG 2012) Tehran Iran May 24-252012

bull H Jouybari-Moghaddam H Javidi Genetic Algorithm Based Optimal Sizing andSitting of Different Distributed Generators for Voltage Profile Improvement and Ac-tive Loss Minimization 13th Iranian Student Conference on Electrical Engineering(ISCEE) Tehran Iran Sep 2010 (in Persian)

Fault Location in High Voltage Shunt Capacitor Banks

Recommended Citation

Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction

Problem statement and research objectives

Challenges

Motivation

Research objectives

Thesis outline

Summary

Fault Location Fundamentals Unbalance Protection

Introduction

Phase voltage differential

Unbalance method for capacitor banks grounded through a neutral capacitor

Unbalance method for capacitor banks grounded through a CT with resistive burden

Phase current unbalance protection for fault location

Neutral voltage unbalance for double wye ungrounded configurations with isolated neutrals

Neutral voltage unbalance for double wye ungrounded configurations with tied neutrals

Summary

SCBs Fault Location Literature Survey

Introduction

Literature Survey

Investigation and review of the SEL method

Single Wye Ungrounded SCB

Double Wye Ungrounded SCB with Neutral Current Measurement

Double Wye Ungrounded SCB with Isolated Neutrals

H-bridge banks with CT in each phase and PT at the tap point

Summary

The Proposed Fault Location Methods

Introduction

Superimposed Reactance (SR) for Ungrounded Single Wye SCB

Determining the involved phase


Adapted SR for Single Wye SCB Grounded through a Capacitor



Adapted SR for Single Wye SCB Grounded through a CT



Enhanced Compensated Neutral Current for Ungrounded Y-Y SCB

Determining the involved phase and section


Enhanced Compensated Neutral Current for Grounded Y-Y SCB



Envision of Additional Unbalance Protection Elements

Additional Voltage Differential Element

Additional Neutral Unbalance Element

Conclusion for applicability of additional protection elements to fault location

Provisions for Algorithms Security and Applications

Compensation for Gradual Changes in the Reactance

Required Data for the Application Setting

The Proposed Algorithms Flowchart

Blinder Counting Schemes and Blocking the Algorithm

Usage and Information Display for Bank OperatorsService Crews

Summary

Evaluation of the Proposed and the Investigated Methods

Introduction






Case Studies with Additional Protection Elements

Y-Y Ungrounded with Neutral Voltage Unbalance-Tied Neutrals


Conclusion on the Results for Additional Protection Elements


Further Investigation on Algorithms Reliability

Simultaneous Failures

Susceptibility to External Disturbances

Regular Updating of the k-factors

Proposed Methods Verification for an Existing Utility System

Summary

Proposed Methods Applications and Online Monitoring

Introduction

Online Monitoring vs Fault Location

Failures Involved Phase Determination Methods

Failures Involved Phase and Section Determination Methods

Demonstrating Fuse Saving for Externally Fused SCBs

Comparing Conventional Unbalance Relaying of a Commercial Relay

The open loop test set-up

Relay outputs analysis

Summary

Summary Conclusions and Future Works

Summary and Conclusions

Future Works

Bibliography

Simulation Settings

Simulated System and Specifications of the SCBs

Plot of Additional Signals During External Unbalance

Additional Simulation Results on Measurement Accuracy

Further on SCBs Protection and Internal Failures

Other protection functions for SCBs

Resistive Potential Devices (RPDs)

Rack bonding

Curriculum Vitae

Abstract

This thesis is focused on developing and investigating methods for locating internalfailures in High Voltage (HV) Shunt Capacitor Banks (SCBs) Integrating fault locationalgorithms into capacitor bank protective relays has become more vital with SCBs beingmore widely in use and unbalance being a major occurrence Specifically this is ofimportance for large (high voltage) SCBs which have a wider search space in terms ofthe number of elements and units that comprise the bank Localizing the fault locationproblem is an attempt towards reducing the outage (repair) time of SCBs with advantagessuch as planning preventive maintenance and reducing unscheduled outages of the SCBs

The challenges for determining the location of internal failures and continuous moni-toring of the SCBs for this application are first no outward indication for the commonfusing technologies of SCBs (internally fused and fuseless) second the offsetting (bal-ancing) effect of subsequent failures against the low impact of the previous failures (ieambiguous failures) third compensating for other sources of unbalance such as manu-facturing tolerances gradual capacitance changes and system unbalances and last lessthan ideal number of available measurements

In this thesis first the ultra sensitive protection unbalance protection that is theconventional method for detecting internal failures is reviewed This protection strategywould be the backbone for fault location methods In the area of monitoring internalfailures and fault location of SCBs very little research work has been reported in theliterature A chapter will cover the existing methods that are either directly related tothis topic or indirectly perform the same application Furthermore a relevant method inthe literature is investigated in more details

Intimate connection exists between bank designs and unbalance protection methodsTherefore different configurations have different advantages or shortcomings in terms offault location Having reviewed various connections the ones that are more common orhave more challenges in terms of available measurements are intended for proposing newmethods for internal failure determination or enhancing the fault location algorithms

In a separate chapter first a new indicating quantity that employs automatic cal-ibrating factors is proposed The method overcomes the mentioned challenges and isfurther adapted to suit three of the common SCB grounding arrangements The indi-cating quantity is referred to as Superimposed Reactance method and can be integratedinto voltage-based unbalance protection functions to enhance the extracted informationfrom detected failures Then current-based unbalance protection methods for doublewye banks are considered and a fault location method that applies a combination ofself-tuning and auto-setting of k-factors is proposed for this type of banks

In another part of the proposed methodrsquos chapter envision of additional unbalanceprotection functions is discussed While it is seldom economic to add voltage or currenttransducers for solely fault location purpose two common protection philosophies withadditional measurements are discussed in terms of fault location applicationIn the last part of the chapter provisions for the proposed algorithm security and alsothe proposed methods usage and information display are presented

The performance of the investigated methods of the literature and the proposed meth-ods are assessed in a separate chapter Various internal failure scenarios and external

Dedication

Acknowlegements

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Tables xvi

34 Summary 29

49 Summary 62

65 Summary 179

Bibliography 184

List of Figures

Each Section 49

List of Tables

List of Appendices

Chapter 1

Introduction

111 Challenges

112 Motivation

May not be detected

H-Bridge

Double Wye

Single Wye

12 Thesis outline

13 Summary 9

13 Summary

Chapter 2

21 Introduction

point Figure 21

VTAP =X2

X1 +X2

VBUS (21)

X1 +X2

KSET =| VTAP

| (24)

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

Vop =| 3V0 minus (X

+ 3)times VN | (28)

XA XB XC

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

3V0 + jX

Rtimes VR = 0 (210)

RtimesVR) Thus

| 3V0 + 3j X I0 |gt Vpickup (211)

cation

IA = IA1 + IA2

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

ZA2+ZA1or

XA2 +XA1

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

28 Summary

Chapter 3

31 Introduction

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

Xfminus VB

Xminus VC

Xfminus VA

minus VBXminus VC

Xminus 1

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

Xf)minus 3V0 + V0

2 + XXf

+ 2(36)

) (37)

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

VA minus VN +XA

(VB minus VN) +XA

(VBminusVN)+XA

η1 =XA

minus 1 (312)

η2 =XA

minus 1

C ) (313)

IN = I lA + I lB + I lC (314)

Kp =Xr

X lp +Xr

p AB or C (316)

IN = KAIA +KAIB

minusKAIB

K1 = KB minusKA

K2 = KC minusKA

KAf =Xr

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

VNlNr3

minus 1

XSpu =X minusXf

) (332)

34 Summary 29

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

34 Summary

34 Summary 31

Chapter 4

41 Introduction

41 Introduction 33

Single Wye SCB

XA XB XC

) =VAXAf

minus 1

) =VAXAf

minus VAXA

VN =(VA

BVB +KACVC

B +KAC

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

XAf+ 1 +KA

B +KAC

minus V0

VN =(VA minus V0)

XAminusXAfXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

XAf = XA (47)

we will have

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

1 + 2βA minus αA

αA + αAKAC + 1

1minus αA

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

p + γp (419)

which implies

XSpup =

For phase B KB

C =KAC

KBA = (KA

B)minus1

A +KBC

For phase C KC

A = (KAC )minus1

A +KCB

XSpup = Ksg

through a Capacitor

= VN(1

) (425)

XA XB XC

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

B +KAC +KA

N +XSpuA ) (428)

B+KAC+KA

N)minusKANV0

γprime

λprime

A = 1 +KAB +KA

C +KAN (431)

γprimeA = γA

λprimeA = λA +KA

XSpup =

γprimep minus λ

VN minus Vp(433)

= VN(1

) (434)

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

through a CT

XA XB XC

IG =VRR

CTR = VR (437)

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

XSpup =

ppprimeprime + jXVR

minusVp(441)

KABVB +KA

Ungrounded Y-Y SCB

IN = I lA + I lB + I lC (443)

Kp =Xr

X lp +Xr

p AB or C (445)

KAf =Xr

X lAf +Xr

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

IN = K1I1 +K2I2 (451)

lowast2 ) (454)

therefore we have

d INdX l

IA (460)

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

d INdXr

(X lA +Xr

A)2IA (462)

∆ IN(pu) =

∆X l

A(pu) times Kx

∆XrA(pu) times 1

Xr = KxXl (464)

Grounded Y-Y SCB

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

d INdXr

(X lA +Xr

A)2IA (469)

∆ INIr

2X(470)

∆ IN(pu) =∆X

2(pu) (471)

ements

TAP (473)

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

∆Vop(pu) = ∆X(pu) (476)

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

d VopdXR

=d(minusksetVp XR

XR1 +XR

(XR)2(479)

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

Vp1 Vp2 || Vp3

Cp 2 pu

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

VPXrsquol

Xrsquor

Cut Set

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus 1Xl

3VN2(1Xl

l minus Cl = Cprime

r minus Cr (486)

Ce = Cutimes Su

times 103 (487)

Kx =Xr

Cutimes PS

Fuseless Bank (492)

C1 C2 = (1

)minus1 (494)

49 Summary

Chapter 5

51 Introduction

Time Axis

Angle Zone

Magnitude Threshold

51 Introduction 65

01 011 012 013 014 015 016 017minus180

Angle Magnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

01 015 02 025 03

Time (s)

01 015 02 025 03

Time(s)

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

01 02 03 04 05 06 070

Time(s)

01 02 03 04 05 06 070

Time (s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

K1 00017|4951 00025|5247 00023|3527 00037|2201

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time(s)

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

Cp = 10015 pu (56)

01 012 014 016 018 02 022 024 026 028 030

Time(s)

VN =CP minus 1

02 025 03 035 04 045minus180

Phase A [Left]

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 025 030123

Time (s) Time (s)

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

lated Neutrals

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 035 040

Time (s)

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

01 015 02 025 03 035 04minus180

X 03Y minus615

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Clearance

FaultOccurance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

01 02 03 04 05 06 070

Time (s)

01 015 02 025 03 035 04 045minus180

minus120

minus60

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

Time(s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time (s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time(s)

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Clearance

DetectionandReset

01 015 02 025 030

Time (s)

Compensated IN IN

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Fault Clearance

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

01 015 02 025 03minus180

minus120

minus60

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

01 015 02 025 03 035 040

I Diff

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 02 03 04 05 06 070

I Diff

Time(s)

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

045 05 055 06 065 07minus180

Time (s)

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

02 04 060

Time (s)02 04 06

Time (s)

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Utility System

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

01 015 02 025 03 03501234

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

Chapter 6

61 Introduction

XDetermining theX X

ambiguous failures

7 Disclaimer 2

02 025 03 035 04minus180

minus120

minus60

Time (s)

02 025 03 035 040

Time (s)

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

XDetermining theX X

XDynamic report of7

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

0 005 01 015 02 025 03 035 04 045 050

Time (s)

02 03 04

Time (s)

02 03 04

Time(s)S

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

02 03 0401234

Time(s)

02 03 0401234

Time(s)

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

a Commercial Relay

VoutVin

IoutIin

23times 5timesradic

65 Summary 179

65 Summary

Chapter 7

72 Future Works 183

72 Future Works

Bibliography

BIBLIOGRAPHY 185

186 BIBLIOGRAPHY

BIBLIOGRAPHY 187

188 BIBLIOGRAPHY

Appendix A

Simulation Settings

Appendix B

S=6P=2

Ce=136F

Ce=608F

Ce=1microF

Ce=36microF

100 MVA

230 KV

50 km 50 km

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

3316 8 3 5 14

Appendix C

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Open polemoment

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

Appendix D

01 015 02 025 03 035 04 0450

minus3

Time(s)

01 015 02 025 03 035 040

minus3

Time(s)

035 04 045 050

Time (s)

0 60 120 180 240 300 360 420 480 540 600 6600

Frequency (Hz)

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Appendix E

E3 Rack bonding

Curriculum Vitae

Publications

Journal papers

Conference Papers


Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction


Challenges

Motivation

Research objectives

Thesis outline

Summary


Introduction







Summary


Introduction

Literature Survey






Summary


Introduction


























Summary


Introduction
















Summary


Introduction








Summary



Future Works

Bibliography

Simulation Settings







Rack bonding

Curriculum Vitae

Dedication

Acknowlegements

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Tables xvi

34 Summary 29

49 Summary 62

65 Summary 179

Bibliography 184

List of Figures

Each Section 49

List of Tables

List of Appendices

Chapter 1

Introduction

111 Challenges

112 Motivation

May not be detected

H-Bridge

Double Wye

Single Wye

12 Thesis outline

13 Summary 9

13 Summary

Chapter 2

21 Introduction

point Figure 21

VTAP =X2

X1 +X2

VBUS (21)

X1 +X2

KSET =| VTAP

| (24)

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

Vop =| 3V0 minus (X

+ 3)times VN | (28)

XA XB XC

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

3V0 + jX

Rtimes VR = 0 (210)

RtimesVR) Thus

| 3V0 + 3j X I0 |gt Vpickup (211)

cation

IA = IA1 + IA2

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

ZA2+ZA1or

XA2 +XA1

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

28 Summary

Chapter 3

31 Introduction

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

Xfminus VB

Xminus VC

Xfminus VA

minus VBXminus VC

Xminus 1

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

Xf)minus 3V0 + V0

2 + XXf

+ 2(36)

) (37)

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

VA minus VN +XA

(VB minus VN) +XA

(VBminusVN)+XA

η1 =XA

minus 1 (312)

η2 =XA

minus 1

C ) (313)

IN = I lA + I lB + I lC (314)

Kp =Xr

X lp +Xr

p AB or C (316)

IN = KAIA +KAIB

minusKAIB

K1 = KB minusKA

K2 = KC minusKA

KAf =Xr

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

VNlNr3

minus 1

XSpu =X minusXf

) (332)

34 Summary 29

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

34 Summary

34 Summary 31

Chapter 4

41 Introduction

41 Introduction 33

Single Wye SCB

XA XB XC

) =VAXAf

minus 1

) =VAXAf

minus VAXA

VN =(VA

BVB +KACVC

B +KAC

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

XAf+ 1 +KA

B +KAC

minus V0

VN =(VA minus V0)

XAminusXAfXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

XAf = XA (47)

we will have

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

1 + 2βA minus αA

αA + αAKAC + 1

1minus αA

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

p + γp (419)

which implies

XSpup =

For phase B KB

C =KAC

KBA = (KA

B)minus1

A +KBC

For phase C KC

A = (KAC )minus1

A +KCB

XSpup = Ksg

through a Capacitor

= VN(1

) (425)

XA XB XC

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

B +KAC +KA

N +XSpuA ) (428)

B+KAC+KA

N)minusKANV0

γprime

λprime

A = 1 +KAB +KA

C +KAN (431)

γprimeA = γA

λprimeA = λA +KA

XSpup =

γprimep minus λ

VN minus Vp(433)

= VN(1

) (434)

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

through a CT

XA XB XC

IG =VRR

CTR = VR (437)

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

XSpup =

ppprimeprime + jXVR

minusVp(441)

KABVB +KA

Ungrounded Y-Y SCB

IN = I lA + I lB + I lC (443)

Kp =Xr

X lp +Xr

p AB or C (445)

KAf =Xr

X lAf +Xr

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

IN = K1I1 +K2I2 (451)

lowast2 ) (454)

therefore we have

d INdX l

IA (460)

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

d INdXr

(X lA +Xr

A)2IA (462)

∆ IN(pu) =

∆X l

A(pu) times Kx

∆XrA(pu) times 1

Xr = KxXl (464)

Grounded Y-Y SCB

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

d INdXr

(X lA +Xr

A)2IA (469)

∆ INIr

2X(470)

∆ IN(pu) =∆X

2(pu) (471)

ements

TAP (473)

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

∆Vop(pu) = ∆X(pu) (476)

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

d VopdXR

=d(minusksetVp XR

XR1 +XR

(XR)2(479)

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

Vp1 Vp2 || Vp3

Cp 2 pu

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

VPXrsquol

Xrsquor

Cut Set

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus 1Xl

3VN2(1Xl

l minus Cl = Cprime

r minus Cr (486)

Ce = Cutimes Su

times 103 (487)

Kx =Xr

Cutimes PS

Fuseless Bank (492)

C1 C2 = (1

)minus1 (494)

49 Summary

Chapter 5

51 Introduction

Time Axis

Angle Zone

Magnitude Threshold

51 Introduction 65

01 011 012 013 014 015 016 017minus180

Angle Magnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

01 015 02 025 03

Time (s)

01 015 02 025 03

Time(s)

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

01 02 03 04 05 06 070

Time(s)

01 02 03 04 05 06 070

Time (s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

K1 00017|4951 00025|5247 00023|3527 00037|2201

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time(s)

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

Cp = 10015 pu (56)

01 012 014 016 018 02 022 024 026 028 030

Time(s)

VN =CP minus 1

02 025 03 035 04 045minus180

Phase A [Left]

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 025 030123

Time (s) Time (s)

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

lated Neutrals

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 035 040

Time (s)

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

01 015 02 025 03 035 04minus180

X 03Y minus615

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Clearance

FaultOccurance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

01 02 03 04 05 06 070

Time (s)

01 015 02 025 03 035 04 045minus180

minus120

minus60

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

Time(s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time (s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time(s)

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Clearance

DetectionandReset

01 015 02 025 030

Time (s)

Compensated IN IN

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Fault Clearance

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

01 015 02 025 03minus180

minus120

minus60

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

01 015 02 025 03 035 040

I Diff

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 02 03 04 05 06 070

I Diff

Time(s)

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

045 05 055 06 065 07minus180

Time (s)

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

02 04 060

Time (s)02 04 06

Time (s)

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Utility System

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

01 015 02 025 03 03501234

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

Chapter 6

61 Introduction

XDetermining theX X

ambiguous failures

7 Disclaimer 2

02 025 03 035 04minus180

minus120

minus60

Time (s)

02 025 03 035 040

Time (s)

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

XDetermining theX X

XDynamic report of7

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

0 005 01 015 02 025 03 035 04 045 050

Time (s)

02 03 04

Time (s)

02 03 04

Time(s)S

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

02 03 0401234

Time(s)

02 03 0401234

Time(s)

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

a Commercial Relay

VoutVin

IoutIin

23times 5timesradic

65 Summary 179

65 Summary

Chapter 7

72 Future Works 183

72 Future Works

Bibliography

BIBLIOGRAPHY 185

186 BIBLIOGRAPHY

BIBLIOGRAPHY 187

188 BIBLIOGRAPHY

Appendix A

Simulation Settings

Appendix B

S=6P=2

Ce=136F

Ce=608F

Ce=1microF

Ce=36microF

100 MVA

230 KV

50 km 50 km

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

3316 8 3 5 14

Appendix C

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Open polemoment

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

Appendix D

01 015 02 025 03 035 04 0450

minus3

Time(s)

01 015 02 025 03 035 040

minus3

Time(s)

035 04 045 050

Time (s)

0 60 120 180 240 300 360 420 480 540 600 6600

Frequency (Hz)

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Appendix E

E3 Rack bonding

Curriculum Vitae

Publications

Journal papers

Conference Papers


Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction


Challenges

Motivation

Research objectives

Thesis outline

Summary


Introduction







Summary


Introduction

Literature Survey






Summary


Introduction


























Summary


Introduction
















Summary


Introduction








Summary



Future Works

Bibliography

Simulation Settings







Rack bonding

Curriculum Vitae

Dedication

Acknowlegements

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Tables xvi

34 Summary 29

49 Summary 62

65 Summary 179

Bibliography 184

List of Figures

Each Section 49

List of Tables

List of Appendices

Chapter 1

Introduction

111 Challenges

112 Motivation

May not be detected

H-Bridge

Double Wye

Single Wye

12 Thesis outline

13 Summary 9

13 Summary

Chapter 2

21 Introduction

point Figure 21

VTAP =X2

X1 +X2

VBUS (21)

X1 +X2

KSET =| VTAP

| (24)

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

Vop =| 3V0 minus (X

+ 3)times VN | (28)

XA XB XC

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

3V0 + jX

Rtimes VR = 0 (210)

RtimesVR) Thus

| 3V0 + 3j X I0 |gt Vpickup (211)

cation

IA = IA1 + IA2

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

ZA2+ZA1or

XA2 +XA1

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

28 Summary

Chapter 3

31 Introduction

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

Xfminus VB

Xminus VC

Xfminus VA

minus VBXminus VC

Xminus 1

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

Xf)minus 3V0 + V0

2 + XXf

+ 2(36)

) (37)

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

VA minus VN +XA

(VB minus VN) +XA

(VBminusVN)+XA

η1 =XA

minus 1 (312)

η2 =XA

minus 1

C ) (313)

IN = I lA + I lB + I lC (314)

Kp =Xr

X lp +Xr

p AB or C (316)

IN = KAIA +KAIB

minusKAIB

K1 = KB minusKA

K2 = KC minusKA

KAf =Xr

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

VNlNr3

minus 1

XSpu =X minusXf

) (332)

34 Summary 29

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

34 Summary

34 Summary 31

Chapter 4

41 Introduction

41 Introduction 33

Single Wye SCB

XA XB XC

) =VAXAf

minus 1

) =VAXAf

minus VAXA

VN =(VA

BVB +KACVC

B +KAC

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

XAf+ 1 +KA

B +KAC

minus V0

VN =(VA minus V0)

XAminusXAfXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

XAf = XA (47)

we will have

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

1 + 2βA minus αA

αA + αAKAC + 1

1minus αA

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

p + γp (419)

which implies

XSpup =

For phase B KB

C =KAC

KBA = (KA

B)minus1

A +KBC

For phase C KC

A = (KAC )minus1

A +KCB

XSpup = Ksg

through a Capacitor

= VN(1

) (425)

XA XB XC

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

B +KAC +KA

N +XSpuA ) (428)

B+KAC+KA

N)minusKANV0

γprime

λprime

A = 1 +KAB +KA

C +KAN (431)

γprimeA = γA

λprimeA = λA +KA

XSpup =

γprimep minus λ

VN minus Vp(433)

= VN(1

) (434)

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

through a CT

XA XB XC

IG =VRR

CTR = VR (437)

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

XSpup =

ppprimeprime + jXVR

minusVp(441)

KABVB +KA

Ungrounded Y-Y SCB

IN = I lA + I lB + I lC (443)

Kp =Xr

X lp +Xr

p AB or C (445)

KAf =Xr

X lAf +Xr

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

IN = K1I1 +K2I2 (451)

lowast2 ) (454)

therefore we have

d INdX l

IA (460)

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

d INdXr

(X lA +Xr

A)2IA (462)

∆ IN(pu) =

∆X l

A(pu) times Kx

∆XrA(pu) times 1

Xr = KxXl (464)

Grounded Y-Y SCB

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

d INdXr

(X lA +Xr

A)2IA (469)

∆ INIr

2X(470)

∆ IN(pu) =∆X

2(pu) (471)

ements

TAP (473)

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

∆Vop(pu) = ∆X(pu) (476)

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

d VopdXR

=d(minusksetVp XR

XR1 +XR

(XR)2(479)

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

Vp1 Vp2 || Vp3

Cp 2 pu

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

VPXrsquol

Xrsquor

Cut Set

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus 1Xl

3VN2(1Xl

l minus Cl = Cprime

r minus Cr (486)

Ce = Cutimes Su

times 103 (487)

Kx =Xr

Cutimes PS

Fuseless Bank (492)

C1 C2 = (1

)minus1 (494)

49 Summary

Chapter 5

51 Introduction

Time Axis

Angle Zone

Magnitude Threshold

51 Introduction 65

01 011 012 013 014 015 016 017minus180

Angle Magnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

01 015 02 025 03

Time (s)

01 015 02 025 03

Time(s)

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

01 02 03 04 05 06 070

Time(s)

01 02 03 04 05 06 070

Time (s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

K1 00017|4951 00025|5247 00023|3527 00037|2201

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time(s)

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

Cp = 10015 pu (56)

01 012 014 016 018 02 022 024 026 028 030

Time(s)

VN =CP minus 1

02 025 03 035 04 045minus180

Phase A [Left]

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 025 030123

Time (s) Time (s)

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

lated Neutrals

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 035 040

Time (s)

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

01 015 02 025 03 035 04minus180

X 03Y minus615

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Clearance

FaultOccurance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

01 02 03 04 05 06 070

Time (s)

01 015 02 025 03 035 04 045minus180

minus120

minus60

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

Time(s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time (s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time(s)

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Clearance

DetectionandReset

01 015 02 025 030

Time (s)

Compensated IN IN

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Fault Clearance

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

01 015 02 025 03minus180

minus120

minus60

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

01 015 02 025 03 035 040

I Diff

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 02 03 04 05 06 070

I Diff

Time(s)

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

045 05 055 06 065 07minus180

Time (s)

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

02 04 060

Time (s)02 04 06

Time (s)

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Utility System

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

01 015 02 025 03 03501234

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

Chapter 6

61 Introduction

XDetermining theX X

ambiguous failures

7 Disclaimer 2

02 025 03 035 04minus180

minus120

minus60

Time (s)

02 025 03 035 040

Time (s)

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

XDetermining theX X

XDynamic report of7

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

0 005 01 015 02 025 03 035 04 045 050

Time (s)

02 03 04

Time (s)

02 03 04

Time(s)S

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

02 03 0401234

Time(s)

02 03 0401234

Time(s)

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

a Commercial Relay

VoutVin

IoutIin

23times 5timesradic

65 Summary 179

65 Summary

Chapter 7

72 Future Works 183

72 Future Works

Bibliography

BIBLIOGRAPHY 185

186 BIBLIOGRAPHY

BIBLIOGRAPHY 187

188 BIBLIOGRAPHY

Appendix A

Simulation Settings

Appendix B

S=6P=2

Ce=136F

Ce=608F

Ce=1microF

Ce=36microF

100 MVA

230 KV

50 km 50 km

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

3316 8 3 5 14

Appendix C

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Open polemoment

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

Appendix D

01 015 02 025 03 035 04 0450

minus3

Time(s)

01 015 02 025 03 035 040

minus3

Time(s)

035 04 045 050

Time (s)

0 60 120 180 240 300 360 420 480 540 600 6600

Frequency (Hz)

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Appendix E

E3 Rack bonding

Curriculum Vitae

Publications

Journal papers

Conference Papers


Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction


Challenges

Motivation

Research objectives

Thesis outline

Summary


Introduction







Summary


Introduction

Literature Survey






Summary


Introduction


























Summary


Introduction
















Summary


Introduction








Summary



Future Works

Bibliography

Simulation Settings







Rack bonding

Curriculum Vitae

Acknowlegements

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Tables xvi

34 Summary 29

49 Summary 62

65 Summary 179

Bibliography 184

List of Figures

Each Section 49

List of Tables

List of Appendices

Chapter 1

Introduction

111 Challenges

112 Motivation

May not be detected

H-Bridge

Double Wye

Single Wye

12 Thesis outline

13 Summary 9

13 Summary

Chapter 2

21 Introduction

point Figure 21

VTAP =X2

X1 +X2

VBUS (21)

X1 +X2

KSET =| VTAP

| (24)

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

Vop =| 3V0 minus (X

+ 3)times VN | (28)

XA XB XC

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

3V0 + jX

Rtimes VR = 0 (210)

RtimesVR) Thus

| 3V0 + 3j X I0 |gt Vpickup (211)

cation

IA = IA1 + IA2

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

ZA2+ZA1or

XA2 +XA1

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

28 Summary

Chapter 3

31 Introduction

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

Xfminus VB

Xminus VC

Xfminus VA

minus VBXminus VC

Xminus 1

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

Xf)minus 3V0 + V0

2 + XXf

+ 2(36)

) (37)

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

VA minus VN +XA

(VB minus VN) +XA

(VBminusVN)+XA

η1 =XA

minus 1 (312)

η2 =XA

minus 1

C ) (313)

IN = I lA + I lB + I lC (314)

Kp =Xr

X lp +Xr

p AB or C (316)

IN = KAIA +KAIB

minusKAIB

K1 = KB minusKA

K2 = KC minusKA

KAf =Xr

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

VNlNr3

minus 1

XSpu =X minusXf

) (332)

34 Summary 29

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

34 Summary

34 Summary 31

Chapter 4

41 Introduction

41 Introduction 33

Single Wye SCB

XA XB XC

) =VAXAf

minus 1

) =VAXAf

minus VAXA

VN =(VA

BVB +KACVC

B +KAC

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

XAf+ 1 +KA

B +KAC

minus V0

VN =(VA minus V0)

XAminusXAfXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

XAf = XA (47)

we will have

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

1 + 2βA minus αA

αA + αAKAC + 1

1minus αA

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

p + γp (419)

which implies

XSpup =

For phase B KB

C =KAC

KBA = (KA

B)minus1

A +KBC

For phase C KC

A = (KAC )minus1

A +KCB

XSpup = Ksg

through a Capacitor

= VN(1

) (425)

XA XB XC

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

B +KAC +KA

N +XSpuA ) (428)

B+KAC+KA

N)minusKANV0

γprime

λprime

A = 1 +KAB +KA

C +KAN (431)

γprimeA = γA

λprimeA = λA +KA

XSpup =

γprimep minus λ

VN minus Vp(433)

= VN(1

) (434)

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

through a CT

XA XB XC

IG =VRR

CTR = VR (437)

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

XSpup =

ppprimeprime + jXVR

minusVp(441)

KABVB +KA

Ungrounded Y-Y SCB

IN = I lA + I lB + I lC (443)

Kp =Xr

X lp +Xr

p AB or C (445)

KAf =Xr

X lAf +Xr

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

IN = K1I1 +K2I2 (451)

lowast2 ) (454)

therefore we have

d INdX l

IA (460)

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

d INdXr

(X lA +Xr

A)2IA (462)

∆ IN(pu) =

∆X l

A(pu) times Kx

∆XrA(pu) times 1

Xr = KxXl (464)

Grounded Y-Y SCB

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

d INdXr

(X lA +Xr

A)2IA (469)

∆ INIr

2X(470)

∆ IN(pu) =∆X

2(pu) (471)

ements

TAP (473)

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

∆Vop(pu) = ∆X(pu) (476)

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

d VopdXR

=d(minusksetVp XR

XR1 +XR

(XR)2(479)

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

Vp1 Vp2 || Vp3

Cp 2 pu

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

VPXrsquol

Xrsquor

Cut Set

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus 1Xl

3VN2(1Xl

l minus Cl = Cprime

r minus Cr (486)

Ce = Cutimes Su

times 103 (487)

Kx =Xr

Cutimes PS

Fuseless Bank (492)

C1 C2 = (1

)minus1 (494)

49 Summary

Chapter 5

51 Introduction

Time Axis

Angle Zone

Magnitude Threshold

51 Introduction 65

01 011 012 013 014 015 016 017minus180

Angle Magnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

01 015 02 025 03

Time (s)

01 015 02 025 03

Time(s)

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

01 02 03 04 05 06 070

Time(s)

01 02 03 04 05 06 070

Time (s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

K1 00017|4951 00025|5247 00023|3527 00037|2201

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time(s)

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

Cp = 10015 pu (56)

01 012 014 016 018 02 022 024 026 028 030

Time(s)

VN =CP minus 1

02 025 03 035 04 045minus180

Phase A [Left]

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 025 030123

Time (s) Time (s)

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

lated Neutrals

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 035 040

Time (s)

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

01 015 02 025 03 035 04minus180

X 03Y minus615

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Clearance

FaultOccurance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

01 02 03 04 05 06 070

Time (s)

01 015 02 025 03 035 04 045minus180

minus120

minus60

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

Time(s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time (s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time(s)

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Clearance

DetectionandReset

01 015 02 025 030

Time (s)

Compensated IN IN

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Fault Clearance

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

01 015 02 025 03minus180

minus120

minus60

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

01 015 02 025 03 035 040

I Diff

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 02 03 04 05 06 070

I Diff

Time(s)

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

045 05 055 06 065 07minus180

Time (s)

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

02 04 060

Time (s)02 04 06

Time (s)

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Utility System

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

01 015 02 025 03 03501234

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

Chapter 6

61 Introduction

XDetermining theX X

ambiguous failures

7 Disclaimer 2

02 025 03 035 04minus180

minus120

minus60

Time (s)

02 025 03 035 040

Time (s)

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

XDetermining theX X

XDynamic report of7

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

0 005 01 015 02 025 03 035 04 045 050

Time (s)

02 03 04

Time (s)

02 03 04

Time(s)S

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

02 03 0401234

Time(s)

02 03 0401234

Time(s)

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

a Commercial Relay

VoutVin

IoutIin

23times 5timesradic

65 Summary 179

65 Summary

Chapter 7

72 Future Works 183

72 Future Works

Bibliography

BIBLIOGRAPHY 185

186 BIBLIOGRAPHY

BIBLIOGRAPHY 187

188 BIBLIOGRAPHY

Appendix A

Simulation Settings

Appendix B

S=6P=2

Ce=136F

Ce=608F

Ce=1microF

Ce=36microF

100 MVA

230 KV

50 km 50 km

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

3316 8 3 5 14

Appendix C

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Open polemoment

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

Appendix D

01 015 02 025 03 035 04 0450

minus3

Time(s)

01 015 02 025 03 035 040

minus3

Time(s)

035 04 045 050

Time (s)

0 60 120 180 240 300 360 420 480 540 600 6600

Frequency (Hz)

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Appendix E

E3 Rack bonding

Curriculum Vitae

Publications

Journal papers

Conference Papers


Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction


Challenges

Motivation

Research objectives

Thesis outline

Summary


Introduction







Summary


Introduction

Literature Survey






Summary


Introduction


























Summary


Introduction
















Summary


Introduction








Summary



Future Works

Bibliography

Simulation Settings







Rack bonding

Curriculum Vitae

Contents

Abstract i

Dedication iii

Acknowlegements iv

List of Tables xvi

34 Summary 29

49 Summary 62

65 Summary 179

Bibliography 184

List of Figures

Each Section 49

List of Tables

List of Appendices

Chapter 1

Introduction

111 Challenges

112 Motivation

May not be detected

H-Bridge

Double Wye

Single Wye

12 Thesis outline

13 Summary 9

13 Summary

Chapter 2

21 Introduction

point Figure 21

VTAP =X2

X1 +X2

VBUS (21)

X1 +X2

KSET =| VTAP

| (24)

(VA minus VNminusjX

+VB minus VNminusjX

+VC minus VNminusjX

Vop =| 3V0 minus (X

+ 3)times VN | (28)

XA XB XC

(VAminusjX

+VBminusjX

+VCminusjX

)timesR = VR (29)

3V0 + jX

Rtimes VR = 0 (210)

RtimesVR) Thus

| 3V0 + 3j X I0 |gt Vpickup (211)

cation

IA = IA1 + IA2

ZA2minusZA1

ZA2ZA1

IA = VAZA2+ZA1

ZA2ZA1

ZA2+ZA1or

XA2 +XA1

Zprime2

Z1 + Zprime2

=Zprime1

Z2 + Zprime1

IH = IA(Zprime2

Z1 + Zprime2

minus Zprime1

Z2 + Zprime1

) (219)

28 Summary

Chapter 3

31 Introduction

VA minus VNX

+VB minus VN

X+VC minus VN

X= 0 (32)

Xfminus VB

Xminus VC

Xfminus VA

minus VBXminus VC

Xminus 1

Xf)minus 3V0

2 + XXf

+ 3V0 (35)

Xf)minus 3V0 + V0

2 + XXf

+ 2(36)

) (37)

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (38)

VA minus VN +XA

(VB minus VN) +XA

(VBminusVN)+XA

η1 =XA

minus 1 (312)

η2 =XA

minus 1

C ) (313)

IN = I lA + I lB + I lC (314)

Kp =Xr

X lp +Xr

p AB or C (316)

IN = KAIA +KAIB

minusKAIB

K1 = KB minusKA

K2 = KC minusKA

KAf =Xr

= (KAf minusKA)IA

= IAXrA

X lA minusX l

(X lA +Xr

A)(X lAf

VA minus VNlXf

+VB minus VNl

X+VC minus VNl

X= 0 (323)

VA minus VNrX

+VB minus VNr

X+VC minus VNr

X= 0 (324)

minus VNlXf

minus VAX

+VNrXminus VNl

X+VNrXminus VNl

X+VNrX

minus VNlX

= 0 (326)

VNlNr3

minus 1

XSpu =X minusXf

) (332)

34 Summary 29

ang(VNlNr minusKV +

V +) = ang(

VNlNrV +

minusK) angVNlNrV +

34 Summary

34 Summary 31

Chapter 4

41 Introduction

41 Introduction 33

Single Wye SCB

XA XB XC

) =VAXAf

minus 1

) =VAXAf

minus VAXA

VN =(VA

BVB +KACVC

B +KAC

VN =VA

XAminusXAfXAf

+ VA +KABVB + VB

minus VB

XAf+ 1 +KA

B +KAC

minus V0

VN =(VA minus V0)

XAminusXAfXAf

XAf+ 1 +KA

B +KAC

+ V0 (46)

XAf = XA (47)

we will have

αA =KA

B minus 1

1 +KAB +KA

βA =KA

C minus 1

1 +KAB +KA

1 + 2βA minus αA

αA + αAKAC + 1

1minus αA

VA minus VNXA

+VB minus VNXB

+VC minus VNXC

= 0 (413)

+VB minus VNXBXA

+VC minus VNXCXA

= 0 (414)

λA = 1 +KAB +KA

C (417)

XSpup =

Xp minusXpf

p + γp (419)

which implies

XSpup =

For phase B KB

C =KAC

KBA = (KA

B)minus1

A +KBC

For phase C KC

A = (KAC )minus1

A +KCB

XSpup = Ksg

through a Capacitor

= VN(1

) (425)

XA XB XC

minus VAXA

minus VBXA

minus VCXA

= VN(1

minus 1

B +KAC +KA

N +XSpuA ) (428)

B+KAC+KA

N)minusKANV0

γprime

λprime

A = 1 +KAB +KA

C +KAN (431)

γprimeA = γA

λprimeA = λA +KA

XSpup =

γprimep minus λ

VN minus Vp(433)

= VN(1

) (434)

VA +KABVB +KA

CVC = VN(1 +KAB +KA

C +KAN) (435)

through a CT

XA XB XC

IG =VRR

CTR = VR (437)

(VAminusjXA

+VBminusjXB

+VCminusjXC

) = IG (438)

minus VAXA

minus VBXA

minus VCXA

= minusjVR (439)

XSpup =

ppprimeprime + jXVR

minusVp(441)

KABVB +KA

Ungrounded Y-Y SCB

IN = I lA + I lB + I lC (443)

Kp =Xr

X lp +Xr

p AB or C (445)

KAf =Xr

X lAf +Xr

which evolves to

ICompN = IAX

X lA minusX l

(X lA +Xr

A)(X lAf +Xr

A)(449)

IN = K1I1 +K2I2 (451)

lowast2 ) (454)

therefore we have

d INdX l

IA (460)

d INdX l

=minusXr

(X lA +Xr

A)2IA (461)

d INdXr

(X lA +Xr

A)2IA (462)

∆ IN(pu) =

∆X l

A(pu) times Kx

∆XrA(pu) times 1

Xr = KxXl (464)

Grounded Y-Y SCB

Kp =Xr

p minusX lp

X lp +Xr

p AB or C (466)

d INdX l

XrAminusX

XlA+Xr

=minus2Xr

(X lA +Xr

A)2IA (468)

d INdXr

(X lA +Xr

A)2IA (469)

∆ INIr

2X(470)

∆ IN(pu) =∆X

2(pu) (471)

ements

TAP (473)

d VopdXL

dX(1minus kset

XL) = Vp ksetX

XL)2 (474)

∆Vop(pu) = ∆X(pu) (476)

d VopdXL

XL1 +XL

= VpminusXL

(XL)2(477)

∆Vop(pu) =minusXL

XL∆XL

1 (pu) (478)

d VopdXR

=d(minusksetVp XR

XR1 +XR

(XR)2(479)

∆Vop(pu) =XL

XL∆XR

1 (pu) (480)

Vp1 Vp2 || Vp3

Cp 2 pu

VN =CP minus 1

CP + 2= 1minus 3

2 + CP

pu (482)

VPXrsquol

Xrsquor

Cut Set

VAminusVNlXprimel

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNlXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus VAminusVNXl

+ VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

VAminusVNXl

+ VBminusVNXl

+ VCminusVNXl

+ VAminusVNXprimer

minus VAminusVNXr

+ VAminusVNXr

+ VBminusVNXr

+ VCminusVNXr

Xprimel

minus 1Xl

3VN2(1Xl

l minus Cl = Cprime

r minus Cr (486)

Ce = Cutimes Su

times 103 (487)

Kx =Xr

Cutimes PS

Fuseless Bank (492)

C1 C2 = (1

)minus1 (494)

49 Summary

Chapter 5

51 Introduction

Time Axis

Angle Zone

Magnitude Threshold

51 Introduction 65

01 011 012 013 014 015 016 017minus180

Angle Magnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 017minus180

180Phase A

of I ra

01 011 012 013 014 015 016 017minus180

180Phase B

of I ra

01 011 012 013 014 015 016 017minus180

180Phase C

Time (s)

of I ra

51 Introduction 67

02 022 024 026 028 03 032 034 036 038minus180

180Phase A

Angle Magnitude

02 022 024 026 028 03 032 034 036 038minus180

180Phase B

02 022 024 026 028 03 032 034 036 038minus180

180Phase C

Time (s)

Detected failure

02 022 024 026 028 03 032 034 036 0380

Phase A

02 022 024 026 028 03 032 034 036 0380

Phase B

02 022 024 026 028 03 032 034 036 0380

Phase C

Time(s)

01 015 02 025 03minus180

180Phase A

I rate

01 015 02 025 03minus180

180Phase B

I rate

01 015 02 025 03minus180

180Phase C

Time (s)

I rate

Not aFailure

DetectedFailure

01 015 02 025 03

Time (s)

01 015 02 025 03

Time(s)

51 Introduction 69

01 02 03 04 05 06 07minus180

AngleMagnitude

01 02 03 04 05 06 07minus180

Time (s)

01 02 03 04 05 06 070

Time(s)

01 02 03 04 05 06 070

Time (s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

AngleMagnitude

01 011 012 013 014 015 016 017minus180

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

01 011 012 013 014 015 016 017minus180

minus60

Time (s)

01 011 012 013 014 015 016 0170

Time(s)

02 025 03 035 04minus180

180Phase A

Angle Magnitude

02 025 03 035 04minus180

180Phase B

02 025 03 035 04minus180

180Phase C

Time (s)

02 025 03 035 040

Phase A

02 025 03 035 040

Phase B

02 025 03 035 040

Phase C

Time(s)

k-factors 10060|09946 10070|09958 10047|09957 100598 |09968 10058 |09947

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 0450

102030405060

Phase A Counter

01 015 02 025 03 035 04 0450

102030405060

Phase B Counter

01 015 02 025 03 035 04 0450

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035minus180

AngleMagnitude

01 015 02 025 03 035minus180

)01 015 02 025 03 035

minus180

Time (s)

01 015 02 025 03 0350

102030405060

Phase A Counter

01 015 02 025 03 0350

102030405060

Phase B Counter

01 015 02 025 03 0350

102030405060

Phase C Counter

Time(s)

01 015 02 025 03 0350

Time(s)

01 011 012 013 014 015 016 017minus180

180phase A

01 011 012 013 014 015 016 017minus180

180phase B

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

180phase A

f I ra

01 011 012 013 014 015 016 017minus180

180phase B

f I ra

01 011 012 013 014 015 016 017minus180

180phase C

Time (s)

f I ra

01 012 014 0160

Time (s)

01 012 014 0160

Time(s)N

01 011 012 013 014 015 016 017minus180

minus120

minus60

Time (s)

01 012 014 016012

Time (s)

01 012 014 016012

Time(s)

K1 00017|4951 00025|5247 00023|3527 00037|2201

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 012 014 016 018 02 022 024 026 028 03minus180

180phase A

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase B

f I ra

01 012 014 016 018 02 022 024 026 028 03minus180

180phase C

Time (s)

f I ra

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04 045 05 055 068

Time(s)

01 015 02 025 03 035 04 045 05 055 060

I Diff

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180phase A

01 015 02 025 03 035 04 045 05 055minus180

180phase B

01 015 02 025 03 035 04 045 05 055minus180

180phase C

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time (s)

01 02 03 04 05012

01 02 03 04 050

Time(s)

Cl = 1088

Cprime

l = 1108

Cr = 6528

Cprimer = 6548

Cl = 25

Cprime

l = 250704

Cr = 2

Cprimer = 200704

Cp = 10015 pu (56)

01 012 014 016 018 02 022 024 026 028 030

Time(s)

VN =CP minus 1

02 025 03 035 04 045minus180

Phase A [Left]

02 025 03 035 04 045minus180

Phase A [Right]

Time (s)

02 025 03 035 04 045minus180

Phase B [Left]

02 025 03 035 04 045minus180

Phase B [Right]

Time (s)

02 025 03 035 04 045minus180

)Phase C [Left]

02 025 03 035 04 045minus180

Phase C [Right]

Time (s)

02 025 03 035 04 0450

Phase A Left Top

02 025 03 035 04 0450

Phase A Right Top

02 025 03 035 04 0450

Time (s)

Phase A Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase B Left Top

02 025 03 035 04 0450

Phase B Right Top

02 025 03 035 04 0450

Time (s)

Phase B Left Bottom

02 025 03 035 04 0450

Time (s)

02 025 03 035 04 0450

Phase C Left Top

02 025 03 035 04 0450

Phase C Right Top

02 025 03 035 04 0450

Time (s)

Phase C Left Bottom

02 025 03 035 04 0450

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 022 024 026 028 03minus180

Time (s)

02 025 030123

Time (s) Time (s)

02 022 024 026 028 03minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 022 024 026 028 03

7minus

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

02 022 024 026 028 03

minus3

rm amp

Time (s)02 022 024 026 028 03

minus3

rm amp

Time (s)

lated Neutrals

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

01 015 02 025 03 0350

Time (s)

01 015 02 025 03 0350

Time(s)

01 015 02 025 03 035 040

Time (s)

01 015 02 025 03 035 04 045minus180

X 03167Y minus779

phase A

01 015 02 025 03 035 04 045minus180

X 03167Y 4096

phase B

01 015 02 025 03 035 04 045minus180

X 03167Y minus1742

phase C

Time (s)

01 015 02 025 03 035 04minus180

X 03Y minus615

AngleMagnitude

01 015 02 025 03 035 04 045minus180

180X 03Y 5722

01 015 02 025 03 035 04 045minus180

Time (s)

01 015 02 025 03 035 04 045minus180

AngleMagnitude

01 015 02 025 03 035 04 045minus180

Time (s)

)InternalFailure

Clearance

FaultOccurance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

FaultOccurance

FaultClearance

0 005 01 015 02 025 03 035 04 045 050

Time (s)

Magnitude (

01 015 02 025 03 035 04 0450

Time(s)

01 015 02 025 03 035 04minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04minus180

180Phase B

01 015 02 025 03 035 04minus180

180Phase C

Time (s)

01 015 02 025 03 035 040

60Phase A Counter

01 015 02 025 03 035 040

60Phase B Counter

01 015 02 025 03 035 040

60Phase C Counter

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B SR

01 015 02 025 03 035 04 045minus180

180Phase C SR

Time (s)

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180Phase A

Angle Magnitude

01 02 03 04 05 06 07minus180

180Phase B

01 02 03 04 05 06 07minus180

180Phase C

Time (s)

01 02 03 04 05 06 070

60Phase A Counter

01 02 03 04 05 06 070

60Phase B Counter

01 02 03 04 05 06 070

60Phase C Counter

Time(s)

01 02 03 04 05 06 070

Time (s)

01 015 02 025 03 035 04 045minus180

minus120

minus60

01 015 02 025 03 035 04 0450

Time(s)

01 02 03 04 05 06 07minus180

180 Phase A SR

Angle Magnitude

01 02 03 04 05 06 07minus180

180 Phase B SR

01 02 03 04 05 06 07minus180

180 Phase C SR

Time (s)

01 02 03 04 05 06 070

15304560

Phase A Counter

01 02 03 04 05 06 070

15304560

Phase B Counter

01 02 03 04 05 06 070

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A SR

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180 Phase B SR

01 015 02 025 03 035 04 045 05 055minus180

180 Phase C SR

Time (s)

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

02 04 06 08 1 12minus180

180Phase A SR

Angle Magnitude

02 04 06 08 1 12minus180

180Phase B SR

02 04 06 08 1 12minus180

180Phase C SR

Time (s)

Phase C open pole

02 04 06 08 1 120

15304560

Phase A Counter

02 04 06 08 1 120

15304560

Phase B Counter

02 04 06 08 1 120

15304560

Phase C Counter

Time(s)

02 04 06 08 1 120

Magnitu

Time (s)

02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

02 025 03 035 04 045minus180

180Phase B

02 025 03 035 04 045minus180

180Phase C

Time (s)

02 025 03 035 04 045012

Phase A

02 025 03 035 04 045012

Phase BN

02 025 03 035 04 045012

Phase C

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

AngleMagnitude

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

102030405060

Phase C Counter

Time(s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045 05 055minus180

180Phase B

01 015 02 025 03 035 04 045 05 055minus180

180Phase C

Time (s)

Must be blocked

01 015 02 025 03 035 04 045 05 0550

Time (s)

Phase A

01 015 02 025 03 035 04 045 05 0550

15304560

Phase A Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase B Counter

01 015 02 025 03 035 04 045 05 0550

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 045 05 0550

Time(s)

02 025 03 035 04 045minus180

180(a)

Angle Magnitude

02 025 03 035 04 0450

Time(s)

01 015 02 025 03minus180

180phase A

f I ra

01 015 02 025 03minus180

180phase B

f I ra

01 015 02 025 03minus180

180phase C

Time (s)

f I ra

Occurance

Detection

01 015 02 025 030

Time (s)

01 015 02 025 03012

01 015 02 025 030

Time(s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time (s)

01 015 02 025 030

15304560

01 015 02 025 030

15304560

01 015 02 025 030

15304560

Time(s)

01 015 02 025 030

Time (s)

gnitud

Compensated IN IN

Clearance

DetectionandReset

01 015 02 025 030

Time (s)

Compensated IN IN

01 015 02 025 03minus180

180phase A

I rate

01 015 02 025 03minus180

180phase B

I rate

01 015 02 025 03minus180

180phase C

Time (s)

I rate

Fault Clearance

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

180phase A

f I ra

01 015 02 025 03 035 04minus180

180phase B

f I ra

01 015 02 025 03 035 04minus180

180phase C

Time (s)

f I ra

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time (s)

01 02 03 040

102030405060

01 02 03 040

102030405060

01 02 03 040

102030405060

Time(s)

01 02 03 04012

Time (s)

01 02 03 04012

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Detection

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 12minus180

180phase A

02 04 06 08 1 12minus180

180phase B

02 04 06 08 1 12minus180

180phase C

Time (s)

Reclosure

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time (s)

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

02 04 06 08 1 120

15304560

Time(s)N

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

01 015 02 025 03minus180

minus120

minus60

Time (s)

01 015 02 025 030

Time (s)

01 015 02 025 030

Time(s)

01 015 02 025 03 035 04minus180

minus120

minus60

Time (s)

01 02 03 040

Time (s)

01 02 03 040

Time (s)

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)N

02 04 06 08 1 120

Time(s)

I+ Iminus

02 04 06 08 1 12minus180

minus120

minus60

Time (s)

02 04 06 08 1 120

Time (s)

02 04 06 08 1 120

Time(s)

02 04 06 08 1 120

Time (s)

01 015 02 025 03 035 040

I Diff

Time(s)

01 015 02 025 03 035minus180

180phase A

01 015 02 025 03 035minus180

180phase B

01 015 02 025 03 035minus180

180phase C

Time (s)

Faultcleared

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

01 015 02 025 03 0350

15304560

Time (s)

01 02 03 04 05 06 070

I Diff

Time(s)

01 02 03 04 05 06minus180

180phase A

f I ra

01 02 03 04 05 06minus180

180phase B

f I ra

01 02 03 04 05 06minus180

180phase C

Time (s)

f I ra

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 025 03 035 04 045 05minus180

Phase A

02 025 03 035 04 045 05minus180

Phase B

02 025 03 035 04 045 05minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 05012

02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055minus180

minus120

minus60

Time (s)

01 02 03 04 050

Time (s)

01 02 03 04 050

Time(s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

01 015 02 025 03 035 04 045 05 055 060

Time (s)

Magnitu

01 015 02 025 03 035minus180

minus120

minus60

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Time (s)

02 022 024 026 028 03 032 034 036 038 04minus180

Phase A 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase B 87minus3

12x 10

minus3

02 022 024 026 028 03 032 034 036 038 04minus180

Phase C 87minus3

Time (s)

12x 10

minus3

045 05 055 06 065 07minus180

Time (s)

045 05 055 06 065 07minus180

Phase A 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase B 87minus3

12x 10

minus3

045 05 055 06 065 07minus180

Phase C 87minus3

Time (s)

12x 10

minus3

02 04 060

Phase A Left Top

02 04 060

Phase A Right Top

02 04 060

Time (s)

Phase A Left Bottom

02 04 060

Time (s)

02 04 060

Phase B Left Top

02 04 060

Phase B Right Top

02 04 060

Time (s)

Phase B Left Bottom

02 04 060

Time (s)

02 04 060

Phase C Left Top

02 04 060

Phase C Right Top

02 04 060

Time (s)

Phase C Left Bottom

02 04 060

Time (s)

02 04 060

87minus3

02 04 060

87minus3

02 04 060

minus3 A

02 04 060

87minus3

02 04 060

87minus3

Time (s)02 04 06

87minus3

Time (s)

02 04 060

Time (s)02 04 06

Time (s)

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase A

Angle Magnitude

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase B

02 021 022 023 024 025 026 027 028 029 03minus180

180Phase C

Time (s)

02 022 024 026 028 03 032minus180

Phase A

02 022 024 026 028 03 032minus180

Phase B

02 022 024 026 028 03 032minus180

Phase C

Time (s)

Utility System

01 015 02 025 03 035minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035minus180

180Phase B

01 015 02 025 03 035minus180

180Phase C

Time (s)

01 015 02 025 03 0350

15304560

Phase A Counter

01 015 02 025 03 0350

15304560

Phase B Counter

01 015 02 025 03 0350

15304560

Phase C Counter

Time(s)

01 015 02 025 03 03501234

Time(s)

01 015 02 025 03 035 04 045minus180

180Phase A

Angle Magnitude

01 015 02 025 03 035 04 045minus180

180Phase B

01 015 02 025 03 035 04 045minus180

180Phase C

Time (s)

01 015 02 025 03 035 04 0450

15304560

Phase A Counter

01 015 02 025 03 035 04 0450

15304560

Phase B Counter

01 015 02 025 03 035 04 0450

15304560

Phase C Counter

Time(s)

01 015 02 025 03 035 04 04501234

Time(s)

02 025 03 035 04 045 05 055minus180

Phase A

02 025 03 035 04 045 05 055minus180

Phase B

02 025 03 035 04 045 05 055minus180

Phase C

Time (s)

02 03 04 050

Time (s)

02 03 04 050

Time(s)

511 Summary 165

02 03 04 0501234

Time(s)

02 03 04 0501234

Time(s)N

511 Summary

Chapter 6

61 Introduction

XDetermining theX X

ambiguous failures

7 Disclaimer 2

02 025 03 035 04minus180

minus120

minus60

Time (s)

02 025 03 035 040

Time (s)

02 025 03 035 04

Phase A Alarm

02 025 03 035 04

Phase B Alarm

02 025 03 035 04

Phase C Alarm

Time(s)

XDetermining theX X

XDynamic report of7

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase BAn

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

02 025 03 035 04 045minus180

minus120

minus60

Time (s)

0 005 01 015 02 025 03 035 04 045 050

Time (s)

02 03 04

Time (s)

02 03 04

Time(s)S

02 025 03 035 04 045minus180

Phase A

02 025 03 035 04 045minus180

Phase B

02 025 03 035 04 045minus180

Phase C

Time (s)

02 03 0401234

Time(s)

02 03 0401234

Time(s)

02 025 03 035 04minus180

180(a) Phase A

Angle Magnitude

02 025 03 035 04minus180

180 Phase B

02 025 03 035 04minus180

180 Phase C

02 025 03 035 040

Time (s)

a Commercial Relay

VoutVin

IoutIin

23times 5timesradic

65 Summary 179

65 Summary

Chapter 7

72 Future Works 183

72 Future Works

Bibliography

BIBLIOGRAPHY 185

186 BIBLIOGRAPHY

BIBLIOGRAPHY 187

188 BIBLIOGRAPHY

Appendix A

Simulation Settings

Appendix B

S=6P=2

Ce=136F

Ce=608F

Ce=1microF

Ce=36microF

100 MVA

230 KV

50 km 50 km

Fig 48 11 1 1 8 1 7

Fig 410 11 1 1 5 1 6

3316 8 3 5 14

Appendix C

01 02 03 04 05 06 074

Time (s)

01 02 03 04 05 06 07minus135

minus130

minus125

minus120

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus150

minus100

minus50

Time (s)

01 02 03 04 05 06 070

Time (s)

01 02 03 04 05 06 07minus200

minus100

Time (s)

Open polemoment

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

0051152253354

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time(s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 015 02 025 03 035 04 045 05 0550

02040608

1121416

01020304050607080

01 015 02 025 03 035 04 045 05 055minus180

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

01 02 03 04 05 06 070

01 02 03 04 05 06 07minus180

Time (s)

Open pole interval

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time (s)

02 04 060

15304560

02 04 060

15304560

02 04 060

15304560

Time(s)

01 02 03 04 05 06 070

Magnitu

Time (s)

I DiffN

Compensated I DiffN

01 02 03 04 05 06 070

Time (s)

I DiffN

Compensated I DiffN

Appendix D

01 015 02 025 03 035 04 0450

minus3

Time(s)

01 015 02 025 03 035 040

minus3

Time(s)

035 04 045 050

Time (s)

0 60 120 180 240 300 360 420 480 540 600 6600

Frequency (Hz)

0 01 02 03 04 05 06 07 08 09 1

ω (pu)

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 04minus05

I N (A

0 005 01 015 02 025 03 035 040

Time(s)

|I N| (

0 005 01 015 02 025 03 035 04minus05

0 005 01 015 02 025 03 035 040

Time(s)

|IN| (A

Appendix E

E3 Rack bonding

Curriculum Vitae

Publications

Journal papers

Conference Papers


Abstract

Dedication

Acknowlegements

List of Figures

List of Tables

List of Appendices

Introduction


Challenges

Motivation

Research objectives

Thesis outline

Summary


Introduction







Summary


Introduction

Literature Survey






Summary


Introduction


























Summary


Introduction
















Summary


Introduction








Summary



Future Works

Bibliography

Simulation Settings







Rack bonding

Curriculum Vitae

Documents

Fault Location in High Voltage Shunt Capacitor Banks