TRANSFORMER MODELLING AND INFLUENTIAL PARAMETERS

TRANSFORMER MODELLING AND INFLUENTIAL

PARAMETERS IDENTIFICATION FOR GEOMAGNETIC

DISTURBANCES EVENTS

A thesis submitted to The University of Manchester for the degree of

PhD

In the Faculty of Engineering and Physical Sciences

2012

RUI ZHANG

School of Electrical and Electronic Engineering

Contents

3

CONTENTS CONTENTS ............................................................................................................................................. 3

LIST OF FIGURES .................................................................................................................................... 6

LIST OF TABLES .....................................................................................................................................12

LIST OF SYMBOL ...................................................................................................................................14

ABSTRACT ............................................................................................................................................17

DECLARATION ......................................................................................................................................18

COPYRIGHT STATEMENT ......................................................................................................................19

ACKNOWLEDGEMENT ..........................................................................................................................20

CHAPTER 1 INTRODUCTION .............................................................................................................21

1.1 INTRODUCTION .................................................................................................................................... 21

1.2 TRANSFORMER CORE SATURATION PROBLEMS ............................................................................................ 21

1.2.1 Inrush currents ......................................................................................................................... 22

1.2.2 Ferroresonance ........................................................................................................................ 24

1.2.3 Geomagnetic induced currents (GIC) ....................................................................................... 26

1.3 OBJECTIVES ......................................................................................................................................... 29

1.4 MAJOR CONTRIBUTION AND ORIGINALITY .................................................................................................. 31

1.5 THESIS OUTLINE .................................................................................................................................... 32

CHAPTER 2 BASICS OF TRANSFORMERS ...........................................................................................34

2.1 INTRODUCTION .................................................................................................................................... 34

2.2 TRANSFORMER STRUCTURE ..................................................................................................................... 34

2.2.1 Main component---winding ..................................................................................................... 35

2.2.2 Main component---transformer core ....................................................................................... 36

2.2.3 Transformer core materials ..................................................................................................... 39

CHAPTER 3 LITERATURE REVIEW .....................................................................................................45

3.1 INTRODUCTION .................................................................................................................................... 45

3.2 POWER SYSTEM OPERATION TRANSIENT---SWITCHING TRANSIENTS ................................................................. 46

3.2.1 Background .............................................................................................................................. 46

3.2.2 Ferroresonance ........................................................................................................................ 47

3.3 POWER SYSTEM NATURAL TRANSIENT---GIC .............................................................................................. 60

3.3.1 Background .............................................................................................................................. 60

3.3.2 GIC effect on power system ..................................................................................................... 61

3.3.3 Historical events....................................................................................................................... 64

Contents

4

3.3.4 Studies on transformer responses to GIC .................................................................................67

3.3.5 Mitigation .................................................................................................................................77

3.4 DISCUSSION AND SUMMARY ....................................................................................................................80

CHAPTER 4 STEADY STATE MAGNETIC CIRCUIT MODELLING FOR TRANSFORMERS ......................... 82

4.1 METHODOLOGY OF TRANSFORMER CORE MODELLING ...................................................................................83

4.1.1 Three-limb transformer core model .........................................................................................83

4.1.2 Five-limb transformer core model ............................................................................................87

4.1.3 Magnetising current calculation ..............................................................................................89

4.1.4 Flux density calculation ............................................................................................................90

4.1.5 Curve fitting ..............................................................................................................................93

4.2 CASE 1: MAGNETISING CURRENT INVESTIGATION ........................................................................................94

4.2.1 132/33 kV, 90 MVA three-limb transformer ............................................................................94

4.2.2 400/275/13 kV, 1000 MVA five-limb transformer ....................................................................98

4.2.3 Comparison of the influence between three-limb and five-limb transformer structure........ 105

4.3 CASE 2: SENSITIVITY STUDY ON BALANCE SITUATION .................................................................................. 116

4.3.1 Impact of magnetic flux density ............................................................................................ 116

4.3.2 Impact of area ....................................................................................................................... 124

4.4 CASE 3: GIC STUDY---SENSITIVITY ON UNBALANCED SITUATION .................................................................. 131

4.4.1 Impact of DC supply level ...................................................................................................... 131

4.5 SUMMARY ........................................................................................................................................ 137

CHAPTER 5 GIC MAGNETIC AND ELECTRICAL CIRCUIT MODELLING ............................................... 140

5.1 INTRODUCTION .................................................................................................................................. 140

5.2 CASE 1: GIC EFFECT ON SINGLE PHASE TRANSFORMER ............................................................................... 140

5.2.1 Single-phase model ............................................................................................................... 140

5.2.2 Simulation of DC only supply ................................................................................................. 143

5.2.3 Winding connection influence ............................................................................................... 151

5.2.4 Transformer core characteristic influence ............................................................................. 152

5.2.5 Network parameter influence ............................................................................................... 156

5.2.6 Simulation of AC & DC supply ................................................................................................ 158

5.3 CASE 2: SENSITIVITY OF TRANSFORMER CORE STRUCTURE ........................................................................... 165

5.3.1 Comparison between YNd connected three single-phase transformers bank and three-phase

three-limb transformer ................................................................................................................... 166

5.3.2 Comparison between YNy connected three single-phase transformers bank and three-phase

three-limb transformer ................................................................................................................... 169

5.3.3 Five-limb transformer ............................................................................................................ 171

5.4 SUMMARY ........................................................................................................................................ 179

Contents

5

CHAPTER 6 LOW FREQUENCY SWITCHING TRANSIENT MAGNETIC AND ELECTRICAL MODELLING . 181

6.1 INTRODUCTION .................................................................................................................................. 181

6.2 DISTRIBUTION NETWORK LAYOUT ........................................................................................................... 181

6.3 CASE 1: BLOOM STREET SUBSTATION CIRCUIT ........................................................................................... 183

6.3.1 Introduction of the circuit ...................................................................................................... 183

6.3.2 Recorded transformer de-energisation voltage and current data ......................................... 184

6.3.3 Simulation model ................................................................................................................... 191

6.3.4 Simulation results and analysis .............................................................................................. 193

6.3.5 Sensitivity study and mitigation ............................................................................................. 205

6.4 CASE 2: RED BANK SUBSTATION CIRCUIT .................................................................................................. 209

6.4.1 Introduction ........................................................................................................................... 209

6.4.2 Simulation and comparison ................................................................................................... 211

6.5 SUMMARY ......................................................................................................................................... 214

CHAPTER 7 CONCLUSION AND FURTHER WORK ............................................................................ 217

7.1 CONCLUSION ..................................................................................................................................... 217

7.1.1 General .................................................................................................................................. 217

7.1.2 Summary of results and main findings .................................................................................. 217

7.2 FURTHER WORK .................................................................................................................................. 220

REFERENCE ......................................................................................................................................... 222

APPENDIX .......................................................................................................................................... 227

1 Matlab Code ................................................................................................................................ 227

2 Impact of Area under GIC situation ............................................................................................. 234

3 Cable information ........................................................................................................................ 242

4 Publication ................................................................................................................................... 242

Word Count: 52,329

List of figures

6

LIST OF FIGURES FIGURE 1-1 INRUSH CURRENT AS A FUNCTION OF REMANENCE AND INSTANT OF SWITCHING-IN OF TRANSFORMER [6] .........23

FIGURE 1-2 BASIC FERRORESONANCE EQUIVALENT CIRCUIT ......................................................................................24

FIGURE 1-3 GEOMAGNETIC DISTURBANCE ............................................................................................................26

FIGURE 1-4 MAGNETISING CURRENT CHANGING BY GIC [22] ..................................................................................28

FIGURE 1-5 INDUCED VOLTAGE DRIVES GIC TO/FROM NEUTRAL GROUND POINTS OF POWER TRANSFORMERS [22] ............29

FIGURE 1-6 DC MODEL FOR CALCULATING GIC[20] ...............................................................................................29

FIGURE 2-1 AVERAGE MAGNETISING CURRENT FOR DIFFERENT WINDING CONNECTION ..................................................35

FIGURE 2-2 THREE-PHASE THREE-LIMB CORE TYPE TRANSFORMER .............................................................................37

FIGURE 2-3 THREE-PHASE FIVE-LIMB TRANSFORMER CORE ......................................................................................38

FIGURE 2-4 AVERAGE MAGNETISING CURRENT IN PER UNIT FOR DIFFERENT CORE STRUCTURE .........................................39

FIGURE 2-5 FERROMAGNETIC MATERIAL HYSTERESIS LOOP [30] ...............................................................................42

FIGURE 2-6 AVERAGE MAGNETISING CURRENT OF DIFFERENT INSTALLATION YEAR OF TRANSFORMERS AT 400/275/13 KV

AND 1000 MVA ...................................................................................................................................43

FIGURE 2-7 LOSSES AND MAGNETISING CURRENTS FROM YEAR TO YEAR .....................................................................44

FIGURE 3-1 ONTARIO HYDRO 230KV SYSTEM [41] ...............................................................................................51

FIGURE 3-2 MULTI-VOLTAGE TRANSMISSION CIRCUIT [47] ......................................................................................51

FIGURE 3-3 525 KV TRANSMISSION SYSTEM BETWEEN BIG EDDY AND JOHN DAY [13] .................................................52

FIGURE 3-4 SINGLE LINE DIAGRAM OF THE BRINSWORTH/THORPE MARSH CIRCUIT ARRANGEMENT [14] ..........................53

FIGURE 3-5 MAIN CIRCUIT COMPONENTS IN DORSEY CONVERTER STATION [16] .........................................................53

FIGURE 3-6 A SIMPLIFIED ONE LINE DIAGRAM IN WHICH THE RISER SURGE ARRESTER RISER POLE EXPLODED [48] ...............54

FIGURE 3-7 33KV CABLE-FED SERVICE TRANSFORMER FERRORESONANCE [17] ............................................................55

FIGURE 3-8 EQUIVALENT CIRCUIT OF THE TRANSFORMER WITH THE TRANSMISSION LINES [13] .......................................57

FIGURE 3-9 TRANSFORMER FLUX AND EXCITING CURRENT RESPONSE TO STEP DC VOLTAGE [68] ......................................68

FIGURE 3-10 SINGLE-PHASE TRANSFORMER MODEL [68] ........................................................................................70

FIGURE 3-11 THREE-PHASE FIVE-LIMB TRANSFORMER MODEL [68] ...........................................................................71

FIGURE 3-12 COMPLETE ELECTRICAL AND MAGNETIC EQUIVALENT CIRCUIT DIAGRAM FOR THREE-PHASE THREE-LIMB STAR-

AUTO TRANSFORMER WITH TERTIARY, Z0 PATH AND TANK SHUNT [70] ..............................................................71

FIGURE 3-13 FEA PLOT OF THE FLUX PATHS FOR THE TANK BASE AND RETURN LIMB OF A ONE-PHASE UNIT OF AN 800 MVA

GENERATOR TRANSFORMER AT THE POINT IN TIME OF PEAK MAGNETISING CURRENT AT 340 A/PHASE FOR A GIC OF 50

A/PHASE [70] .......................................................................................................................................73

FIGURE 3-14 FEA PLOT OF FLUX DENSITY THROUGH A CORE BOLT [70] ......................................................................73

FIGURE 3-15 EXCITING-CURRENT HARMONIC SEQUENCE COMPONENTS [68] ..............................................................76

FIGURE 3-16 THE RELATIONSHIP OF THE EXCITING CURRENT HARMONICS AND GIC FOR TRANSFORMERS WITH DIFFERENT CORE

DESIGN [74]..........................................................................................................................................77

FIGURE 3-17 GIC MITIGATION SCHEME INSIDE POWER TRANSFORMER [77]................................................................80

FIGURE 4-1 FLOW CHART OF CHAPTER 4’S WORK ...................................................................................................82

List of figures

7

FIGURE 4-2 EQUIVALENT MAGNETIC CIRCUIT OF THREE-PHASE THREE-LIMB TRANSFORMER ........................................... 83

FIGURE 4-3 THREE-LIMB TRANSFORMER MODEL WITH RETURN PATH ........................................................................ 84

FIGURE 4-4 EQUIVALENT MAGNETIC CIRCUIT OF THREE-PHASE THREE-LIMB TRANSFORMER WITH RETURN PATH ................ 85

FIGURE 4-5 EQUIVALENT MAGNETIC CIRCUIT OF THREE-PHASE FIVE-LIMB TRANSFORMER .............................................. 88

FIGURE 4-6 EQUIVALENT CIRCUITS WITH OPEN CIRCUIT TEST ....................................................................... 89

FIGURE 4-7 CURVE FITTING RESULT FOR JAPAN NIPPON STEEL CORPORATION MATERIALS .............................................. 91

FIGURE 4-8 FLOW CHART OF THE MATLAB PROGRAMME ...................................................................................... 92

FIGURE 4-9 MATERIAL NON-LINEAR CHARACTERISTICS ........................................................................................... 95

FIGURE 4-10 THREE-PHASE MAGNETISING CURRENTS OF DIFFERENT SUPPLIED VOLTAGE LEVEL ....................................... 96

FIGURE 4-11 FLUX DENSITY AND PERMEABILITY OF THE µ0µR BY VARYING MAGNETIC FIELD INTENSITY .............................. 99

FIGURE 4-12 THREE-PHASE FIVE-LIMB TRANSFORMER CORE MAGNETISING CURRENTS OF DIFFERENT SUPPLIED VOLTAGE LEVEL

........................................................................................................................................................ 101

FIGURE 4-13 CURRENT SEQUENCE COMPONENT CONTENT OF DIFFERENT SUPPLIED VOLTAGE LEVEL ............................... 102

FIGURE 4-14 FREQUENCY CONTENTS OF LINE MAGNETISING CURRENTS OF DIFFERENT SUPPLIED VOLTAGE LEVEL .............. 103

FIGURE 4-15 FLUX DENSITY IN 5-LIMB TRANSFORMER CORE .................................................................................. 104

FIGURE 4-16 FIELD INTENSITY IN 5-LIMB TRANSFORMER CORE ............................................................................... 104

FIGURE 4-17 COMPARISON OF MAGNETISING CURRENTS IN THREE-LIMB AND FIVE-LIMB TRANSFORMER ........................ 106

FIGURE 4-18 COMPARISON OF CURRENT SEQUENCE COMPONENT CONTENTS IN THREE-LIMB AND FIVE-LIMB CORE

TRANSFORMERS ................................................................................................................................... 107

FIGURE 4-19 COMPARISON OF FREQUENCY CONTENTS OF MAGNETISING CURRENTS IN THREE-LIMB AND FIVE-LIMB

TRANSFORMERS ................................................................................................................................... 107

FIGURE 4-20 FLUX DENSITY AND FIELD INTENSITY IN THREE-LIMB TRANSFORMER ....................................................... 108

FIGURE 4-21 FLUX DENSITY AND FIELD INTENSITY IN FIVE-LIMB TRANSFORMER .......................................................... 109

FIGURE 4-22 COMPARISON OF MAGNETISING CURRENTS IN THREE-LIMB AND FIVE-LIMB TRANSFORMERS AT 100% RATED

VOLTAGE ............................................................................................................................................ 110

FIGURE 4-23 COMPARISON SEQUENCE CONTENTS OF MAGNETISING CURRENTS TWO DIFFERENT CORE STRUCTURES ......... 110

FIGURE 4-24 COMPARISON FREQUENCY CONTENTS OF LINE MAGNETISING CURRENTS AT 100% RATED VOLTAGE............. 111

FIGURE 4-25 FLUX DENSITY AND FIELD INTENSITY IN THREE-LIMB TRANSFORMER AT 100% RATED VOLTAGE ................... 112

FIGURE 4-26 FLUX DENSITY AND FIELD INTENSITY IN FIVE-LIMB TRANSFORMER AT 100% RATED VOLTAGE ...................... 112

FIGURE 4-27 COMPARISON OF MAGNETISING CURRENTS IN 3 & 5-LIMB TRANSFORMERS AT NON-LINEAR REGION ........... 113

FIGURE 4-28 COMPARISON OF CURRENT SEQUENCE CONTENTS IN 3&5 LIMB TRANSFORMER AT NONLINEAR REGION ....... 113

FIGURE 4-29 COMPARISON OF FREQUENCY CONTENTS OF THREE-LIMB AND FIVE-LIMB TRANSFORMERS MAGNETISING

CURRENTS AT NONLINEAR REGION ........................................................................................................... 114

FIGURE 4-30 FLUX DENSITY AND FIELD INTENSITY IN THREE-LIMB TRANSFORMER AT NONLINEAR REGION ........................ 115

FIGURE 4-31 FLUX DENSITY AND FIELD INTENSITY IN FIVE-LIMB TRANSFORMER AT NONLINEAR REGION .......................... 116

FIGURE 4-32 FLUX DISTRIBUTION IN FIVE-LIMB TRANSFORMER AT LINEAR REGION ..................................................... 117

FIGURE 4-33 FREQUENCY CONTENTS OF FLUX DENSITIES IN FIVE-LIMB TRANSFORMER AT LINEAR REGION ....................... 118

FIGURE 4-34 FLUX DISTRIBUTION IN DIFFERENT PARTS OF FIVE-LIMB TRANSFORMER AT KNEE REGION ............................ 119

List of figures

8

FIGURE 4-35 FREQUENCY CONTENTS OF FLUX DENSITIES IN FIVE-LIMB TRANSFORMER AT KNEE REGION ......................... 119

FIGURE 4-36 SIDE YOKE FLUX DENSITIES WAVEFORMS BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY .................. 120

FIGURE 4-37 FREQUENCY CONTENTS OF FLUX DENSITIES IN SIDE YOKE BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY

........................................................................................................................................................ 121

FIGURE 4-38 PHASE ANGLE CONTENTS OF FLUX DENSITIES IN SIDE YOKE BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY

........................................................................................................................................................ 122

FIGURE 4-39 MAIN YOKE FLUX DENSITIES WAVEFORMS BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY ................ 122

FIGURE 4-40 FREQUENCY CONTENTS OF FLUX DENSITIES IN MAIN YOKE BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY

........................................................................................................................................................ 123

FIGURE 4-41 PHASE ANGLE CONTENTS OF FLUX DENSITIES IN MAIN YOKE BY VARYING THE MAXIMUM MAIN LIMB FLUX DENSITY

........................................................................................................................................................ 124

FIGURE 4-42 SIDE YOKE FLUX DENSITIES WAVEFORMS AT DIFFERENT AREA RATIOS AT THE SUPPLYING MAXIMUM FLUX DENSITY

OF 1.1 T ............................................................................................................................................ 126

FIGURE 4-43 MAIN YOKE FLUX DENSITIES WAVEFORMS AT DIFFERENT AREA RATIOS AT THE SUPPLYING MAXIMUM FLUX

DENSITY OF 1.1 T ................................................................................................................................ 126


OF 1.54 T .......................................................................................................................................... 127


DENSITY OF 1.54 T .............................................................................................................................. 127

FIGURE 4-46 FREQUENCY CONTENTS OF FLUX DENSITIES IN SIDE YOKE BY VARYING RATIO OF CROSS-SECTION AT KNEE REGION

........................................................................................................................................................ 128

FIGURE 4-47 FREQUENCY CONTENTS OF FLUX DENSITIES IN MAIN YOKE BY VARYING RATIO OF CROSS-SECTION AT KNEE REGION

........................................................................................................................................................ 128


OF 1.9 T ............................................................................................................................................ 129


DENSITY OF 1.9 T ................................................................................................................................ 129

FIGURE 4-50 FREQUENCY CONTENTS OF FLUX DENSITIES IN SIDE YOKE BY VARYING RATIO OF CROSS-SECTION AT NONLINEAR

REGION ............................................................................................................................................. 130

FIGURE 4-51 FREQUENCY CONTENTS OF FLUX DENSITIES IN MAIN YOKE BY VARYING RATIO OF CROSS-SECTION AT NONLINEAR

REGION ............................................................................................................................................. 130

FIGURE 4-52 LINE MAGNETISING CURRENTS IN THREE-LIMB TRANSFORMER AT LINEAR REGION BY VARYING DC SUPPLY LEVEL

........................................................................................................................................................ 132

FIGURE 4-53 PHASE MAGNETISING CURRENTS IN THREE-LIMB TRANSFORMER AT LINEAR REGION BY VARYING THE DC SUPPLY

LEVEL ................................................................................................................................................ 132

FIGURE 4-54 FLUX DENSITIES DISTRIBUTIONS IN THREE-LIMB TRANSFORMER AT LINEAR REGION BY VARYING THE DC SUPPLY

LEVEL ................................................................................................................................................ 133

List of figures

9

FIGURE 4-55 FIELD INTENSITIES DISTRIBUTIONS IN THREE-LIMB TRANSFORMER AT LINEAR REGION BY VARYING THE DC SUPPLY

LEVEL ................................................................................................................................................ 133

FIGURE 4-56 PHASE MAGNETISING CURRENTS IN THREE-LIMB TRANSFORMER (NO DC, 0.1 WB) ................................. 134

FIGURE 4-57 PHASE MAGNETISING CURRENTS IN THREE-LIMB TRANSFORMER (0.15 WB, 0.2 WB) .............................. 135

FIGURE 4-58 FLUX DENSITY DISTRIBUTIONS IN THREE-LIMB TRANSFORMER BY VARYING THE DC SUPPLY LEVEL ................ 135

FIGURE 4-59 FIELD INTENSITY DISTRIBUTIONS IN THREE-LIMB TRANSFORMER BY VARYING THE DC SUPPLY LEVEL ............. 136

FIGURE 4-60 FLUX DENSITY DISTRIBUTION IN THE THREE-LIMB TRANSFORMER .......................................................... 137

FIGURE 4-61 FIELD INTENSITY DISTRIBUTION IN THE THREE-LIMB TRANSFORMER ....................................................... 137

FIGURE 5-1 CORE Λ-I CURVE FROM THE THREE-PHASE TRANSFORMER ..................................................................... 142

FIGURE 5-2 SINGLE PHASE TRANSFORMER MODEL ............................................................................................... 143

FIGURE 5-3 SINGLE PHASE TRANSFORMER SIMULATION MODEL IN ATP ................................................................... 144

FIGURE 5-4 THREE SINGLE-PHASE TRANSFORMER BANK SIMULATION MODEL IN ATP .................................................. 144

FIGURE 5-5 (A) PRIMARY SIDE CURRENT AND FLUX UNDER DC EXCITATION-FULL WAVEFORMS ..................................... 145

FIGURE 5-6 EQUIVALENT CIRCUIT OF THE SIMULATION MODEL ............................................................................... 146

FIGURE 5-7 SIMPLIFIED EQUIVALENT CIRCUIT AT STEP-RESPONSE STAGE IN YND CONNECTION ...................................... 146

FIGURE 5-8 TIME CONSTANT AND THE FINAL VALUE OF THE STEP RESPONSE CURRENT ................................................. 147

FIGURE 5-9 PRIMARY CURRENT AND CORE CURRENT AT THE PSEUDO-FLAT STAGE ...................................................... 148

FIGURE 5-10 FINAL STABLE VALUE OF THE PRIMARY CURRENT ................................................................................ 149

FIGURE 5-11 CORE FLUX AND PRIMARY CURRENT ................................................................................................ 150

FIGURE 5-12 SIMPLIFIED THREE SINGLE-PHASE TRANSFORMERS MODEL IN ATPDRAW ................................................ 151

FIGURE 5-13 CORE FLUX AND PRIMARY CURRENT IN THE SIMULATION FOR YNY THREE SINGLE-PHASE TRANSFORMERS BANK

........................................................................................................................................................ 151

FIGURE 5-14 SIMPLIFIED EQUIVALENT CIRCUIT AT STEP-RESPONSE STAGE FOR YNY CONNECTION .................................. 152

FIGURE 5-15 Λ-I CURVES (A): THREE CURVES IN ONE FIGURE (B): KNEE AREAS OF THREE CURVES .................................. 153

FIGURE 5-16 SIMULATION RESULTS FOR MODELS WITH DIFFERENT CORE CURVES ....................................................... 154

FIGURE 5-17 THREE CURVES FOR UPWARD AND DOWNWARD SHIFTING ................................................................... 155

FIGURE 5-18 SIMULATION RESULTS FOR MODELS WITH DIFFERENT CORE CURVES (A): PRIMARY CURRENT (B): FLUX ......... 155

FIGURE 5-19 A SYSTEM RESISTANCE ADDED IN CIRCUIT WITH TRANSFORMER MODEL .................................................. 156

FIGURE 5-20 A SYSTEM INDUCTANCE ADDED IN CIRCUIT WITH TRANSFORMER MODEL ................................................ 157

FIGURE 5-21 IMPACTS OF THE SHUNT CAPACITANCE ............................................................................................ 158

FIGURE 5-22 THREE SINGLE-PHASE TRANSFORMERS BANK IN YND CONNECTION ....................................................... 159

FIGURE 5-23 SIMULATION RESULTS FOR PHASE A (A): PRIMARY CURRENT (B): STEP-RESPONSE OF PRIMARY CURRENT (C):

MAGNETISING CURRENT (D): CURRENT REFERRED FROM SECONDARY WINDING ............................................... 160

FIGURE 5-24 SATURATED PART OF PRIMARY CURRENT, MAGNETISING CURRENT AND SECONDARY DELTA CONNECTED WINDING

CURRENT REFERRED TO PRIMARY SIDE ...................................................................................................... 160

FIGURE 5-25 YNY SINGLE PHASE TRANSFORMER BANK UNDER NO LOAD CONDITION................................................... 163

FIGURE 5-26 SIMULATION RESULTS FOR PHASE A (A): PRIMARY CURRENT (B): MAGNETISING CURRENT (C): STARTING

MOMENT (D): SATURATION MOMENT ...................................................................................................... 164

List of figures

10

FIGURE 5-27 COMPARISON BETWEEN YND CONNECTED 3 SINGLE PHASE TRANSFORMERS BANK AND THREE-PHASE THREE-

LIMB TRANSFORMER ............................................................................................................................ 166

FIGURE 5-28 ZERO SEQUENCE EFFECTS ON THE NO LOAD PRIMARY CURRENT OF THE YND THREE-LIMB TRANSFORMER (A)

INFINITY ZERO SEQUENCE IMPEDANCE (B) DEFAULT ZERO SEQUENCE IMPEDANCE.............................................. 168

FIGURE 5-29 COMPARISON BETWEEN YNY CONNECTED 3 SINGLE PHASE TRANSFORMERS BANK AND THREE-PHASE THREE-LIMB

TRANSFORMER .................................................................................................................................... 169

FIGURE 5-30 ZERO SEQUENCE EFFECTS ON THE NO LOAD PRIMARY CURRENT OF THE YNY THREE-PHASE THREE-LIMB

TRANSFORMER (A) INFINITY ZERO SEQUENCE IMPEDANCE (B) ZERO SEQUENCE IMPEDANCE BETWEEN INFINITY AND

DEFAULT VALUE (C) DEFAULT ZERO SEQUENCE IMPEDANCE .......................................................................... 170

FIGURE 5-31 PRIMARY SIDE CURRENT WITH AC AND DC SUPPLY ........................................................................... 172

FIGURE 5-32 PRIMARY SIDE CURRENT WITH PURE DC SUPPLY ONLY ........................................................................ 172

FIGURE 5-33 PRIMARY SIDE CURRENT OF YYD, YND AND YNY CONNECTION TRANSFORMER ........................................ 175

FIGURE 5-34 PRIMARY SIDE CURRENT WAVEFORM WITH MAIN-SIDE YOKE AREA RATIO MODIFIED ................................. 177

FIGURE 5-35 SIDE YOKE AND MAIN LIMB Λ-I CURVES WITH DIFFERENT MAIN-SIDE YOKE AREA RATIO ............................. 177

FIGURE 6-1 TYPICAL UK DISTRIBUTION NETWORK DIAGRAM ................................................................................. 182

FIGURE 6-2 SOUTH MANCHESTER SUBSTATION (SMS) AND BLOOM STREET SUBSTATION (BSS) LAYOUT ...................... 183

FIGURE 6-3 SINGLE LINE DIAGRAM OF THE CIRCUIT .............................................................................................. 184

FIGURE 6-4 LINE VOLTAGES AT TRANSFORMER 33 KV TERMINALS .......................................................................... 185

FIGURE 6-5 LINE CURRENTS AT TRANSFORMER 132 KV TERMINALS ........................................................................ 186

FIGURE 6-6 LINE VOLTAGES AT TRANSFORMER 33 KV TERMINALS – ZOOMED WAVEFORMS FOR 40 MS ......................... 187

FIGURE 6-7 CURRENTS AT TRANSFORMER 132KV TERMINALS – ZOOMED WAVEFORMS FOR 40 MS .............................. 188

FIGURE 6-8 VOLTAGES/CURRENTS OF THE TRANSFORMER NEAR TO THE INITIATION OF FERRORESONANCE ...................... 188

FIGURE 6-9 VOLTAGES/INTEGRATED FLUXES OF THE TRANSFORMER ....................................................................... 189

FIGURE 6-10 VOLTAGES/CURRENTS OF THE TRANSFORMER PLOTTED IN THE SAME GRAPH .......................................... 190

FIGURE 6-11 VOLTAGES/INTEGRATED FLUXES OF THE TRANSFORMER PLOTTED IN THE SAME GRAPH ............................. 191

FIGURE 6-12 132/33 KV NETWORK SIMULATION MODEL IN ATPDRAW ................................................................. 192

FIGURE 6-13 SIMULATION RESULTS OF SECONDARY SIDE LINE VOLTAGES ................................................................. 193

FIGURE 6-14 SIMULATION RESULTS OF PRIMARY SIDE LINE CURRENTS ..................................................................... 194

FIGURE 6-15 SIMULATION RESULTS OF VOLTAGES/CURRENTS NEAR TO THE INITIATION OF FERRORESONANCE ................. 194

FIGURE 6-16 MODEL OF SOURCE AND CIRCUIT BREAKER....................................................................................... 196

FIGURE 6-17 CABLE MODEL VIEWS .................................................................................................................. 197

FIGURE 6-18 EQUIVALENT CIRCUIT OF THREE-LIMB CORE ..................................................................................... 198

FIGURE 6-19 SIX ZONES WITHIN ONE CYCLE ....................................................................................................... 199

FIGURE 6-20 SWITCHING AT POSITIVE ZONES ..................................................................................................... 199

FIGURE 6-21 SWITCHING AT NEGATIVE ZONES .................................................................................................... 200

FIGURE 6-22 Λ-I CURVE BEFORE AND AFTER MODIFICATION .................................................................................. 203

List of figures

11

FIGURE 6-23 RESULTS COMPARISON: (A) RECORDED TEST DATA FOR THE VOLTAGE AND CURRENT WAVEFORM (A) FOR THE

VOLTAGE AND CURRENT WAVEFORM BEFORE MODIFIED, (B) FOR THE VOLTAGE AND CURRENT WAVEFORM AFTER

MODIFIED ........................................................................................................................................... 204

FIGURE 6-24 SIMULATION RESULTS: (A) SECONDARY SIDE VOLTAGE; (B) PRIMARY SIDE CURRENT .................................. 206

FIGURE 6-25 SIMULATION RESULTS BY VARYING THE CABLE LENGTH ........................................................................ 207

FIGURE 6-26 ADDING A SECOND CIRCUIT BREAKER FOR DISTRIBUTION NETWORK ....................................................... 207

FIGURE 6-27 SIMULATION RESULTS: (A) THREE-PHASE CABLE VOLTAGES; (B) THREE-PHASE SECONDARY SIDE LINE VOLTAGES; (C)

THREE-PHASE CIRCUIT BREAKER CURRENTS; (D) THREE-PHASE PRIMARY SIDE CURRENTS ..................................... 208

FIGURE 6-28 ADDING PARALLEL RESISTOR FOR DISTRIBUTION NETWORK .................................................................. 209

FIGURE 6-29 SIMULATION RESULTS: (A) THREE-PHASE LINE VOLTAGES AT SECONDARY SIDE; (B) PRIMARY SIDE CURRENTS .. 209

FIGURE 6-30 WHITEGATE SUBSTATION AND RED BANK SUBSTATION LAYOUT ........................................................... 210

FIGURE 6-31 COMPARISON OF SINGLE LINE DIAGRAM OF THE BLOOM STREET AND RED BANK CIRCUIT .......................... 210

FIGURE 6-32 ATP SIMULATION MODEL OF RED BANK CIRCUIT ............................................................................... 211

FIGURE 6-33 COMPARISON OF TWO TRANSFORMERS’ DATA .................................................................................. 212

FIGURE 6-34 COMPARISON OF THE DATA OF TWO CABLES ..................................................................................... 212

FIGURE 6-35 SIMULATION RESULTS OF RED BANK (A) SECONDARY SIDE LINE VOLTAGES (B) PRIMARY SIDE CURRENTS ........ 213

FIGURE 6-36 SIMULATION RESULTS BY VARYING THE CABLE LENGTH ........................................................................ 214

FIGURE 1 SIDE YOKE MAGNETIC FLUX DENSITY AT 70% SUPPLIED AC VOLTAGE AND 0.1WB DC ................................... 234

FIGURE 2 MAIN YOKE MAGNETIC FLUX DENSITY AT 70% SUPPLIED AC VOLTAGE AND 0.1WB DC ................................. 235

FIGURE 3 MAXIMUM VALUE OF EACH HARMONIC IN THE SIDE YOKE ......................................................................... 235

FIGURE 4 MAXIMUM VALUE OF EACH HARMONIC IN THE MAIN YOKE ....................................................................... 236

FIGURE 5 SIDE YOKE MAGNETIC FLUX DENSITY AT RATED SUPPLIED AC VOLTAGE AND 0.1WB DC ................................. 237

FIGURE 6 MAIN YOKE MAGNETIC FLUX DENSITY AT RATED SUPPLIED AC VOLTAGE AND 0.1WB DC ............................... 237

FIGURE 7 MAXIMUM VALUE OF EACH HARMONIC IN THE SIDE YOKE ......................................................................... 238

FIGURE 8 MAXIMUM VALUE OF EACH HARMONIC IN THE MAIN YOKE ....................................................................... 238

FIGURE 9 SIDE YOKE MAGNETIC FLUX DENSITY AT 110% SUPPLIED AC VOLTAGE AND 0.1WB DC ................................. 239

FIGURE 10 SIDE YOKE MAGNETIC FLUX DENSITY AT 110% SUPPLIED AC VOLTAGE AND 0.1WB DC ............................... 240

FIGURE 11 MAXIMUM VALUE OF EACH HARMONIC IN THE SIDE YOKE ....................................................................... 240

FIGURE 12 MAXIMUM VALUE OF EACH HARMONIC IN THE MAIN YOKE ..................................................................... 240

List of tables

12

LIST OF TABLES TABLE 1-1 INRUSH EXPERIENCES .........................................................................................................................23

TABLE 1-2 FERRORESONANCE EXPERIENCES[19] ....................................................................................................25

TABLE 2-1 HISTORICAL DEVELOPMENT OF THE CORE STEELS [4] ................................................................................41

TABLE 3-1 CAUSE OF SYSTEM TRANSIENTS AND FREQUENCY RANGES [1] ....................................................................45

TABLE 3-2 DISSOLVED GAS ANALYSIS OF THE TRANSFORMER [13] .............................................................................56

TABLE 3-3 GIC EVENTS REPORTED IN THE WORLDWIDE ...........................................................................................65

TABLE 3-4 GIC EVENTS REPORTED IN UK .............................................................................................................66

TABLE 3-5 LOSSES AND TEMPERATURE RISES FOR ONE PHASE OF AN 800-MVA GENERATOR TRANSFORMER WITH A GIC OF

50 A/PHASE AND A 240 MVA THREE-PHASE FIVE-LIMB AUTO TRANSFORMER WITH A GIC OF 100 A/PHASE, BOTH FOR

DURATION OF 30 MIN, AND FOR THE CONDITION OF NO LOAD. SHUNTS FOR THE FIVE-LIMB AUTO ARE ASSUMED TO BE

WRAPPED IN 2 MM THICK PRESSBOARD [70] ...............................................................................................74

TABLE 3-6 ASSESSMENT OF ACCEPTABLE GIC CURRENT LEVELS AND RISK FOR DURATION FROM 15 TO 30 MIN ..................74

TABLE 3-7 ADVANTAGES AND LIMITATIONS OF MITIGATION DEVICES ..........................................................................79

TABLE 4-1 132/33 KV DIMENSIONS DATA ...........................................................................................................94

TABLE 4-2 COMPARISON THE RMS MAGNETISING CURRENTS IN FIELD TEST DATA AND SIMULATION RESULTS .....................97

TABLE 4-3 PHASE ANGLE CALCULATED FOR MAGNETISING CURRENTS FOR THREE PHASES ...............................................98

TABLE 4-4 400/275/13 KV FIVE-LIMB TRANSFORMER DATA ...................................................................................99

TABLE 4-5 PHASE ANGLE FOR EACH MAGNETISING CURRENT IN EACH PHASE ............................................................. 101

TABLE 4-6 COMPARISON THE RMS MAGNETISING CURRENT IN SIMULATION RESULTS AND FIELD TEST DATA ................... 101

TABLE 4-7 RMS VALUE OF PHASE CURRENT ....................................................................................................... 102

TABLE 4-8 ARTIFICIAL FIVE-LIMB TRANSFORMER DATA BASED ON 132/33 KV DIMENSIONS DATA ................................ 105

TABLE 4-9 MAXIMUM FLUX DENSITY IN SIDE YOKE AND MAIN YOKE ........................................................................ 118

TABLE 4-10 MAXIMUM FLUX DENSITY IN SIDE YOKE AND MAIN YOKE ...................................................................... 120

TABLE 4-11 MAXIMUM FLUX DENSITY AT FUNDAMENTAL AND THIRD HARMONIC FREQUENCY IN SIDE YOKE .................... 121

TABLE 4-12 MAXIMUM FLUX DENSITY AT FUNDAMENTAL AND THIRD HARMONIC FREQUENCY IN MAIN YOKE .................. 123

TABLE 4-13 RATIO VARIATIONS OF THE CROSS SECTION ........................................................................................ 125

TABLE 4-14 MAXIMUM MAGNITUDE OF FLUX DENSITY......................................................................................... 126

TABLE 4-15 PEAK VALUES OF THE PHASE CURRENTS FOR DIFFERENT CASES ............................................................... 136

TABLE 5-1 132/33 KV TRANSFORMER TEST REPORT DATA ................................................................................... 141

TABLE 5-2 SYMBOL EXPLANATIONS FOR THE CALCULATION OF TRANSFORMER PARAMETERS ........................................ 142

TABLE 5-3 VALUES OF TRANSFORMER MODEL PARAMETERS .................................................................................. 142

TABLE 5-4 IMPACTS OF SYSTEM RESISTANCES ON TRANSFORMER PERFORMANCE UNDER GIC OR DC BIAS ...................... 156

TABLE 5-5 IMPACTS OF SYSTEM INDUCTANCES ON TRANSFORMER PERFORMANCE UNDER GIC OR DC BIAS .................... 157

TABLE 5-6 RELATIONSHIP BETWEEN THE SUPPLIED DC LEVEL AND THE FINAL PEAK CURRENT VALUE .............................. 161

TABLE 5-7 LOAD EFFECTS ON GIC PERFORMANCE OF THE YND SINGLE PHASE TRANSFORMER BANKS ............................. 162

TABLE 5-8 RELATIONSHIP BETWEEN THE SUPPLIED DC LEVEL AND THE FINAL PEAK CURRENT VALUE .............................. 164

List of tables

13

TABLE 5-9 LOAD EFFECTS FOR THE YNY SINGLE PHASE TRANSFORMERS BANK ............................................................ 165

TABLE 5-10 COMPARISON BETWEEN YND CONNECTED TRANSFORMERS BANK AND THREE-PHASE THREE-LIMB TRANSFORMER

........................................................................................................................................................ 167

TABLE 5-11 COMPARISON BETWEEN YND CONNECTED TRANSFORMERS BANK AND THREE-PHASE THREE-LIMB TRANSFORMER

........................................................................................................................................................ 170

TABLE 5-12 BASIC INFORMATION AND TEST DATA OF THE THREE-PHASE FIVE-LIMB TRANSFORMER ................................ 171

TABLE 5-13 KEY PARAMETERS OF THE PRIMARY SIDE CURRENT WITH PURE DC VOLTAGE SUPPLY ................................... 173

TABLE 5-14 KEY PARAMETERS OF THE PRIMARY SIDE CURRENT WITH AC&DC VOLTAGE SUPPLIED ................................ 174

TABLE 5-15 SIMULATION RESULTS FOR THE PRIMARY SIDE CURRENT IN ALL FOUR TYPE OF CONNECTION ......................... 175

TABLE 5-16 SIMULATION RESULTS FOR MAIN-SIDE YOKE AREA RATIO MODIFIED ........................................................ 176

TABLE 5-17 SIMULATION RESULTS FOR THE KEY PARAMETERS BY VARYING SYSTEM R .................................................. 178

TABLE 5-18 SIMULATION RESULTS FOR THE KEY PARAMETERS BY VARYING SYSTEM L .................................................. 179

TABLE 6-1 132KV THREE-PHASE FAULT LEVEL INFORMATION IN SOUTH MANCHESTER SUBSTATION .............................. 195

TABLE 6-2 RESISTIVITY OF CONDUCTIVE MATERIALS USED IN CABLES ........................................................................ 196

TABLE 6-3 RELATIVE PERMITTIVITY OF INSULATING MATERIALS USED IN CABLES ......................................................... 196

TABLE 6-4 DIMENSION OF SINGLE CORE CABLE .................................................................................................... 197

TABLE 6-5 INPUT DATA OF THE 132KV CABLE ..................................................................................................... 197

TABLE 6-6 RELATIONSHIP BETWEEN RESISTANCE VALUE AND TIME CONSTANT ........................................................... 201

TABLE 6-7 RELATIONSHIP BETWEEN CHOPPING CURRENT VALUE AND FIRST PEAK VOLTAGE .......................................... 202

TABLE 6-8 132 KV THREE-PHASE FAULT LEVEL COMPARISON BETWEEN BLOOM STREET CASE AND RED BANK CASE .......... 211

TABLE 1 MAXIMUM MAGNITUDE IN 50HZ OF FLUX DENSITY .................................................................................. 236

TABLE 2 MAXIMUM MAGNITUDE IN DC FLUX DENSITY .......................................................................................... 236





List of symbol

14

LIST OF SYMBOL Symbol Explanation Unit

µ permeability of materials H/m

Al cross-section area of limb m2

Am cross-section area of main yoke m2

As cross-section area of side yoke m2

At cross-section area of transformer tank m2

B magnetic flux density T

Bab flux density at yoke AB T

Bbc flux density at yoke BC T

Beff flux density RMS value of applied voltage T

Bls flux density at left side yoke T

Bmax maximum flux density in transformer core T

Brs flux density at right side yoke T

C capacitance F

Cseries circuit breaker grading capacitance or phase-to-phase

capacitance of lines F

Cshunt total phase-to-earth capacitance of circuit F

f frequency of system Hz

H magnetic field intensity A/m

Hab field intensity at yoke AB A/m

Hbc field intensity at yoke BC A/m

Hls field intensity at left side yoke A/m

Hrs field intensity at right side yoke A/m

Iab line A to line B current A

Ibc line B to line C current A

Ica line C to line A current A

IRMS RMS value of current A

Is short circuit test current A

K0 dc voltage level V

L inductance H

L1 effective length of limb m

Lm effective length of main yoke m

List of symbol

15

Lp total inductance in the primary circuit m

Lp.w winding inductance per phase on primary side H

Ls effective length of side yoke m

Ls.w winding inductance per phase on secondary side H

Msat inductance of the magnetising circuit in saturation H

Po 100% voltage open circuit test losses W

PS short circuit test losses VA

RAB reluctance at main yoke AB A/Wb

RBC reluctance at main yoke BC A/Wb

RC core resistance per phase Ω

Rls reluctance at left side yoke A/Wb

Rlt reluctance at left side tank A/Wb

RN grounding resistance Ω

ROA reluctance at limb A A/Wb

ROB reluctance at limb B A/Wb

ROC reluctance at limb C A/Wb

Rp total resistance in the primary circuit m

Rp.w winding resistance per phase on primary side Ω

Rrs reluctance at right side yoke A/Wb

Rrt reluctance at right side tank A/Wb

Rs.w winding resistance per phase on secondary side Ω

Sb power base VA

τ the thickness of material mm

V0 peak phase-ground operation voltage V

Vab line A to line B voltage V

Vbc line B to line C voltage V

Vca line C to line A voltage V

Vg peak phase-ground voltage when transformers operate at knee

area V

VH primary side voltage V

Xc core inductance H

Xp.w winding reactance per phase on primary side Ω

Xs.w winding reactance per phase on secondary side Ω

List of symbol

16

Zb impedance base on primary side Ω

λ0 DC flux linkage level Wb

λs saturation flux linkage level Wb

ρ resistivity of material Ω∙m

ω natural frequency, related to frequency ƒ by ω = 2 π ƒ Hz

ФA phase A flux Wb

ФAB yoke AB flux Wb

ФB phase B flux Wb

ФBC yoke BC flux Wb

ФC phase C flux Wb

Фls left side yoke flux Wb

Фlt left side tank flux Wb

Фm flux peak value in the main-limb of core Wb

Фrs right side yoke flux Wb

Фrt right side tank flux Wb

http://en.wikipedia.org/wiki/Frequency

Abstract

17

ABSTRACT Power transformers are a key element in the transmission and distribution of electrical

energy and as such need to be highly reliable and efficient. In power system networks,

transformer core saturation can cause system voltage disturbances or transformer

damage or accelerate insulation ageing. Low frequency switching transients such as

ferroresonance and inrush currents, and increasingly what is now known as geomagnetic

induce currents (GIC), are the most common phenomena to cause transformer core

saturation.

This thesis describes extensive simulation studies carried out on GIC and switching

ferroresonant transient phenomena. Two types of transformer model were developed to

study core saturation problems; one is the mathematical transformer magnetic circuit

model, and the other the ATPDraw transformer model.

Using the mathematical transformer magnetic circuit model, the influence of the

transformer core structure on the magnetising current has been successfully identified

and so have the transformers' responses to GIC events. By using the ATPDraw

transformer model, the AC system network behaviours under the influence of the DC

bias caused by GIC events have been successfully analysed using various simulation

case studies. The effects of the winding connection, the core structure, and the network

parameters including system impedances and transformer loading conditions on the

magnetising currents of the transformers are summarised.

Transient interaction among transformers and other system components during

energisation and de-energisation operations are becoming increasingly important. One

case study on switching ferroresonant transients was modelled using the available

transformer test report data and the design data of the main components of the

distribution network. The results were closely matched with field test results, which

verified the simulation methodology.

The simulation results helped establish the fundamental understanding of GIC and

ferroresonance events in the power networks; among all the influential parameters

identified, transformer core structure is the most important one. In summary, the five-

limb core is easier to saturate than the three-limb transformer under the same GIC

events; the smaller the side yoke area of the five-limb core, the easier it will be to

saturate. More importantly, under GIC events a transformer core could become

saturated irrespective of the loading condition of the transformer.

Declaration

18

DECLARATION

I declare that no portion of the work referred to in the thesis has been submitted in

support of an application for another degree or qualification of this or any other

university or other institute of learning.

Copyright statement

19

COPYRIGHT STATEMENT

(i). The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and s/he has given The

University of Manchester certain rights to use such Copyright, including for

administrative purposes.

(ii). Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents Act

1988 (as amended) and regulations issued under it or, where appropriate, in accordance

with licensing agreements which the University has from time to time. This page must

form part of any such copies made.

(iii). The ownership of certain Copyright, patents, designs, trade marks and other

intellectual property (the “Intellectual Property”) and any reproductions of copyright

works in the thesis, for example graphs and tables (“Reproductions”), which may be

described in this thesis, may not be owned by the author and may be owned by third

parties. Such Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of the relevant

Intellectual Property and/or Reproductions.

(iv). Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-

property.pdf), in any relevant Thesis restriction declarations deposited in the University

Library, The University Library’s regulations (see

http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s

policy on presentation of Theses.

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-property.pdf

http://www.campus.manchester.ac.uk/medialibrary/policies/intellectual-property.pdf

http://www.manchester.ac.uk/library/aboutus/regulations

Acknowledgement

20

ACKNOWLEDGEMENT

Completing my PhD degree is probably the most challenging activity of my first 27

years of my life. The best and worst moments of my doctoral journey have been shared

with many people. It has been a great treasure to spend several years in the School of

Electrical and Electronic Engineering at the University of Manchester, and the

University and its members will always remain dear to me.

My first sincere gratitude must go to my supervisor Dr Haiyu Li and advisor Professor

Zhongdong Wang. They patiently provided the vision, the encouragement and advice

necessary for me to proceed through the doctoral program and to complete my thesis. I

wish to particularly thank Professor Wang for her encouragement; she has been a strong

and supportive adviser to me throughout my PhD research, she has also given me great

freedom to pursue independent work. She serves as a role model to me.

I am greatly indebted to Electricity North West Ltd and the University of Manchester

for the financial sponsorship of my PhD research, out of which a full scholarship was

provided.

I would also like to thank Dr. Keith Cornick, Mr. Alan Darwin, Mr. Paul Jarman, Mr.

Darren Jones and Mr. Tony Byrne for their technical support throughout the project.

To all my colleagues in the transformer research group and others in Ferranti building

of the School of Electrical and Electronic Engineering, I appreciate your company and

thank you for providing an enjoyable working environment. Special thanks to my senior

colleague, Dr. Ang Swee Peng, for his support, guidance and suggestions; I owe him

my heartfelt appreciation.

I wish to thank my parents and all my family. Their love provided me the inspiration

and the driving force. I owe them everything and wish I could show them just how

much I love and appreciate them.

Finally, I would like to dedicate this work to my paternal grandparents who left us

without being able to see my PhD graduation. I hope that this work makes them proud.

Chapter 1 Introduction

21


1.1 Introduction

Power transformers are a key element in the transmission and distribution of electrical

energy and as such need to be highly reliable and extremely efficient. In addition to

these requirements are the evolving needs for operation at even higher voltages and

powers, that is, operation up to 1100 kV a.c. and higher, power ratings above 1000

MVA. Over the past few decades, the most important advance in transformer

technology has been the improvement of core steel materials and the reduced core

losses. The associated feature is that characteristic of the core steel material has also

rapidly changed such that the B-H loops are now sharper in the knee area.

These advances, while greatly solving the higher efficiency requirement, however,

brought about, and/or, exacerbated, core saturation problems such as ferroresonance and

geomagnetic induce current (GIC) problems.

It must also be recognised in this context that changes in the design and layout of power

systems and their operation, have also contributed to the transformer problems and will

not be overlooked, for the core saturation problem also depends upon system switching

and operating conditions. It is a problem of the interaction between the transformer and

the system.

The power transformers which will be addressed in this thesis are those that connect

generation to transmission, sub-transmission and distribution systems, and that have

powers from a few MVA to 1000 MVA, and voltages from 11 kV to 400 kV.

1.2 Transformer core saturation problems

Core saturation manifested itself as the phenomena such as inrush current,

ferroresonance and geomagnetic induce current (GIC), which are transient in nature as

compared with steady-state situation for power system operation.

Transient voltages in an electrical system network are normally caused by the opening

and closing of the circuit breakers for normal energisation and de-energisation actions,


22

and for clearing faults caused by short circuits or lightning strikes. After the transient

voltages, the system settles down to the steady state.

Although the transient state is short, the components in the power system can be

subjected to higher voltage stresses, which possibly lead to the failure of the component

or even a system outage.

Transients are classified into four categories: 1) low frequency oscillations 2) slow front

surges, 3) fast front surges, 4) very fast front surges. The frequency range covers 0.1 Hz

to 50 MHz [1].

The following sub-sections describe the basics of inrush current, ferroresonance and

GIC phenomena, note that inrush current phenomenon is given here for the complete

picture of core saturation problems and will not be the topic to be studied in this PhD

thesis.

1.2.1 Inrush currents

A transformer magnetising inrush current is an example case where the nonlinear

properties of circuit elements are involved. When a transformer is energised, the

transient current would occur, due to the transformer iron core nonlinear characteristics.

Normally, the steady state magnetising current values are around 0.5 to 2% of the rated

current [2]. However, during the inrush current phenomena the value of the magnetising

current would achieve several times the rated current [3, 4].

The influential parameters for the magnitude of the inrush overcurrent may include the

network parameters and transformer parameters. The network parameters include the

source impedance, the losses in the network, system voltage level and switching angle.

The transformer parameters include the remanence of the core, the winding connections,

and the losses of the transformer [5].

Figure 1-1 shows that the inrush current as a function of remanence and instant of

switching on the transformer, the changing of the magnetising currents and the flux

waveforms.


23

Figure 1-1 Inrush current as a function of remanence and instant of switching-in of transformer [6]

It is assumed that the remanent flux density is around 80% of the nominal flux density,

and the flux density at the saturation point is 1.3 times the nominal flux density.

Consequently the flux density is a function of the actual remanent flux density and the

instant of switching shown in Figure 1-1. If the switch voltage is closed at a voltage

zero point then the total flux density is 2.8 times the nominal flux density of the

transformer. When the transformer saturates, saturation currents will appear and the

magnitudes are much higher than the nominal situation due to the nonlinearity of the

core materials.

Transformer inrush current phenomena have been experienced many times in the past

and it is difficult to avoid system energisation situations. In Table 1-1 there are several

real cases recorded in the power systems when a transformer is energised.

Table 1-1 Inrush experiences

Voltage Level Transformer Type Peak Current Level Winding

Connection

750 kVA Three-phase core type

transformer

10.35 times peak of

full-load current Y-Δ [5]

960 V/20 kV

2.05 MVA

Step-up generator

transformer

9 times peak of full load

current Δ-Y [7]

15/132 kV

155 MVA

Step-up generator

transformer

5.5 times peak of full

load current Δ-Y [8]

138/21 kV

315 MVA

Distribution

transformer

2.06 times peak of the

full-load current Y-Δ [9]

21/132 kV

500 MVA

Step-up generator

transformer

1.5 time peak of the

full-load current Δ-Y [3]

As we can see from Table 1-1, the inrush transient phenomena can happen anywhere in

the power system including generation, transmission and distribution transformers. And


24

normally, the peak magnitude of an inrush current is higher than the full-load current

and the transformer with a higher power rating has a lower inrush current level [5].

During the inrush phenomena, the noise originates from the transformer core and

winding vibration [10].

1.2.2 Ferroresonance

A resonance takes place in a linear R, L and C circuit when the source is tuned to the

natural frequency of the LC circuit where the inductive and the capacitive reactance

cancel each other. However, in the case of ferroresonance, the resonance occurs at the

given frequency of the power system when one of the inductances of the saturated core

matches with the capacitance of the network, and the occurrence of ferroresonance in a

power system is triggered by the reconfiguration of the network by switchgear operation;

after the switching operation, the network is changed into a circuit consisting of mainly

a capacitor in series with the saturable core of a transformer at no-load or light-load

condition.

A simplified single-phase model of the network after the switching operation is shown

in Figure 1-2. In this ferroresonant equivalent RLC circuit, the resistance and

capacitance are linear, and the inductance of the transformer is nonlinear. The

capacitance is contributed by either a cable or transmission line connected to the

transformer or the open circuited circuit breaker grading capacitors. The resistor RC

represents the transformer core losses, Cshunt is the total phase-to-earth capacitance of

the circuit which can be the capacitance between two transmission lines or the

capacitance of underground cables, Cseries is the circuit breaker grading capacitance or

the phase-to-phase capacitance of the lines. Lm is the non-linear magnetising inductance

of the transformer core.

Rc

CseriesSupplyvoltage

LmCshunt

Figure 1-2 Basic ferroresonance equivalent circuit


25

The non-linear components could be saturated in the ferroresonance circuit in Figure

1-2 after the system is reconfigured to clear the faults or due to the normal operations.

The energy stored in the capacitances would transfer to the non-linear core inductance

and this results in transient voltages that are usually higher than the nominal voltage of

the transformer so it would push the core into saturation; once the non-linear inductance

is saturated, the magnitude of the current in the circuit would become high. In addition,

during the ferroresonance transient phenomena, an overvoltage occurs and the

magnitude of the overvoltage can reach normally 1.5 times of the rated voltage [11].

Due to the transformer core non-linearity, when the transformer core goes into

saturation, the harmonic contents would be increased, and then the losses of the core

would also be increased. Besides, during the ferroresonance the transformer would

make noise due to core vibration [12].

Ferroresonance phenomena were experienced at different voltage levels of power

system as reported in [13-18]. The recorded experiences in which the networks have

been reconfigured into ferroresonance susceptible circuits are given in Table 1-2.

Table 1-2 Ferroresonance experiences[19]

System

Voltage

Level

Ferroresonance Circuit

Origin of capacitor Type of transformer

525kV 30.5 km transmission line Autotransformer

400kV 37 km transmission line Autotransformer

275kV Circuit breaker's grading capacitor

and ground capacitor Wound voltage transformer

230kV Circuit breaker's grading capacitor

and ground capacitor Wound potential transformer

34.5kV Cable capacitor Pad-mounted transformer

12kV Cable capacitor Station service transformer

According to existing experience and wisdom and, due to the fact that power

transformers have good cooling systems which use oil to cool the transformers, the heat

generated during ferroresonance is dissipated by a significant amount of circulating oil

to bring the heat out of the transformer tank, so power transformers can still withstand

the ferroresonance from a thermal point of view. However the potential damage of the

sustaining ferroresonance could be to speed up the ageing process in the transformer

due to localised overheating. On the other hand, there is not sufficient margin in the

cooling system’s capacity in a voltage transformer and earthing transformer, due to the

fact that both components will not be able to withstand the sustaining ferroresonance


26

well. When ferroresonance occurs on those transformers, they will have increased

probabilities of failure.

1.2.3 Geomagnetic induced currents (GIC)

The earth is frequently being bombarded by charged particles emitted from the sun, and

this effect is referred to a ‘solar wind’. Solar winds follow the so-called sunspot cycle

which is 11 years. Some solar activity produces intense bursts of solar wind lasting for

several days’ duration [20]. A geomagnetic disturbance (GMD) occurs when the

magnetic field embedded in the solar wind is opposite to that of the earth as shown in

Figure 1-3. This disturbance would distort the earth’s magnetic field.

Figure 1-3 Geomagnetic disturbance

Geomagnetic Induced Currents (GIC) is the ground end of the complicated space

weather chain starting from the Sun. They refer to currents driven in technological

systems, like power transmission line, oil and gas pipelines, phone cables, and railway

systems, by the geo-electric field induced by a geomagnetic disturbance or storm at the

Earth’s surface.

1.2.3.1 GIC impact on transformers

GIC have been widely studied for years and the research started after the first time solar

wind behaviour, when all telegraph lines in operation in the south of England were

stopped simultaneously by earth currents in 1840 [21].

GIC are a problem in high-geomagnetic-latitude areas, which are around 55˚-70˚. The

geoelectric field is the largest in the areas of high earth resistivity near the aurora zone.

Therefore, GIC is more pronounced in northern latitudes in the areas of igneous rock

Earth

Geomagnetic disturbance

Sun

Sunspot

Sun electron


27

with high earth resistivity. Coastal areas are another region of high susceptibility to GIC

because the induced current flowing in the ocean meets a higher resistance as it enters

the land. This is enhanced by charge accumulation at the coast [22].

In the power systems, GIC are (quasi-)dc currents and the frequency range is about 1Hz

or less. GIC can enter and leave the power system by way of the star connection, and

solidly earthed neutrals of autotransformers, and consequently cause saturation of the

transformer core [22]. This would make the transformer core work at the non-linear

region and the magnetising current would significantly increase during the GIC events.

The harmonics would be generated by the saturated transformer core, and the harmonics

would go through the electrical network system, which would then lead to the

unnecessary relay tripping, and would also increase reactive power demands, voltage

fluctuations and drops or even a blackout of the whole system. These can have a severe

impact on the system, including on the transformer itself; the transformer experiencing

GIC can overheat and, in the worst case, be permanently damaged [23].

In Figure 1-4, the left side figure shows the approximation of a typical power

transformer excitation characteristic under the normal working condition, and the right

side shows the two straight line piece-wise approximation of a typical power

transformer excitation characteristic under GIC conditions. It can be seen that the

transformer under normal operation works in the linear region of the magnetic

characteristic, and the magnetising current is quite small (normally about 0.5% of the

rated load current). However with GIC, the flux is offset and is driven past the knee area

of the core saturation curve during the positive half-cycle with a large magnetising

current. The transformer works in both the linear and therefore the non-linear regions.

The flux offset for a given GIC magnitude depends on the ultimate slope of the

saturation curve.


28

Figure 1-4 Magnetising current changing by GIC [22]

1.2.3.2 GIC level

The factors in the electrical systems which determine the GIC levels are: power system

orientation, lengths of transmission lines, electrical resistance, transformer type and

connection and station grounding.

From the statistical data provided by the Geomagnetic Laboratory in Canada, based on

records over several decades, the maximum GIC in the north-south direction grid is 10

A per phase in every one year and 30 A per phase in every ten years; but for the east-

west direction grid it is more severe compared with the north-south direction grid, the

maximum GIC in the east-west direction grid is 78 A per phase in every one year and

234 A per phase in every ten years; so the direction of the grid is much more important

in determining the GIC level than anything else.

The earth surface potential between two grounded Y-connected transformer neutrals

would produce a GIC which goes through transmission lines. The level of earth surface

potential is mainly determined by the lengths between the two grounded Y-connected

transformers. The longer the distance, the higher the potential created. Figure 1-5 shows

how GIC currents go through the circuit by passing though the grounded transformer

neutral point.


29

Figure 1-5 Induced voltage drives GIC to/from neutral ground points of power transformers [22]

Due to the earth surface potential, the GIC current is a Quasi-DC low frequency source,

and all the system components are normally modelled by the DC resistance which

include transmission line resistance, transformer winding resistance and grounding

resistance. In addition, all the resistance value would determine the GIC level. Figure

1-6 shows the DC model for one phase. And there must be two Y connection

transformers with a long transmission line for the GIC to occur.

Figure 1-6 DC model for calculating GIC[20]

1.3 Objectives

In the power system network, transformer saturation can cause voltage disturbance

problems and transformer damage or at least the speeding up of insulation ageing

through excessive heating.

Low frequency switching transients such as ferroresonance, inrush currents and what is

now increasingly known as geomagnetic induce currents (GIC), are the most common

phenomena to cause transformer core saturation.

Grounded transformer neutrals

Transmission line

Earth

L

Y

G


30

Although the ferroresonance and the GIC phenomena have been investigated for

decades, there are new challenges because of the improvements in transformer core

materials and lower loss components used in the power system. Besides, the

investigations of these phenomena have increased in recent years due to severe system

and transformer failures.

Most research focuses on individual transformers and the phenomena which cause core

saturation. Transformers were modelled and voltage/current waveforms were analysed.

These studies provided a limited comparison between different types of transformer

installed in the system, and concentrated on a simplified core representation; they did

not fully consider core saturation issues in system studies. Besides, the three-phase

transformer core model still needs further development in order to accurately simulate

the associated problems mentioned before.

With these problems in mind, this research project will develop two main simulation

models: a mathematical transformer magnetic circuit model based on the elementary

magnetic circuit theory; a transient model for the complete network modelling and for

carrying out the low frequency transient study for the interpretation and understanding

of the behaviour of transformers and the interaction between the transformer and the

system. The main objectives of this thesis are outlined below:

1. To build a mathematical transformer magnetic circuit model based on magnetic

circuit models. Taking practical examples of a three-phase three-limb two

winding transformer and a three-phase five-limb auto-transformer for

comparison, to discuss the influence of core structure and core materials; then to

perform sensitivity studies with this model to determine the effect of the model

parameters under balanced and unbalanced situations; thereby to identify the key

parameters of transformers and systems which significantly affect the

phenomena.

2. To identify the correlation between the GIC primary current waveform and the

winding type, core structure type, and the system parameters.

3. To develop a more accurate model of ferroresonance for use in transmission and

distribution systems that not only matches with the field test results but also

identifies the key parameters of the ferroresonance. Based on the system model,

sensitivity studies of different sets of system parameters in combination with the

circuit-breaker grading capacitance, the cable-ground capacitance and the


31

transformer characteristics were carried out, in order to identify how these

parameters influence the ferroresonance phenomena.

1.4 Major contribution and originality

In this research, two simulation models were developed: a mathematical transformer

magnetic circuit model and a transient model.

The flux distribution and magnetising currents were analysed based on the transformer

magnetic circuit model. Moreover, the three-limb core with zero sequence flux return

path transformer magnetic model can be used to deal with the unbalanced situation, and

the fluxes distribution and magnetising currents were analysed.

The low frequency transient studies for the interpretation and understanding of the

behaviour of transformers and the interaction between the transformer and the system

were carried out by using the complete transient network model. And the key influential

parameters were also pointed out.

The achievements of this research are as follows:

1. The influences of core structure and core material on magnetising current

waveform and flux distribution under balanced (normal operation) and

unbalanced (AC+GIC) situations, by using the developed magnetic circuit core

model, were illustrated.

2. The fundamental understanding of GIC and ferroresonance events in the power

networks, by using the ATP model, was established.

3. Among all the influential parameters identified, transformer core structure is the

most important one. The five-limb core is easier to be saturated than three-limb

core under the same GIC events; the smaller the side yoke area of five-limb core,

the easier it will be saturated.

4. More importantly, under GIC events, a transformer core could become saturated

irrespective of the loading condition of the transformer if it is a strong network.

In summary, it helps the industry to understand systemically how GIC influences the

transformer itself, and the system operation. The key parameters identified by the

sensitivity study are: solar storm level, transformer structure, size ratio of side yoke to


32

main yoke for a five-limb transformer and the system impedance which includes

resistance and inductance.

1.5 Thesis outline

This thesis consists of six chapters which reflect the progress of the research in

achieving the objectives previously outlined.

Chapter 1 Introduction: as already noted gives general background and describes the

general structure of the work.

Chapter 2 Basics of transformers: introduces the basic fundamental theory of

transformers, including the transformer core materials, core structure and core losses;

and also the transformer winding structure.

Chapter 3 Literature review: the literature review provides an overview of the power

system transients produced by ferroresonance and GIC conditions and their influence on

networks and network components. A review of the GIC and ferroresonance influence

on the power system and its transformers is also provided. The methodologies of

investigation are reviewed, in terms of modelling and parameter analysis.

Chapter 4 Steady state magnetic circuit modelling for transformers: using

equivalent magnetic circuits to model the transformer core, three-limb and five-limb

transformer core models are represented which include ideal three-limb, three-limb with

return path and five-limb core. All the models were verified for accuracy by using the

manufactures’ test report data. The magnetising currents affected by the core structure

types are discussed and the conclusions are drawn. One GIC case study involved using

the magnetic circuit model and sensitivity studies into the parameter influences were

carried out.

Chapter 5 GIC magnetic and electrical circuit modelling: using ATPDraw

simulation software to simulate the GIC influences on the transformer and to analyse

the current waveforms using Fourier analysis. The theory of the phenomena is given

first. Secondly, further investigation into the influence of the winding and transformer

core structure is discussed. The conclusions are drawn.

Chapter 6 Low frequency switching transient magnetic and electrical modelling:

investigations of de-energisation switching transients were carried out on a 132 kV


33

distribution network in the UK. The current and voltage signals produced by these

operations were fully monitored. They are based on available field data and also circuit

layout diagrams, transformer factory test results, cable design data etc. A simulation

model of this network was built-up and sensitivity studies carried out; certain

modifications were made to the ATP network model for this purpose. The results were

compared with the recorded signals to obtain an understanding of the phenomena

involved. Good agreement between recorded and simulated results was obtained and

some of the main parameters in the process were identified.

Chapter 7 Conclusion and future work: presents the conclusions drawn from this

study and proposals for the future work.

Chapter 2 Basics of transformers

34


2.1 Introduction

In this chapter, the basics of transformer are introduced, in terms of the main

components of transformer structure, i.e. winding and core. Statistical analysis was

conducted on the open-circuit test data of National Grid transmission transformers,

which were built over last four decades with the influence of changes and evolutions of

material and structure. The results are presented in this chapter to illustrate the variety

and complexity of core saturation issue when individual transformer is concerned.

2.2 Transformer structure

A transformer is a device that transfers electrical energy from one circuit to another

through inductively coupled conductors---the transformer’s windings. Primary and

secondary windings are wound concentrically around a transformer core. The major

function of the core is to provide the maximum magnetic coupling between the two

windings, and the major objective for the transformer designer is to try and minimise

the loss of power which includes the core loss and winding loss.

The main components of a power transformer are winding and core.

The main components of a power transformer are winding and core. For the winding

structure type there are disc type and layer type windings. The disc type winding may

be classified as, a continuous disc winding, an inter-shielded disc winding, and an inter-

leaved disc winding, these are normally used for the HV winding [24]. The layer type

winding is less common for HV windings, but more common for low voltage windings

at 11 kV and below, and is also used as the tertiary windings in auto-transformers [4].

For the core structure type there are single-phase core and three-phase core structures,

for single-phase transformers there are three typical core structure types, which are

single phase both limbs wound, single-phase centre limb only wound and single-phase

cruciform [4]; for three-phase core there are two typical core structure types which are

widely used in the UK, they are the three-limb core and the five-limb core. The

transformer core is made up of electric steel laminations, the purpose of which is to


35

reduce eddy current core losses as well as to provide a low reluctance path for the

magnetic flux linking the primary and secondary windings.

2.2.1 Main component---winding

In general, there are categories of three-phase two-winding transformers and three-

phase three-winding transformers. Normally, it is reasonable to have three-phase delta

connected (Δ) windings in a transformer, for delta windings can absorb the third order

harmonic. A two-winding transformer normally uses a star-delta connection, if it is not

an auto-transformer. A three-winding transformer is a star-star-Δ or auto (A)-Δ

connection. The star connection (Y) is generally used on the high voltage side whilst the

delta is used on the low voltage side. The generator step-up transformer usually uses the

Δ-Y connection, the delta side is connected to the generator side and the star side

connected to the transmission side. Then the transmission transformers will have a Y-Y-

Δ or A-Δ connection.

Since National Grid is the operator of the transmission system in the UK, their

transformers are Y-Y-Δ, Y-A-Δ and Y-A (occasionally) connected. As we know, the

existence of the tertiary windings affects the harmonic contents of the magnetising

currents. Figure 2-1 shows the average three-phase magnetising current (The word

magnetising current is equivalent to an open circuit current) value for different

transformer winding connections. In total, twenty one transformers of 275/132 kV, 240

MVA from the National Grid database were selected for the analysis. Seven

transformers are in each group of the same connection.

Figure 2-1 Average magnetising current for different winding connection

For Y-Y-Δ and Y-A-Δ, the 13 kV tertiary winding exists and it is used for the open

circuit test; however in Y-A connection there is no 13 kV tertiary winding, then the

open circuit test would be carried out at 132 kV. In Figure 2-1, the results of Y-A

0

5

10

15

20

25

Y-Y-Δ Y-A Y-A-Δ

Ma

gn

etiz

ing

cu

rren

t (A

)

Connection

Average Magnetizing current for different connection

No Load Current(A) φA No Load Current(A) φB No Load Current(A) φC

Average magnetising current for different winding connections

Mag

ne

tisi

ng

curr

en

t (A

)

Connection


36

connection are normalised and converted from the 132 kV star connections to 13 kV

delta connection results.

2.2.2 Main component---transformer core

As mentioned before, there are two types of core structure which are well used in the

UK; one is a three-limb transformer core and the other is a five-limb transformer core.

For the same capacity transformer, the five-limb core one can be lower in height than

the three-limb core one and it is more convenient to transport; however the core loss is

higher than the three-limb transformer [25].

In order to take full advantage of the circular winding interior space, the lamination-

stacked core cross area is arranged into an approximately circular section. The

transformer manufacturers use different-width laminations to build up the core; however

the width variation depends on the lamination manufacturers. Usually, the width

variation is 10mm. Therefore, the core filling rate of the cross area is around 90% [26].

Due to the fact that the core consists of laminations, the mechanical strength of the

laminations cannot withstand its own weight, so core steel bolts were used in the past to

hold the core laminations together by bolts passing though the limb and the yoke.

However, these holes and bolts would increase the magnetic reluctance in the flow

direction of flux which means it would increase the core loss and, in extreme situations

the flux would find other paths partially outside the transformer core, going through

other metal components in the transformer such as transformer tank, core clamping and

so on. The current reference technology is to use bands of either steel or glass fibre to

hold laminations to the core limb and to use metal-frame clamping structure to hold

laminations to the yoke.

The overlapping of lamination at the joint area is important so that it is able to decrease

or increase the core loss; actually most of the core loss is from the yoke and limb joints.

The 45-degree mitred overlapping is usually used to overlap the lamination in five steps

[10], the more steps there are, the harder it is to build the core ; so the optimal five step

one is chosen mainly due to economics.

The general layout of a three-phase three-limb transformer and the flux in the core are

shown in Figure 2-2 (a) and (b).


37

The L1 and Lm are the effective length of the limb and yoke; Al represents the cross-

section area of the limb and the yoke. The three-phase fluxes for the three-limb core are

indicated by ФA, ФB, and ФC. In the three-limb arrangement, three limbs are wound by

windings which correspond to the three phases. Each limb is joined together by the top

and bottom yoke, which complete the magnetic circuit. One characteristic is that the

cross-section areas of the top and bottom yokes are equal to that of the limb (Al);

therefore, when the transformer works under the linear region in normal working

conditions, the flux in the yoke is equal to the nearby limb; the flux through each limb is

sinusoidal since the voltages applied across the winding are sinusoidal. Ideally, as long

as the fluxes are at the same magnitude and their phase angles are electrically 120° apart,

the fluxes will cancel each other in the top and bottom yokes. Consequently, for applied

three-phase balanced voltages, no flux return path is required [26]. However, if there is

the unbalanced voltage component, the flux has to travel along a high-reluctance path

through a very long air gap and come back to the core again.

ΦA ΦB ΦC

(-ΦA)

(-ΦC)

(-ΦC)

(-ΦA)

Lm

Ll

Al

(a) (b)

Figure 2-2 Three-phase three-limb core type transformer

The general layout of a three-phase five-limb transformer and the flux in the core are

shown in Figure 2-3 (a) and (b). As in the three-phase three-limb core, the effective

length of the limb is denoted as Ll. The main yoke and side yoke effective lengths are

indicated by Lm and Ls respectively. The cross-sectional area of the side yoke is given as

the main yoke, while the cross-section areas for the main limb and the main yoke are

taken as Al and Am. The three main centre limbs carry three-phase fluxes ФA, ФB, and

ФC. Фls and Фrs represent the fluxes at the side yokes.

In a five-limb transformer, the three-phase windings are wound on the middle three

limbs similar to a three-limb transformer, the difference is that there are two extra limbs,


38

one on each side of the three main limbs, and the cross-section areas are smaller than

those of the main limbs. The cross-section of the main yoke is not equal to, like the

three-limb transformers, but smaller than the main limb cross-section area. These two

side yokes are for carrying extra flux when the transformer meets the unbalanced

situation or the main yoke cannot carry more flux, without going into saturation.

The flux variation in the main and side yoke of five-limb core was investigated by

English Electric Company Limited and was reported in October 1968 in order to

evaluate the iron losses [26]. It was discovered that the fluxes in the yoke and side

yokes are non-sinusoidal because the flux in a main limb has two alternative paths when

flowing into the yoke, neither of which is pre-determined.

Core Yoke AB

Core Limb A

Winding Set A Winding Set C

Core Limb B Core Limb C

Core Yoke BC

HV Winding LV Winding

Side Yoke

Side Limb Side Limb

Side Yoke

(a)

ΦA ΦB ΦC

(ΦAB)

(ΦBC)

(ΦBC)

(ΦAB)Lm

Ll

Al

Ls

Am As

(Φls) (Φrs)

(b)

Figure 2-3 Three-phase five-limb transformer core

Comparisons of the magnetising currents were made of the two types of transformer

core structures operated by National Grid UK, which are three-limb and five-limb core

type transformers. Due to the structural difference, the magnetising currents are


39

different for the three-limb and five-limb core. As mentioned earlier, the magnitudes of

the magnetising currents are mainly determined by the magnetising loop length if the

core materials used are the same. However, the transformers selected used different

materials to build the cores so the magnitudes of the open circuit currents cannot be

compared without being normalised.

Figure 2-4 shows the results of the three-phase average magnetising current for two

different core structures under the same voltage level and same power rating. One phase

current of the lowest value is regarded as per unit base. There are eight three-limb and

eight five-limb transformers examined, which are picked up from the same 400/275 kV

voltage level and 1000 MVA power rating.

Figure 2-4 Average magnetising current in per unit for different core structure

The open circuit current values for the three phases show that the unbalanced situation

in terms of the magnitudes of the magnetising currents of the five-limb core is greater

than that of the three-limb core. In other words, the ratio between the yoke length and

the limb length of the transformer core, and the area ratio, yoke area to limb area, of

transformer would determine the unbalanced situation.

2.2.3 Transformer core materials

There are three different types of magnetic materials which are diamagnetic materials,

paramagnetic materials and ferromagnetic materials [27].

Ferromagnetic materials, which have a large and positive susceptibility to an external

magnetic field, are widely used to build power transformers.

1.00 1.00

1.12

1.02

1.42

1.23

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

3-limb 5-limb

Ma

gn

etiz

ing

cu

rren

t (p

.u.)

Core structure

Average magnetizing current for different core structure


Average magnetising current for different core structures

Mag

ne

tisi

ng

curr

en

t (p

.u.)

3-Limb 5-Limb

Core structure


40

In order to build a transformer, we need the transformer core to provide low reluctance

and high permeability. So the ferromagnetic materials are suitable for the transformer

core construction. However, the hysteresis loop is one of the important characteristics of

the magnetic properties of ferromagnetic materials. A hysteresis loop shows the

relationship between the induced magnetic flux density (B) and the magnetising force

(H). It is often referred to as the B-H loop. The voltage supply corresponds to B and the

magnetising current corresponds to H, due to H*l = N*I (l is the magnetic loop length,

N is the turn number, I is the magnetising current). There are two ways to represent the

characteristics of the material which are the B-H curve (hysteresis loop) and the

Lambda-I curve (lambda is the total flux in the transformer core).

Superficially, the transformer core structure has not been through great changes,

although small changes have been made and designers have been constantly working to

reduce core losses. The core loss at specified frequency includes two parts: the first is

hysteresis loss which is dependent on the area of the hysteresis loop, and the second is

eddy current loss which is dependent mainly on the thickness of the material. The

components of core loss are represented by these equations:

Hysteresis Loss: 1 max ( / )n

hW k fB W kg

Eddy current Loss: 2 2 2

2 / ( / )e effW k f t B W kg

where k1 and k2 are constants for the material

f is the frequency, Hz

τ is the thickness of the material, mm

ρ is the resistivity of the material, Ω∙m

Bmax is the maximum flux density, Tesla

Beff is the flux density RMS value of the applied voltage, Tesla

n is the ’Steinmetz exponent’ which is a function of the material [28].

When a ferromagnetic material is magnetized in one direction, it will not relax back to

zero magnetization when the imposed magnetising field is removed. It must be driven

back to zero by the opposite source. If an alternating magnetic field is applied to the

material, its magnetization will trace out a loop which is called hysteresis loop. The area

enclosed by this loop is proportional to the hysteresis loss.


41

Normally the hysteresis loop can be separated into three parts being the linear region,

knee region and non-linear region. For all the transformers, the designer tries to use the

minimum material to transfer maximum energy from primary to secondary windings, so

the aim is to ensure that, in operation, the flux excursions do not pass through and

beyond the knee point. In this region the relative permeability of the material is still at a

high level which is around 6000 or more depending on the core material [29].

The early transformer cores were made from high-grade wrought iron; however it was

recognised that the addition of small amounts of silicon or aluminium to the iron greatly

reduced the hysteresis losses, increased permeability and also increased the resistivity,

which also resulted in reduced eddy current losses [4]. Table 2-1 shows that as

transformers evolved at different stages of development, different materials were used

for the transformer core application.

Table 2-1 Historical development of the core steels [4]

Steels Types Period Losses

(@ 1.5 T, 50 Hz) Usage

Hot-rolled Steels Until 1940s 7 W/kg /

Cold-rolled Steels

(Grain-oriented steel)

1940s-

1960s 1.5 W/kg

Early transformer

production in

general usage

High Permeability Steels 1965s-Now

1 W/kg (Reduction of

30-40% in hysteresis

loss)

Early transformer

production in power

transformer usage

Domain Refined Steels 1983s-Now 0.85W/kg (@1.7 T) Newer transformer

in general usage

Amorphous Steels 1970s-Now 0.28 W/kg

Where very low

core loss is

required; costly

Microcrystalline Steels / 0.56 W/kg (@1.7 T) /

Figure 2-5 shows the general comparison between the characteristics of the modern

materials and the characteristics of the old materials.


42

Figure 2-5 Ferromagnetic material hysteresis loop [30]

The left side of the figure shows the characteristics of the modern materials and the

right side shows the characteristics of the old materials. It can be seen that the modern

materials have fewer losses compared to those of the old materials. Also, the maximum

flux density can reach much higher values in the modern materials. The knee point for

the modern materials is also higher, being around 1.7 T, whereas for the older materials

it is only 1.4 T [29].

The high permeability grain-oriented and the domain refined steels have a better

orientation compared with conventional steel; and also that at flux densities of 1.7 T and

higher, that permeability are three times higher than that of the best conventional steel,

and the stress sensitivity of loss and magnetostriction is lower. However, the magnitude

of the eddy current loss of conventional and the new material are very similar [31].

There are three factors which would influence the magnetising currents, and they are the

core steel material, core structure and winding connection.

Statistically the test reports of transformers serving in the National Grid were analysed.

They are of 400/275/13 kV, 400/275 kV, 275/132/33 kV, 275/132/13 kV or 275/132 kV,

being examined in terms of the open circuit test current of three phases. The test reports

showed the existence of the differences of three-phase open circuit currents all

transformers. Comparison was also made on the transformers manufactured at different

years. For different decades, the manufactures might use different types of material for

the transformer core. The magnitude of the magnetising current is determined by the

core material subject to the same building method. Figure 2-6 shows the open circuit

current distribution versus the transformer designs from the 1960s to 2000s.

New materials Older materials


43

Figure 2-6 Average magnetising current of different installation year of transformers at 400/275/13

kV and 1000 MVA

The columns in red, yellow and blue of the figure represent the magnetising currents of

phase A, B and C. It can be seen that overall the data of the 1990s is lower than the data

of the 1960s. As mentioned before, the cold-rolled steels (Grain-oriented steel) were

used as transformer core material in the 1960s. Afterwards, not only were newer

materials produced for core material in order to reduce the hysteresis losses such as high

permeability steels, domain refined steels and amorphous steel, the production process

was also improved, to further reduce the losses of the core steel.

Figure 2-7 (a) shows that the improvement in magnetic properties over the past 80 years

[31]; and (b) is the survey made in the research work on the magnetising currents from

the manufactures’ test reports of 400/275/13 kV, 1000 MVA transformers in National

Grid. It can be seen that as the improvement of the material’s characteristics, both the

material loss and the permeability characteristics improve.

0

5

10

15

20

25

30

35

1968 1972 1973 1976 1986 1987 1991 1992 1992 1992 1993 1995 1996 1997 1998 1998 1998 2001 2001 2001

Ma

gn

etiz

ing

cu

rren

t (A

)

Year

Magnetizing current for 1000MVA


Newer core steelsOlder core steels

Magnetising current for 1000MVA transformers

Mag

ne

tisi

ng

curr

en

t (A

)

Year

(a) [31]


44

Figure 2-7 Losses and magnetising currents from year to year

0

10

20

30

40

50

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Cu

rre

nt(

A)

Year

Magnetizing current for different year

(b)

Magnetising current for different years

Chapter 3 Literature review

45


3.1 Introduction

This chapter provides a literature review on the transient studies of the system network,

in particular, switching ferroresonance transients and GIC phenomena. Both are

associated with transformer core saturation problems. Background knowledge was

acquired on how to understand the reasons for the ferroresonance phenomena and the

geomagnetic induce current phenomena are also introduced; the investigation methods

are summarised and the mitigation methods are also relayed in this chapter.

Generally, the transient phenomena would be separated into different frequency ranges

from DC to about 50MHz. The transient phenomena appear as transitions from one

steady state condition to another. The primary cause of such disturbances in a system

are closing or opening of a circuit breaker or another switching equipment, short-

circuits, earth faults or lightning strokes.

Table 3-1 shows the overview on the different causes of transient phenomena and their

most common frequency ranges [1].

Table 3-1 Cause of system transients and frequency ranges [1]

Cause Frequency Range

Transformer energisation 0.1 Hz - 1 kHz

Ferroresonance

Load rejection 0.1 Hz - 3 kHz

Fault clearing 50/60 Hz - 3 kHz

Fault initiation 50/60 Hz - 20 kHz

Line energisation 50/60 Hz - 20 kHz

Line reclosing 50/60 Hz - 20 kHz

Transient recovery voltage 50/60 Hz - 20 kHz

Terminal faults 50/60 Hz - 20 kHz

Short line faults 50/60 Hz - 100 kHz

Multiple re-strikes of circuit breaker 10 kHz - 1 MHz

Lightning surges, faults in substations 10 kHz - 3 MHz

Disconnector switching and faults in GIS 100 kHz - 50 MHz

From this table, we can see that, the frequency range of transformer switching transient

is around 0.1Hz to 1 kHz, which belongs to the low frequency range. The CIGRE

working group classified the frequency range of the system transients into four different

groups [1]. The switching transients and the GIC all belong to the low frequency range.


46

3.2 Power system operation transient---switching

transients

3.2.1 Background

Switching transients are the most frequently occurring transient phenomena in the

power system. The system network needs maintenance, capacitor bank switching,

energisation of the loads and transformers and also the new network synchronization

such as the wind farm and so on; all of those operations would cause switching

transients.

For the transformers, two main switching transient phenomena would occur which are

magnetising current inrush when a transformer is switched on to the network; and

ferroresonance when the transformer is switched off at off-load or light-load condition.

Ferroresonance is one of the core saturation phenomena which could cause overvoltages

and overcurrents at the terminals of a transformer. Besides overvoltages and

overcurrents, when the core saturates, the overfluxing issue can also cause local

overheating of transformer insulation [32]. Overfluxing possibly include two definitions:

one is when core lamination goes into the saturation region of the λ-I curve, the other is

when the flux leaks out of the joint area and goes into the insulation/metal clamping

frame area.

Inrush is another phenomenon where a transformer can be pushed into the deep

saturation, and the maximum magnitude value of the current value can achieve several

times the nominal load current. During the period of inrush the iron loss and copper loss

are extremely high.

Electric stress on transformer insulation caused by overvoltages, and thermal stress

caused by overheating and overcurrents, can result in transformer failures. This is one of

the main reasons why a network operator is worried about the ferroresonance and inrush

phenomena.


47

3.2.2 Ferroresonance

3.2.2.1 Background

Ferroresonance is defined as the steady-state mode of operation that exists when an

alternating voltage of sufficient magnitude is applied to a circuit consisting of

capacitance and ferromagnetic inductance which are repeated each half cycle [33].

Ferroresonance is an old topic and there are substantially large volumes of literature

studying this practical phenomenon experienced by transmission & distribution

networks upon state-changing events such as switching or fault operations. The first

published work, which simply defined the ferroresonance phenomenon as transformer

resonance, was written by J.Bethenod in 1907 [34]. The word ferroresonance was first

used in the 1920s by P.Boucherot [35] to describe the series resonance involving

capacitance and nonlinear inductance of the transformer core. It was in the 1930s that

the subject of ferroresonance generated practical interest when the use of series

capacitors for voltage regulation caused ferroresonance in distribution systems [36],

resulting in damaging overvoltage. The first analytical work was presented by

Rüdenberg in the 1940s [37] and in the 1950s a more detailed analytical work was

completed by Hayashi [38].

Ferroresonance can be split into sustained and transient ferroresonant phenomena;

sustained ferroresonance has the power system acting as the supply source for the

resonating phenomenon; for example via inter-circuit overhead lines a no-load

transformer is supplied by the power system and it is possible to have sustained

ferroresonance [14, 39]; the overvoltage can be sustained for a long time. [40] described

the sustained fundamental mode and sub-harmonic mode of the ferroresonance in the

real network in the UK. On the other hand the transient ferroresonance phenomenon is

normally supplied by a limited energy source such as a capacitor made of a length of

cable, after a switching operation which isolates part of the network. [12] gave an

example about the transient ferroresonant experience, where the limited energy stored in

the cable is transferred between the cable and the saturated transformer; the transfer

continues until system losses have absorbed all the energy.

A special publication on the Practical Aspects of Ferroresonance [11] has been written

by the IEEE Working Group on “modelling and analysis of systems transients using


48

digital programs”. One of the tasks of the Working Group is to provide a comprehensive

survey of the ferroresonance issues reported in the literature.

According to [11], 129 papers are reviewed and categorised as practical, including

seven different classes of ferroresonant circuits, which are

1) Transformer accidentally energised on one or two phases

2) Transformer energised through the grading capacitance of one or more open

circuit breakers

3) Transformer connected to a series compensated transmission line

4) Voltage transformer connected to an isolated neutral system

5) Capacitor voltage transformer

6) Transformer connected to a de-energised transmission line running in parallel

with one or more energised lines

7) Transformer supplied through long transmission lines or cables with low short-

circuit power.

All the circuits above must contain at least: a non-linear inductance (ferromagnetic and

saturable), a capacitor, a voltage source (generally sinusoidal) and low losses. The

initiation of ferroresonance needs some types of switching event such as load rejection,

fault clearing or single phase switching or loss of system grounding.

The same IEEE Working Group also produced a paper focusing on analysis and

modelling guidelines for slow transients, i.e. the study of ferroresonance [41]. A

comparison between single-phase and three-phase transformer modelling was carried

out for ferroresonance. The three-phase system cannot be modelled accurately by using

per phase simulation, due to the transformer core configuration and winding connection.

A complete three-phase model needs to be used. It is also mentioned that to represent

the transformer core, the core configuration must be considered and the saturation

characteristic must be accurately modelled [42]. Circuit breaker opening time and

sequence also play an important role for ferroresonance.

In the power system, saturable inductances can exist in the form of power transformers,

voltage measurement inductive transformers (VT) and shunt reactors; for capacitances,

there are cables and long transmission lines, capacitive voltage transformers, series or

shunt capacitor banks, and voltage grading capacitors in circuit-breakers and so on. A

ferroresonance phenomenon is more likely to be created with minimal load or a low

level of damping, and for unbalanced 3-phase excitation with coupling between phases,


49

or between circuits of double-circuit lines. Besides, the initial conditions of capacitor

and inductor also influence the ferroresonance phenomena such as: the level of residual

flux in the magnetic core and the initial charge on the capacitive components [43].

The consequences of ferroresonance can be untimely tripping of protection devices (due

to overvoltages and overcurrents) and destruction of equipment such as power

transformers or voltage transformers (overvoltages, overcurrents and overfluxing).

3.2.2.2 Ferroresonance effect on transformer

Ferroresonance phenomena often occur during normal circuit operation and circuit

faults in the power system; some cases happen due to the grading capacitance

transferring energy to transformers or inductive components, some are due to the

coupling capacitance between two circuits transferring energy to transformers or

inductive components, and some are due to the ground capacitance transferring energy

to transformers or inductive components; but the fundamental theory underlying these

phenomena are quite simple; because there are non-linear inductance and capacitance in

the network, and during the circuit reconfiguration the energy from capacitance would

discharge to non-linear inductance and furthermore push the transformer into saturation,

and depending on the resistance value of network, the ferroresonance would display in

two ways: one is the sustained mode due to low loss; the other one is the decayed mode.

Most of the case studies were carried out via field tests or using network modelling to

investigate ferroresonance phenomena, those researchers focused on the network level

in the study of transient phenomena. However, not only are overvoltages and

overcurrents experienced by transformers during ferroresonance, but overfluxing can

also occur [32], and the associated local overheating is regarded as one of the long-term

ageing factors. When ferroresonance events happen, the core must be saturated, and it

would cause the relative permeability of the iron core to decrease from the linear region,

which is several thousands, to that of saturation region, which is only tens [44]; the flux

would leak out from the core to the clamping frame, oil and other components inside the

transformer tank or even the tank which could produce more local heating of these

components.

The eddy current loss is not only dependent on the square of frequency but is also

directly proportional to the square of the thickness of the material. Since the laminations

of transformer core are produced by using a special process, the thickness is much


50

thinner than the other components, i.e. around 0.23mm---0.35mm [4]. Reduction of

eddy current loss in a transformer core is achieved by building up the core from a stack

of thin laminations and increasing the resistivity of the lamination material in order to

make it less easy for eddy currents to flow. However when the flux goes through other

components in the transformer due to core saturation, it may create more eddy current

losses, because the clamping frame are much thicker than the laminations. It may cause

partial overheating problems; thereby the ageing of the insulation would be accelerated.

During the ferroresonance events, the abnormal noise created by the vibration can be

heard [12], which means the insulation would not only be subjected to thermal stress but

also mechanical stress which may cause deterioration more quickly than anticipated,

particularly where the core has been loose. In extreme situations, this may lead to eddy

current heating, excessive gassing and eventually localized core melting and failure [45].

There are a number of less critical modes of deterioration, which can give diagnostic

indicators and need to be identified. One is where core overheating occurs if the number

of cooling vents is inadequate; this would be a long term deterioration mode, but still

evolve combustible gases. Another is where the clamping releases, which allows some

support structure to be electrically isolated. Dissolved gases and insulation resistance

checks (if the main earth connection is accessible) are the relevant diagnostic methods

[46].

3.2.2.3 Historical events

There are some real cases of ferroresonance phenomena in the power systems. In the

following sections, details of the case study are summarised and discussed.

Ontario Hydro reported on examples of ferroresonance occurring in their Cataraqui

230/115 kV autotransformer upon de-energisation of 230 kV line and the 115 kV busbar

[41]. Figure 3-1 shows the system layout, the 230kV line is in the 173 m wide

transmission corridor in parallel with two 500 kV and another two 230 kV transmission

lines. The shared corridor is 20 miles long. The transformer marked in the figure

experienced ferroresonance and the circuit breaker also experienced a high recovery

voltage.


51

Figure 3-1 Ontario Hydro 230kV System [41]

In [47] experts from Manitoba Hydro and Ontario Hydro stated that the close coupling

of parallel circuits with similar or higher voltage increases the risk of ferroresonance in

the disconnected transformers. Based on system configurations of Dual Element Source

Network (DESN) stations, it is shown that 59 km of parallel 230 kV and 32 km of

parallel 500 kV transmission lines were sufficient to cause ferroresonance in a 230/115

kV transformer (auto connected transformer), the circuit configuration is shown in

Figure 3-2.

Figure 3-2 Multi-Voltage transmission circuit [47]

X3H

X4H

X552A

14.25ml. 5.75ml.

X2H

X1HLENNON 500

LENNON 230

KINGSTONGARDINER TS

HINCHINBROOKE TS

16

.57

ml.

TO HAWTHORNE 500 TS

CATARAQUI TS


52

In [13] a three-phase 1000 MVA 525/241.5 kV Y-connected bank of autotransformers,

located at the Big Eddy Substation of Bonneville Power Administration (BPA) in Dallas,

Oregon, is connected to the 525 kV side through a disconnecting switch to 30.5 km of

line and a circuit breaker located at John Day Substation. A local circuit breaker is

provided on the 230 kV bus at Big Eddy. Parallel and on the same right-of-way is the

525 kV John Day-Oregon City line which is shown in Figure 3-3.

Figure 3-3 525 kV transmission system between Big Eddy and John Day [13]

In [14], a 400 kV circuit was identified as a suitable circuit that could be induced into

ferroresonance and tests were planned to examine the disconnector’s capability of

quenching the ferroresonance. The purpose of the tests was to first establish the

likelihood of the occurrence of ferroresonance on SGT 1 shown in Figure 3-4. There is a

parallel overhead line circuit, the coupling distance is 37 km and the feeder has a 1000

MVA 400/275/13 kV power transformer (auto connected transformer). This circuit is

susceptible to ferroresonance when a series of switching operations are carried out in

the following way: the disconnector X303 and the circuit breaker T10 are opened. All

the disconnectors (X103, X113) and circuit breaker X420 connecting to busbar 2 are in

service. The circuit is reconfigured by the opening circuit breaker X420. On SGT 1

ferroresonance would occur.


53

Figure 3-4 Single line diagram of the Brinsworth/Thorpe Marsh circuit arrangement [14]

[16] was published by Jacobson D.A.N. in 1995, the ferroresonance occurred in Dorsey

HVDC converter station, where 230 kV ac bus is comprised of four bus sections on

which the converter valves and transmission lines are terminated. The configuration of

the circuit is shown in Figure 3-5. Firstly, bus A2 was removed from service to

commission replacement breakers, current transformers and to perform disconnects

maintenance and trip testing. After approximately 25 minutes, a potential transformer

(PT) failed catastrophically causing damage to equipment up to 33 m away. The

switching procedure resulted in the de-energised bus and the associated PTs being

connected to the energised bus B2 through the grading capacitors (5061 pF) of nine

open 230 kV circuit breakers. A station service transformer, which is normally

connected to bus A2, had been previously disconnected. A ferroresonance condition

caused the failure of one PT.

Figure 3-5 Main circuit components in Dorsey Converter Station [16]

SGT1

Thorpe Marsh

400 kV

T10 OPENX303 OPEN

Brinsworth

275 kV

SGT2

X420 POW

Switching

Cable 170 m

Cable 170 m

X103

CLOSED

X113

CLOSED

Transmission Line-Side A

Transmission Line-Side B

Dorsey Converter Station Bus

B2 A2

Equivalent source:

Z1=0.212+j*4.38 Ω

(12000 MVA)

Z0=0.307+j*0.968 Ω

Grading

Capacitance

(325-7500 pF)

SST

PT1

PT2

AC filters

(755 MVAr)

Bus

Capacitance

matrix

Stray Capacitance

(4000 pF)


54

Literature [48] described a ferroresonance phenomenon in a 12 kV distribution feeder

connected to a station service transformer (Dyn connected transformer) and

underground cable terminated with riser pole surge arrester. The circuit and the surge

arrester exploded are shown in Figure 3-6. Ferroresonance circuit was formed when

switching operations were carried out by firstly transferring the customer loads to

another feeder via closing the tie switch, secondly opening the circuit breaker which is

the one yellow marked at the feeder and finally opening the disconnector switch.

Figure 3-6 A simplified one line diagram in which the riser surge arrester Riser pole exploded [48]

The incidence of MOV arrester explosion quoted in [17] is concerned with a shopping

mall supplied by a 34.5 kV distribution system via cable-connected pad-mounted

transformer (Dyn connected transformer). The root cause of the occurrence of

ferroresonance is that one of the lines connected to the cable was open as a result of an

automobile accident which is shown in Figure 3-7. This in turn reconfigured the

network into ferroresonance susceptible circuit consisting of the line and cable

capacitance in series with the transformer core.

BAY2BAY1

Substation

BUS 2BUS 1

Opened

CB

Station Service

Transformer

112.5 kVA

350 m. Underground Cable

Arrester

9 kV. 10 kA

Disconnector

Switch

Loads

Tie S

witch


55

Figure 3-7 33kV cable-fed service transformer ferroresonance [17]

From all the cases introduced above, literature [13, 14, 41, 47] it can be noted that the

transformer connected to a de-energised transmission line running in parallel with one

or more energised lines and ferroresonance is due to the coupling capacitance between

the two nearby transmission lines. The energy continuing to sustain the ferroresonance

is supplied from the other transmission line by passing through the coupling capacitance.

In [16], the transformer is energised through the grading capacitance of circuit breakers,

and the energy passes through the grading capacitance to supply to the transformer and

sustain the ferroresonance phenomena. In [48], the transformer is supplied through a

long distance cable with very low resistance, it can then be sustained by the energy

transferring between the ground capacitance of the cable and non-linear inductance of

the transformer. In [17], this ferroresonance event occurred due to the open circuited

one phase of the three-phase transmission line. The transformer was not permanently

damaged, but the MOV arrester exploded.

3.2.2.4 Investigation method

Due to the development of numerical technology, more and more investigations are

being carried out using software modelling, but there are still some field tests being

carried out. Looking at the above literature mentioned from investigation method

perspective, most of the case studies follows the following procedure: ferroresonance

phenomena occurred, the data of the phenomena are recorded; and the modelling of the

system circuit is then carried out by using a proper piece of modelling software; once


56

the model is verified by the recorded data, then more case studies based on this

validated model, such as the parameters sensitivity studies, would be carried out.

In literature [41], the circuit was simulated by using EMTP. There are 18 transmission

lines coupled with one another which included two double-circuit 230 kV lines, and an

existing 500 kV line, and a future 500 kV line. The sensitivity simulation study was

carried out by changing the value of the resistive load so as to understand the situation

once the 115 kV circuit breaker is opened. Results show that the damping resistance (i.e.

load) can work quite well for damping the ferroresonance but it will worsen the

recovery voltage on the circuit breaker.

In literature [47], the model of the circuit was built in EMTP software and the analysis

is from the system operation point of view i.e. protection of the facilities in the power

grid to discuss the reconfiguration by the switching. Six potential phenomena were

discussed which included voltage unbalanced problems, residual load voltage problems,

ferroresonance problems, breaker recovery voltage problems, ground switch duty

problems and working ground problems. The mitigation method for each of those issues

has been concluded.

In literature [13], when the Big Eddy line was being prepared for line maintenance,

immediately before the line was de-energised, the transformer was connected to a load

which was 170 MW real power and 140 MVAR reactive power at the 230-kV bus. The

switching sequence was to first open the 525-kV circuit breaker at John Day, leaving

the transformer bank connected to the line. Secondly, 230-kV circuit breaker at Big

Eddy was opened. Nine minutes later the gas accumulation alarm relay operated on the

C-phase transformer and ferroresonance was estimated to last for about 5 minutes, but it

did not cause the transformer failure. The DGA test was conducted on the transformer

oil and Table 3-2 shows the gas analysis after the occurrence of the ferroresonance.

However, Table 3-2 does not give the gas volume in ppm and the sum of percentage of

the gases is not equal to 100%, nevertheless the main gases are carbon monoxide and

hydrogen.

Table 3-2 Dissolved gas analysis of the transformer [13]

Gas Type Content percentage

Hydrogen 22.2%

Methane 3.3%

Acetylene 0.2%

Carbon monoxide 32.0%

Carbon dioxide 10.0%


57

Through the dissolved gas analysis it was concluded that when the transformer is in

ferroresonance condition it is subjected to the issue of local overheating of parts by the

stray flux when the core is saturated, and also due to the overvoltage in ferroresonance

the transformer oil had the problem of partial discharge [49].

This heating may not cause serious damage in a few minutes but probably will do so if

the ferroresonance is allowed to continue being sustained without detection. The

simulation was carried out by using an electronic differential analyser (EDA) which is

an analog simulation method. Figure 3-8 shows the equivalent circuit of the

ferroresonance circuit. This ferroresonance occurred mainly due to the transmission line

coupling capacitance which can make the energy pass through to the disconnected

transformer.

Figure 3-8 Equivalent circuit of the transformer with the transmission lines [13]

In literature [14], the simulation analysis was carried out by using ATPDraw software.

The model is very similar to that in [13]; there are two main components which are the

coupling capacitance between the transmission line and the non-linear inductance of the

transformer. And the sensitivity studies were carried out by varying the transmission

line length and the switching time to look into their influence on the peak value of the

ferroresonance voltages and currents. The results show that the ferroresonance is a

stochastic function which really depends on the initial condition and the parameters in

the circuit system. In literature [32, 45], investigation of this case is continued; the finite

element model of the transformer was built in the attempt to understand the situation

inside the transformer. It was found that during the ferroresonance, the transformer

saturated in a cyclic way at different parts and the flux would be distorted; it is more

severe at the core bolt area, which would create the localized overheating of the core

bolt area.


58

And again in literature [16], it also used EMTP software to build the network model and

did the analysis at the system level and a mitigation method was given in this paper.

This ferroresonance occurrence is mainly because of the high grading capacitance value

of the SF6 circuit breakers and the energy can pass through the grading capacitance to

the transformers PT1 and PT2. The ferroresonance has two periods; one is the chaotic

mode which is determined by the breaker opening times, pre-switch voltage and the

exact values of all parameters in each phase; the other one is the steady state

fundamental mode and the overvoltage achieves 1.3 per unit of the normal peak value.

In literature [48], there is a surge asserter connected in the circuit; as we know that the

function of the surge asserter is to protect against the overvoltage; however the

overvoltage created by the ferroresonance occurred in such a way that, due to the

amount of energy passing through, the surge asserter is exploded. Two comparison field

tests were carried out by using the same circuit configuration but with two different

conditions, one having arresters installed and the other having no arresters. For the case

that had no arresters, the chaotic mode ferroresonance and sub-harmonic mode

ferroresonance occurred, having a 4.14 per unit and 2.69 per unit peak overvoltage

respectively. For the case that had arresters, only the fundamental mode ferroresonance

appeared with only 1.5 per unit peak overvoltage, but after around 30 seconds the

arrester of the one-phase exploded. This is due to the high energy and lower voltage of

the sustained ferroresonance passing through the arrester but without becoming fully

conductive.

3.2.2.5 Mitigation

There are several mitigation methods used widely in the power system to minimise

ferroresonance overvoltages and overcurrents.

In [41], due to the several transmission lines nearby, the coupling capacitor would

facilitate the occurrence of ferroresonance in one of the substations. In the mitigation

method used, a damping resistance load is added at the secondary of the transformer as

well as surge arresters to control the overvoltages.

In [47], the same reason as in [41], that transmission line capacitance coupling would

bring the transformer into ferroresonance; and in this paper there are several mitigation

methods proposed, which add resistance to the secondary of the transformer as the same


59

as that mentioned in the previous paper, add an individual circuit breaker instead of the

disconnector and use ground switching to pass all the energy through to the earth.

In [16], since the circuit breakers are upgraded from vacuum to SF6 circuit breaker, then

the grading capacitance would achieve up to 7500 pF. The high value grading

capacitance would allow the energy passing through from the source side to the

disconnected side and then the ferroresonance phenomena would occur. For the

mitigation of this case study, a 200 Ohm/phase damping resistor is installed on the

secondary side of the station service transformer to eliminate ferroresonance for faulted

and un-faulted bus clearing.

In [13], several mitigation methods were suggested which include transposing the

parallel transmission lines and reducing the coupling capacitance value; adding damping

resistance to decrease the trapped charge on the line; providing a delta winding for the

transformer for the zero-sequence current and trapping harmonics; grounding the Y-

connected HV windings through a resistor or closing the delta-connected tertiary

windings through a resistor; short-circuit any set of transformer windings; and adding a

circuit breaker to disconnect the transformer from the line. Adding a tertiary winding is

not an economical solution, but adding a switching resistance is the most economical

method to mitigate the ferroresonance. And the simplest and surest way to prevent

ferroresonance is to disconnect the transformer from the line soon after disconnecting

the transformer and line from the rest of the power system.

In [48], two mitigation methods were presented. First, the procedure of the switching

sequence, which is alternated between the circuit breaker and the disconnector switch, is

changed. This solution was proved by field tests and has no extra cost. Secondly, a

resistance load can be applied to the secondary side of the transformer, since the

resistance can dampen the energy, and in this case if the resistance load is more than 1%

of the transformer rated load, the ferroresonance can be avoided.

In [17], a few mitigation methods were given such as, installing a three-phase circuit

breaker at the front of the transformer; ensuring the transformer is loaded while being

switched off; and opening the three-phase circuit breaker simultaneously.

To summarize the mitigation methods in the literature; several common methods are

proposed which are: adding a damping resistance to damp the ferroresonance

phenomena in a short period, controlling the circuit breaker opening time in order to


60

control the initial condition to minimize the ferroresonance magnitude and adding an

extra circuit breaker before the transformer.

3.3 Power system natural transient---GIC

3.3.1 Background

The influence of geomagnetic storms on the earth has been recorded for 162 years. The

first geomagnetic storms affected telegraph systems in 1847 in England. They

occasionally struck the few telegraph lines which were between Derby and Rugby,

Derby and Birmingham, Derby and Leeds and Derby and Lincoln; the storms lasted for

a few minutes to one or more hours [42]. Then in September 1859, it was found that

telegraph lines between Boston and Portland were able to disconnect their batteries and

“for more than one hour they held communication with the aid of celestial batteries

alone” [21, 50].

The influence of geomagnetic storms not only affected telegraph systems, but other

systems too, such as radio communication systems, pipeline systems [21, 51, 52], power

system and so on.

From the early 1940s it was found that the large transient fluctuations in the earth's

magnetic field can cause power system disturbances. These large transient fluctuations

are due to geomagnetic storms, triggered by solar winds. The first record of the

magnetic storms influence on power systems was in 1940 by Davidson, where there

were tripping transformer banks in northern USA and Canada due to the voltage dips

and the increase of reactive power consumption. And the worst event happened in

March, 1989 in Canada; the power system experienced one of the most severe

geomagnetic storms. The GIC saturated the transformer iron core on the Hydro-Quebec

power system and then the whole system blacked out [53, 54]. When the transformer

iron core saturated, it would be the source to generate harmonics and then caused the

tripping of static VAR compensators. This led to voltage fluctuation and power swings

that caused a trip out of the lines from James Bay and the collapse of the system [54].

Several transformers had over 100A geomagnetically induced current passing through

the neutral point of the transformers.


61

During magnetic storms, geomagnetically induced currents are produced in the power

system, entering and leaving the system through grounded neutrals of wye-connected

transformers. The GIC in a particular transformer can be many times larger than the

RMS value of the ac exciting current, resulting in severe half-cycle saturation with a

number of associated problems. One of these problems is the increased reactive power

demand of the transformers, which occurs in the system widely, and can be of sufficient

magnitude to cause intolerable voltage drop at points on the system.

3.3.2 GIC effect on power system

3.3.2.1 Effect on transformer

GIC can enter the grounded neutral of the Y-connected power transformer windings and

pass to the transmission line. GIC divides equally among the three phases and biases the

excitation characteristics of the transformer. It only takes low levels of GIC to drive the

transformer into half-cycle saturation because the transformer is usually designed to be

near saturation during normal ac operation.

Transformers use steel in their cores to enhance their transformation capability and

efficiency, but this core steel introduces nonlinearities into their performance. Common

design practice minimises the effect of the nonlinearity while also minimising the usage

of core steel materials. Therefore, transformers are usually designed to operate over a

predominantly linear range of the core steel characteristics. For the generator

transformer, they usually work at the point of 1.7T (the knee point of the core steel is

1.75T), because the load will not change much; for the transmission level power

transformers, they work in the range of 1.6-1.65T; and for the distribution level

transformers, they work at 1.5T, due to the frequent change of load hence the variation

of voltage.

In Chapter 2, it was introduced that when a transformer is half-cycle saturated, the

magnetising current is increased significantly. The copper loss and the core loss would

increase extensively. Depending on the transformer design and core structures, there is a

sequence which describes from the low to the high sensitivity for the transformer facing

the GIC events:


62

three-phase core form three-limb core

three-phase core form five-limb core

three-phase shell form seven-limb core

three-phase shell form conventional core

single-phase shell or core form

Because of the extreme saturation that occurs on one-half of the cycle, an extremely

large and asymmetrical exciting current is now drawn by the transformer. Spectrum

analysis reveals that this distorted exciting current is rich in even as well as odd

harmonics. Since the exciting current lags the system voltage by 90 degrees, it creates

reactive power loss in the power system. Under normal conditions, this reactive loss is

very small. However, the several orders of magnitude increase in exciting current under

half-cycle saturation and also results in extreme reactive-power losses in the transformer.

The large reactive power loss contributes to a dangerous drop in system voltage, and the

supplied harmonics create the potential for system relaying problems.

In addition to the power system being affected in terms of harmonics and reactive power

demands, the transformer itself can be severely stressed by this mode of operation. With

the magnetic circuit of the core steel saturated, the magnetic flux will flow through

adjacent paths such as the transformer tank or core-clamping structures. The flux in

these alternative paths can reach the densities found in the heating elements of an

electric kitchen stove [53]. The hot spots, that may then form, can severely damage the

insulation, produce gassing and combustion of the transformer oil, or lead to other

serious internal failures of the transformer [55].

3.3.2.2 Effect on generator

GIC is blocked from most generators because it is common practice to use a Δ-Y step-

up transformer connected to the generator. However, the generator is still subjected to

harmonics and voltage unbalance caused by transformer half-cycle saturation. It is

possible that the even harmonics could cause excessive heating in the rotor end rings

and the positive sequence harmonics could cause mechanical vibrations. The heating

potential of harmonic and unbalanced stator currents is approximately proportional to

the root of the frequency, in the rotor reference frame, and to the magnitude of the

current squared. The heating value of the harmonic currents can be related to an

equivalent negative-sequence fundamental current. Conventional negative-sequence

relays for generator protection are designed to respond to fundamental frequency

Low

High


63

imbalance. They may respond improperly or not at all to harmonic currents during the

GIC events. Once the generator is tripped by the relay, the reliability of the power grid

would be decreased, and in the worst scenario leads to a whole grid black out [56].

3.3.2.3 Effect on protective relaying

There were an unusually large number of false trips and some equipment damage during

the March 13, 1989 geomagnetic storm. It became evident that the belief that only the

extreme northern transmission is affected by geomagnetically induced currents (GIC) is

false [57].

None of the previous magnetic storms had ever caused as many incorrect relay

operations as in this storm. The North American Electric Reliability Council reported 30

automatic operations during a two-day period. The most obvious change in the field of

protective relaying is the increased use of electronic relays. Some of the electronic

relays measure the peak values of the currents and are sensitive to harmonics. In the past,

most protection schemes were based on electromechanical relays, which measured the

effective values of the currents. During magnetic storms, when the harmonic content on

the system increases substantially due to the half-cycle saturation of power transformers,

the peak measuring relays operate at a 20-30% lower effective current than

electromechanical relays. A peak measuring electronic overcurrent relay triggered one

major disturbance during the March 1989 storm [53]. By increasing the settings of the

peak measuring relays to accommodate the higher harmonics during GIC conditions,

the risk of false trips can be reduced, but concerns remain that this will degrade the

protection.

Another factor is the increased dependence of power systems on reactive power (VAR)

compensators and shunt capacitor banks for voltage control. Many of these shunt

capacitors are grounded and protected against unbalance with neutral overcurrent relays.

These banks are vulnerable to false trips during geomagnetic storms because the

capacitor exhibits low impedance to harmonics. Zero-sequence harmonic and

fundamental voltages result in a neutral current, and can trip the bank. Zero-sequence

harmonics are not limited to the triple orders when three-phase transformer banks are

saturated by GIC [22].

In an electromechanical relay the energy from the GIC turns the disc. In a 1980s

electronic relay the peak value of the current signal divided by root two is used to


64

operate the relay, consequently the operating behaviour is different to an

electromechanical relay. In a 1990 – 2010 relay the operating signal is the Fourier

extraction of the 50 Hz component of the current signal, consequently this behaves

differently to an electromechanical or electronic relay.

3.3.2.4 Effects on communications

In addition to the disruption of power transmission, solar phenomena can interfere with

utility communication systems. Utilities use many different types of communication

media, including wire line facilities, radio systems, satellite communications, and fibre

optic systems. Some of these can be affected by various solar phenomena. Solar

emissions (both radiation and solar wind) cause ionization of the earth's upper

atmosphere (the ionosphere) and the solar wind particles cause perturbations to the

earth's magnetic field. The ionospheric effects result in changes to propagation

characteristics of radio waves, while the magnetic effects cause disturbances to wire line

facilities [57].

The ionosphere is responsible for the reflection of radio waves upon which long

distance High Frequency (HF) communication relies. Its characteristics are also

responsible for the lack of reflections upon which Very- and Ultra-High Frequency

(VHF and UHF) and microwave communication rely. Solar disturbances can result in

increased absorption and fading of HF signals and in unwanted reflections of VHF,

UHF, and microwave signals.

Power line carrier systems are impacted by GIC because of the harmonic currents

generated by transformer saturation. These same harmonic currents can also cause

secondary interference to adjacent wired communication facilities by magnetic

induction. The least solar impact is felt by fibre optic communication systems. The only

known interfering mechanism is the potential disruption of fibre optic system power

supplies caused by GIC-induced currents on metallic conductors used to provide power

[57].

3.3.3 Historical events

There are some real cases of the influence made by geomagnetic storms on the power

systems. The following sections detail the case studies.


65

3.3.3.1 Worldwide GIC events

Geomagnetic effects on ground-based electrical systems have been observed for over

150 years. Table 3-3 shows the historic of the events that happened worldwide.

Table 3-3 GIC events reported in the worldwide

Date Location Effects Detail

24th

Mar,1940

North

America

and

Eastern

Canada

Communicati

ons

Radiotelephone circuit, service to ships at

sea, along distance land telephone and

teletype [20]

Power system

10 power systems in eastern Canada and

northeastern US: voltage dips (up to

10%), transformer banks tripped, large

increases or swings in reactive power,

transformer fuses blow in distribution

network(2400/4150V) [20]

22nd

Sep,1957

North

America Power system

230kV CB tripped due to third harmonic

increased currents produced by

transformer saturation [58]

10-11 Feb,

1958

North

America

(Ontario,

Toronto)

Power system

Large reactive power flows, two

generation transformers simultaneously

tripped, temporary blackout [59]

Swedish Power system

Power supplies of repeater station fuse

blowing [60]

13th

November,

1960

Swedish Power system

30 circuit breakers tripped

simultaneously [58]

4th

August,

1972

North

America Power system

three transformers tripped, a capacitor

bank relayed off [61]

Canada Power system

increasing reactive power demanded and

the voltage drop, and one of the

communications cable had outage [61]

British

Columbia

Hydro

Power system A 230 kV transformer exploded [61]

19th

December,

1980

St. James

Bay,

Canada

Power system A 735 kV transformer failed [62]

13th April,

1981

St. James

Bay,

Canada

Power system A 735 kV transformer failed [62]

April 1986 Canada Power system 749-km 500-kV transmission line tripped

[20]

On 13th

March,

1989

Canada Power system

SVC's tripped out, voltage drop, the

frequency increased, transmission line

tripped, blackout; transformer, surge

arrester, shunt reactor failed [63]


66

It can be seen from the table that, most events under studies are the ones that happened

in North America and North European countries. Most literature [20, 59-64] is from

North America, some is from Northern Europe and one case is from South Africa. The

reason that North America investigated the GIC is due to the higher voltage level long

distance transmission line and also because the grid there is much more complex, i.e. a

substantial number of components and many different designs working together. The

consequences of the GIC events in North America include: failed communications

system; voltage dip; increases or swings in reactive power; fuse blow in the low voltage

grid; relay misoperation tripping the circuit breaker then tripping the lines, generators,

transformer banks, power transformers and SVC. The most severe consequence is that

the power transformers exploded and failed. For the North European countries, due to

the high latitude, over thirty circuit breakers were tripped simultaneously and it caused a

blackout lasting about 20-50 minutes [20]. For South Africa, where the ambient

temperature is much higher than that of North American and North European countries,

although there are no direct transformer failure cases, 15 transformers were damaged

after a few months of the GIC, one of which was beyond repair [64].

3.3.3.2 UK GIC events

The power transmission and distribution network of the UK experienced significant

GIC effects during past geomagnetic storm events; Table 3-4 shows the events over the

past years.

Table 3-4 GIC Events reported in UK

Date Location Effects and Detail

13th Jul,

1982 Scotland Voltage dip [65]

20th

Oct,

1989

England and Wales

(Norwich Main in East Anglia,

Pembroke in Wales, Indian

Queens in Cornwall)

Transformer neutrals vary from +5 A to -

2 A, harmonic content increased, and two

transformers failed [65]

8th-9th

Nov,

1991

Harker in the north of England Harmonic content increased [65]

23rd

Oct,

2003

Scottish Border

42 A flowing to Earth in a single

transformer at east-west 400 kV power

line [66]


67

It can be seen that similar effects were reported such as voltage dip, increased harmonic

content, and failed transmission transformers. On 13th-14th July 1982, the South of

Scotland Electricity Board reported a voltage dip caused by geomagnetic storms [65].

On 20th October, 1989, the transformer neutral current varied from +5 A to -2 A at

Norwich Main in East Anglia, Pembroke in Wales, and Indian Queens in Cornwall for

ten minutes. Two identical 400/132 kV, 240 MVA transformers at Norwich Main and

Indian Queens failed, the voltage dips on the 400 and 275 kV systems were up to 5%;

and very high levels of even harmonic currents were experienced due to transformer

saturation by the geomagnetic storms [65]. On 8th-9th November, 1991, at Harker

substation in the north of England measurement on one of the transformers showed that

the harmonic content increased due to a geomagnetic storm [65]. On 23rd October,

2003, one of the 400kV transmission level transformers, near to Eskdalemuir

observatory was measured with a GIC current of 42 A [66].

A summary of the effects of GIC on the power systems in the UK was written by I.

Arslan Erinmez from National Grid Company, as described below: huge reactive power

swings of around 50–70 MVAR per generator and operation of generator negative

sequence current alarms; there are voltage dips on the 400 kV and 275 kV transmission

level system up to 5% and the distribution level system from 5% up to 20%; there are

DC currents passing through the neutral point of a transformer, transformer saturation,

local overheating inside the transformer. This created a high level harmonic content on

the transmission system and active and reactive power swings between England and

Scotland [67].

3.3.4 Studies on transformer responses to GIC

In this section, the transformer saturation mechanism is specifically described in

addition to the saturation time calculation. Besides, the effects of GIC on different

transformer structures are also compared from single-phase banks to a three-phase

transformer. A brief introduction to harmonics issues is then presented.

3.3.4.1 Transformer saturation equilibrium and saturation time

The quasi-dc earth-surface voltage difference, applied to the power system via the

grounding points by the geomagnetic disturbance, initially appears across grounded-

wye transformers. Because transformer flux is the integral of the applied voltage, the


68

flux has a sinusoidal component proportional to the ac voltage, lagging by ninety

degrees, plus a steadily-increasing quasi-dc offset.

As the flux offset increases, the crests of the flux waveform exceed the saturation level

of the transformer core resulting in essentially unidirectional exciting-current pulses.

The exciting-current pulses have a dc component, as well as fundamental and harmonic

components, and the voltage drop resulting from this dc flowing through the system

resistance reduces the dc voltage applied to the transformer magnetising inductance.

The flux offset continues to increase at a steadily decreasing rate until the voltage drop

equals the dc earth-surface voltage difference and there is no longer dc voltage across

the transformer. When this dc voltage equilibrium is reached, the flux offset ceases to

increase and the half-cycle saturation continues as long as the dc source is present. The

earth surface voltage difference, divided by the total resistance, is identical to the GIC

current flow. Thus, the flux offset appearing in a transformer during a geomagnetic

disturbance is that offset which results in a dc exciting-current component exactly equal

to the net GIC flowing into the transformer terminals, as is necessary for Kirchhoff’s

Laws to be satisfied for the direct-current component.

The offset saturation equilibrium is demonstrated by the EMTP simulation in [68],

shown as in Figure 3-9. In this simulation, a step dc voltage of superimposed on a per

unit nonlinear inductor model which is also excited by a one per-unit ac voltage source.

The nonlinear inductor, which represents a transformer's magnetising reactance, is in

series with a 0.015 per unit resistor.

Figure 3-9 Transformer flux and exciting current response to step dc voltage [68]

At t = 0, application of the dc step source begins upward ramping of the sinusoidal flux

peaks. As the positive peaks of the flux reach the saturation level, unidirectional

exciting-current pulses result. At the end of this simulation, equilibrium is reached and


69

Fourier analysis of the last cycle reveals an exciting-current dc component of 0.1 per

unit, which is equal to the 0.0015 per unit dc voltage divided by the dc resistance.

The important result verified by this simulation is that, in the steady state, the

transformer will saturate only to the degree required for the dc-component of the

exciting-current to be exactly equal to the GIC. Thus, the steady-state saturation

condition during GIC excitation can be defined by the following boundary conditions:

DC exciting-current component equal to the per-phase GIC

Sinusoidal flux is defined by the ac voltage, including harmonics distortion

components

The time for DC current to reach a steady state in the circuit, i.e. saturation time, was

calculated by the equation below and proposed in [69].

2/31/2

0 0

0 0

2 ( )1 /( ) 2.23

2 31 /

g sat p

p N

V V f M LVi It s

f K K R Ri I

(3.1)

Where,

Vg, the peak phase-ground voltage when the transformers operate at the knee point;

V0, the peak phase-ground operation voltage;

K0, the dc voltage;

/i I , the ratio between the mean current reached and the final dc current;

Msat, the inductance of the magnetising circuit in saturation;

Lp, the total inductance in the primary circuit;

Rp, the total resistance in the primary circuit;

RN, the grounding resistance;

These results prove that the equation can be used to evaluate the transformer saturation

time when a GIC voltage is applied. On the whole, it gives a rather shorter saturation

time than the real one, except when the transformer is near to the total saturation stage.

In this case, the formula may show a slightly longer time than the reality.

Moreover, [69] compares the saturation condition of a no-load transformer with a

different winding connection. The presence of a delta connection can significantly

prolong the time the saturation phenomenon takes to reach the steady state. This means


70

that the saturation time can be very long on the power system (in the order of 1 min or

more) when the dc voltage applied to the magnetising inductance is very low.

3.3.4.2 Effects of different transformer core structures

Since the 1990s, many researchers have investigated the effects caused by different

transformer core structures, e.g. [68, 70-72]. The relevant research work can be divided

into two main parts: transformer magnetic circuit modelling; calculation with the aid of

finite-element analysis (FEA) and experimental tests.

For the transformer modelling, there are several different types of model widely used. In

this section, we focus on lower frequency transient transformer modelling. As we know,

the transformer core will be represented by the low frequency transformer model; and

the transformer core characteristic would be much more important than anything else in

order to model the transformer behaviours accurately.

a) Transformer magnetic circuit modelling

For single-phase transformer, [68] assumed that the winding is extended to the full

height of the core window. Figure 3-10 shows the cross-section of a single-phase

transformer with the gross flux paths identified and its lumped model of the magnetic

circuit with reluctances has a one-to-one correspondence with the flux paths. This

circuit may be reduced to a flux source, representing the coil, in series with a single

nonlinear reluctance. The unsaturated reluctance of this model is 0.015 per unit, and the

fully-saturated reluctance is equal to the reciprocal of the per unit air-core inductance.

The per unit flux base is the crest fundamental frequency flux magnitude required to

induce a rated crest flux in the winding, and base MMF is created by a rated crest

current through the coil. Thus, the base reluctance is the ratio of these two bases.

Figure 3-10 Single-phase transformer model [68]


71

Figure 3-11 represents the magnetic circuit used to analyse three phase five-limb core-

form transformer, RL represents the main core limbs for each phase, RY the upper and

lower yokes interconnecting the main limbs, and ROL represents the outer limbs. The

yokes are assumed to have 70% of the core-steel-sectional area of the main limbs, and

the outer limbs have 50% of the main-limb cross section. R1 and R2 here are the non-

core flux path inside each coil, and the non-core return path respectively.

Figure 3-11 Three-phase five-limb transformer model [68]

However, the model limitations due to approximation still need to be noted: the

complex 3D magnetic fields are represented by lumped element circuits, which do not

precisely account for variations in flux density along the length of a core limb or for the

effects of winding thickness; inter phase magnetic coupling of the winding coils via

paths outside of the core are not considered; the magnetic effects of tank walls,

structural members or flux shields are not specifically represented.

P. R. Price built a complete electrical and magnetic circuit diagram for three-phase

three-limb star-auto transformer with tertiary including the tank shunt effect, as shown

in Figure 3-12 [70].

Figure 3-12 Complete electrical and magnetic equivalent circuit diagram for three-phase three-limb

star-auto transformer with tertiary, Z0 path and tank shunt [70]


72

It can be seen that the electrical circuit includes the AC source, line impedance and

primary & secondary side winding impedance; and the magnetic circuit includes three-

limb transformer core, the zero sequence air return path and tank path in parallel

connected with the transformer core. According to the model, a numerical solution is

then sought for the fluxes and currents by using an iterative Newton-Raphson

minimisation routine. Such a representation is ultimately the best for transformer

modelling, and ideally should be coded into a stand-alone transformer model and be

used in ATP software.

b) Transformer finite element model

The finite element method, its practical application often known as finite element

analysis (FEA), is a numerical technique for finding approximate solutions of partial

differential equations (PDE) as well as of integral equations. The solution approach is

based either on eliminating the differential equation completely (steady state problems),

or rendering the PDE into an approximating system of ordinary differential equations.

Computer technology is advancing all the time, computing speed has improved in recent

years, the finite element method in engineering design and analysis has become more

widespread, and has become the most effective way to analyse engineering issues and to

solve complex computational problems.

Although different physical properties, specific formula and mathematical models of the

different problems under study are used in the finite element method, the basic steps for

solving them are the same: geometry, mesh, solution and post process. In short, the

finite element method can be divided into three steps: pre-treatment, processing and

post-processing. Pre-treatment is building a finite element model to complete mesh;

processing uses the related equations and iterative algorithm to obtain results; post-

processing is the collection and the processing of results.

[70] employed a time-stepping FEA program to directly derive the losses in various

transformer components due to the complex flux waveforms, without the need to

resolve them into individual harmonics. It analysed the magnetic-field plot under

saturated conditions in the solid conducting structural components which comprise

magnetic and nonmagnetic materials. These include tanks, core clamps, flux shunts and

core bolts.


73

The escape of flux into the tank base and the concentration of flux and current is clearly

evident from Figure 3-13, which depicts the situation of a section through a core return

limb adjacent to a tank base and wall where a normal magnetising flux would be

contained within the core dimensions. Rather than showing the main flux in the core

which is multiple orders of magnitude higher than the leakage flux, the figure shows

only the flux leakage out of the transformer core.

Figure 3-13 FEA plot of the flux paths for the tank base and return limb of a one-phase unit of an

800 MVA generator transformer at the point in time of peak magnetising current at 340 A/phase

for a GIC of 50 A/phase [70]

Besides, the important case of a core bolt is also shown here as Figure 3-14, revealing

how the flux path through the bolt is concentrated to the outer surface during a 50 A

GIC situation.

Figure 3-14 FEA plot of flux density through a core bolt [70]

Table 3-5 outlines the losses and temperature rises for the single-phase generator and

autotransformer examples cited in [70]. It must be noted that while the losses quoted are

those for an entire component, the temperature rises are based on much localized


74

heating of the components at no load as revealed by the FEA studies. Under load, the

extra losses and temperature rises increase the risk of gassing.

Table 3-5 Losses and temperature rises for one phase of an 800-MVA generator transformer with a

GIC of 50 A/phase and a 240 MVA three-phase five-limb auto transformer with a GIC of 100

A/phase, both for duration of 30 min, and for the condition of no load. Shunts for the five-limb auto

are assumed to be wrapped in 2 mm thick pressboard [70]

Single-phase Transformer Five-limb Auto-Transformer

Part Loss (W) Temp. ( ) Loss (W) Temp. ( )

Core Bolt 140 160 230 240

Tank 48000 25 53000 150

Tee Beam - - 182000 150

Shunt 5000 15 500000 500

After that, [70] gives Table 3-6 to indicate the risk of tripping arising from Buchholz

operation due to gassing for different core structures of three phase with separate delta

and steel tank.

Table 3-6 Assessment of acceptable GIC current levels and risk for duration from 15 to 30 min

Transformer Core Type GIC Current (A/phase)

5 10 25 50 100

Three-limb without core bolts None Low Low Low Possible

Three-limb with core bolts in limbs

& yokes Low Low Low Low Possible

Five-limb without core bolts in

yokes or limbs Low Low Low Possible High

Five-limb with core bolts in yokes &

limbs Low Possible Possible Possible High

Three single-phase transformer bank

without core bolts yokes or limbs Low Low Possible Possible High

Three single-phase transformer bank

with core bolts in main and return

limbs

Low Possible High High High

In [72], S. Lu examined the single-phase and three-phase design transformers under

GIC situation using the FEA method. The conclusion is that a transformer core

saturation pattern is determined by both the core configuration and the core limb

dimensions. The effects of different ratio of the side limb and main limb cross sectional

areas ,which are 1:1, 2:1, (1/2):1, (1/4):1, on a single-phase three-limb transformer core

structure are discussed. It was concluded that under the same DC level, the larger side

limb cross sectional area results a lower DC flux density while there is a higher DC flux

density in the main limb. Comparing the main limb saturation level, the one with the

largest side limb will saturate first; comparing the side limb saturation level, the one


75

with the smallest side limb will saturate first. For the cross sectional area ratio of (1/2):1

for the side limb and main limb, the entire core will reach saturation point at the same

time.

According to the results of FEA for the three-phase five-limb, the three-phase seven-

limb core type structures and the shell type three-phase three-limb, [72] gives the order

of increasing susceptibility to GIC in terms of core structure: three-phase five-

limb three-phase seven-limb shell type three-phase three-limb.

The problems were also structured by experiment. In [71], N.Takasu first verified that

single-phase three-limb cores are most susceptible and three-phase three-limb cores

least susceptible by studying using three typical small-scale models.

c) Harmonics issues

Harmonic current will inevitably occur during transformer saturation due to GIC. Since

harmonics will influence the operation of system, it is not surprising that many

researchers have been studying this topic. [68] argues that transformer core topology

has a major impact on the magnitude and characteristics of exciting currents resulting

from GIC (Figure 3-15). Three-phase shell-form and five-limb core-form transformers

exhibit profound magnetic imbalance when GIC is applied, resulting in unbalanced

phase exciting currents. The resulting negative- and zero-sequence currents can

adversely impact system relaying and generators. Based on the study of a detailed

lumped magnetic circuit model of a single phase shell form transformer developed in

[73], some observations are made:

The RMS value, the DC component, and the fundamental component of

excitation current all increase monotonically with respect to the GIC level, with

the exception that the fundamental will stay at a fixed level after certain high

GIC value.

All harmonics except the DC and fundamental components will disappear

eventually with the increase of GIC.


76

Figure 3-15 Exciting-current harmonic sequence components [68]

In addition, Figure 3-16 explores the relationship of the exciting current harmonics and

GIC for transformers with different types of core design [74].


77

Figure 3-16 The relationship of the exciting current harmonics and GIC for transformers with

different core design [74]

3.3.5 Mitigation

A number of devices have been developed to block the flow of GIC, such as series

capacitors, dc bucking motors and resonant converters. Only some of them have been

proved to be applicable.

In this section, an overview of their design concepts, technical advantages and

limitations will be given by contrasting them with the performance requirements of an

ideal blocking device; some of the design concepts will be further illustrated with more

detail.

In general, the ideal blocking device should be the one that blocks all GIC, and

introduce no complications to the normal ac operation of the system. As for system

performance, the device should not cause the following concerns: degradation of system

operation reliability, strength and flexibility; substantive increase of stress to any system

component. The device itself is required to perform a continuous operation in the


78

system and should be reliable during the following conditions: normal and abnormal

steady-state conditions; transient overvoltage contingencies and system faults [75].

There are two types of design concept: passive and active. Passive devices were

designed to block or restrain the flow of GIC current by using resistors or capacitors.

For active devices, they were designed to counteract the GIC current by using an

adjustable current source which can generate a reverse dc current or a reverse

magnetomotive force.

One of the common passive devices is the transmission line series capacitor which can

effectively block the flow of GIC in a specific transmission line. However, the frequent

application of autotransformers complicates the situation, because this type of

transformer allows the GIC to have different flow through the series and common

windings. Hence, the transmission line series capacitor will block the GIC at one

voltage level but will still allow the GIC to flow unimpeded through the other side.

Bearing such a concern in mind, the idea of blocking the GIC current at the transformer

neutral would be more attractive [76]. Passively, this could be achieved by attaching

either resistor or capacitor to the transformer neutral. Actively, this might be achieved

by connecting a separately excited dc motor between the transformer neutral and ground

to inject a reverse dc current.

Apart from blocking the GIC outside the transformer, a method to place an auxiliary

winding on the transformer closed-delta winding has also been proposed. The auxiliary

winding is connected to a current source which can be controlled to cancel the

magnetomotive force generated by the GIC flowing through the high-voltage windings

[77].

The above design concepts should be thoroughly justified by the performance

requirements. Meanwhile, they should be cost-efficient. Table 3-7 is a list of technical

advantages and limitations by contrasting all the design concepts with the performance

and cost requirements.


79

Table 3-7 Advantages and limitations of mitigation devices

Advantages Limitations

Transmission line

series capacitors

[78]

Standard product

and mature

technology

Expensive and difficult to achieve system-

wide application;

May increase system susceptibility to sub-

synchronous resonance;

Adjustable current

sources [78] [79]

Least intervention

to system

grounding

Difficult to achieve total elimination of GIC;

Low efficiency: the dc current generate from

the current supply could be more than ten

times larger than the compensation current;

Capability to withstand system transients is

questionable;

Require precise measurement of GIC

direction and magnitude;

Neutral series

grounding

resistance [80]

Stable and reliable

passive device;

weakly dependent

on the network

configuration;

Only compensate part of the GIC current;

Calculation of appropriate resistance value

requires consideration of geological

structures, soil characteristics and

interaction with pipeline networks, which

also vary with transformer locations;

When the resistance value is big, it will

affect the protection settings;

Neutral series

grounding

capacitor [76, 81,

82]

Completely block

out all the GIC;

Standard product

and mature

technology;

It may hinder the ability of relay systems to

detect and discriminate fault currents;

Careful design of the bypass systems is

needed to achieve insulation coordination

and tolerate worst fault current;

May lead to ferroresonance condition;

Unlike neutral blocking schemes that install blocking devices between transformer

neutral and the ground, the one proposed in [77] suggests mitigating the GIC inside the

transformer. The idea is suitable for those transformers already equipped with a closed-

delta winding, as present on generator step-up transformers. This closed-delta winding

allows the use of a very moderately rated auxiliary winding and controlled current

source. The diagram shown in Figure 3-17 indicates the potential location of the

auxiliary winding.


80

Figure 3-17 GIC mitigation scheme inside power transformer [77]

One study was centred on a step-up transformer rated 525/22.8 kV, YNd, banked from

three single-phase units each rated above 300 MVA. The high voltage and auxiliary

windings have about 1000 and 100 turns respectively. In order to compensate the GIC

which is averaging 10 A in the neutral (over ten minutes), the auxiliary winding needs a

current rating of approximate 30 A to achieve an MMF balance in the core.

The location of the auxiliary winding interior to a delta winding has been evaluated in

[57]. It was found that the induced voltage is greater if the auxiliary winding is moved

up from its optimal position, and less if the auxiliary winding is moved towards the

geometric centre of the transformer.

To apply such a scheme, the capability of the auxiliary winding and the controlled

source used to compensate for GIC need to survive from fault, lighting, switching and

other transient conditions; however if they can succeed or not is still under investigation.

3.4 Discussion and summary

A brief description of switching transient and GIC phenomena in power systems is

given in this chapter. This is followed by a review of the historical research experience

including the waveform analysis, system parameter analysis and transformer saturation

analysis.

A literature review of transformer saturation is organised into two categories, which

result from operational transient and natural transient events, respectively.

As for the switching transients, energisation and de-energisation are represented by the

circuit breaker switching on and off. During these operations, the system network would

have transient states and the transformer could be saturated due to the sudden change

between two steady-state situations. Various investigation methods were used in this


81

field, such as simulations, field tests and validations. More importantly, if the

simulation model was verified by the field test results sensitivity studies were usually

conducted on the key parameters, to identify the worst scenario and so on.

On the other hand, in the field of GIC, researchers from two main fields (i.e. geology

and electrical power engineering) are involved. In this literature review, the electrical

power engineering perspective is mainly provided. The GIC events appeared in the

power system following the solar wind cycle which is normally about 11 years per cycle,

and it could bring operational issues and equipment issues. Various investigations were

conducted and they were mainly associated with power system operation, i.e. reactive

power consumption, voltage drop and protection mal-functions.

A transformer model was used as a tool to facilitate the system side of investigations,

and the transformers were normally modelled with some simply and rather crude

representations.

This research project focuses much more on the transformer itself. How to accurately

model the transformer structure, core and winding, and the transformer’s magnetising

current under ferroresonance and GIC are the main areas of focus for research.

This is particularly important since we know that all the issues in the power system side

related to transformer core saturation, are associated with the behaviour of the

transformer itself. As far as the simulation is concerned, once the transformer is

saturated, taking GIC as an example, how much reactive power is absorbed, how the

voltage drop is formulated and the consequences of affecting the stability of system, is

controlled largely by the accuracy of the transformer model.

In the following chapters, the research work on modelling transformer behaviours under

core saturation problems is described. Two types of models are developed to facilitate

the understanding and interpretation of the GIC and ferroresonance phenomena.

Chapter 4 Steady state magnetic circuit modelling for transformers

82

Chapter 4 Steady state magnetic

circuit modelling for transformers

From Chapter 3, it is known that transformer core modelling methods are essential for

the investigation to be carried out. The accuracy of the transformer model will mainly

determine the validities of the following study results. In this chapter, the work focuses

on transformer core modelling; using the mathematical method to represent the flux

distribution in different transformer core structures. The objects under study are three-

phase three-limb transformers and five-limb three-phase transformers.

Figure 4-1 shows the logic for the whole chapter.

Transformer model

Simple three-limb transformer core

model

Three-limb with return path

transformer core model

Five-limb transformer core

model

Validation by transformer open circuit test data

Comparison of structure effect on

flux distribution and magnetizing

current

Comparison of ratio of side yoke

and main yoke area effect on flux

distribution and magnetizing current

Use an artificial five-limb transformer core parameters

Use a real five-limb transformer core

parameters

Matched with the open-circuit test

data, ready to be used for GIC calculation

Comparison of different working

point effect on flux distribution and

magnetizing current

Build of a three-limb transformer core

model

Build of a three-limb transformer core

model


Balanced situation

Unbalanced situation


Comparison of ratio of side yoke

and main yoke area effect on flux

distribution and magnetizing current

(See in Appendix)

Figure 4-1 Flow chart of chapter 4’s work


83

4.1 Methodology of transformer core modelling

4.1.1 Three-limb transformer core model

4.1.1.1 Simplified three-limb transformer core model

In order to simplify the analysis, there are some assumptions made as follows: the

leakage flux is ignored; the main flux is uniformly distributed along the cross-section of

core; the influence of hysteresis, eddy current and core saturation are neglected; the core

joints are not considered; the three phases flux, ФA, ФB and ФC are sinusoidal and the

120˚ phase relationship to each other.

The instantaneous values of the flux at phase A, B and C are given by:

tmA cos,

)120cos( tmB ,

)240cos( tmC , where Фm is the

flux peak value in the main-limb of core.

The equivalent magnetic circuit of a three-limb transformer is shown in Figure 4-2. In

the figure, R is the reluctance, F is the magneto-motive force (MMF) and Ф is the

magnetic flux.

Figure 4-2 Equivalent magnetic circuit of three-phase three-limb transformer

In an ideal situation three-phase symmetrical fluxes give:

0 (4.1)A B C


84

Due to the structure of the three-limb transformer, the flux in the yoke area is equal to

that in the side limb. Since the fluxes applied at the limbs (ФA, ФB and ФC) are

sinusoidal, the fluxes at the yoke of the three-limb transformer are also sinusoidal.

4.1.1.2 Improved three-limb transformer core model

From the last section, the calculation of the three-limb transformer is quite

straightforward. However, this kind of model cannot be used for the calculation of a

saturation situation, because in this model there is no return path considered for the

saturated flux to escape. Therefore, an improved three-limb transformer core model is

presented here.

If the transformer works under a saturation situation, the fluxes, or at least some of them,

would leak out from the transformer core structure, and go through oil, the transformer

tank wall and other components.

In order to simulate the leaked flux, there are two return paths created in the model.

Figure 4-3 shows the improved transformer core model, in which the blue part

represents the transformer core and the green part represents the transformer tank and

oil gaps.

Figure 4-3 Three-limb transformer model with return path

It can be seen from the above figure, that the fluxes are not only going through the

transformer core structure, but also through the transformer tank. Figure 4-4 shows the

equivalent magnetic circuit of the three-phase three-limb transformer with return path.


85

Figure 4-4 Equivalent magnetic circuit of three-phase three-limb transformer with return path

For the circuit shown in Figure 4-4, four meshes are defined. Фlt, ФAB, ФBC and Фrt are

assigned to four meshes respectively with the flow direction being mirror symmetric of

the centre.

Kirchhoff Voltage Law (KVL) for magnetic field is applied at each mesh, one at a time,

employing the fact that in the direction of flux Ф the MMF drop across the reluctance is

ФR. The MMF drop across the reluctance is taken in the direction of the mesh flux. The

total MMF drops are set equal to the MMF rise across the MMF source. For example,

the MMF drop across Rlt is ФltRlt while across ROA is (Фlt – ФAB)∙ROA. The derivation of

the formula is presented as follows:

Since the mesh fluxes are given by Фlt, ФAB, ФBC and Фrt a set of four mesh-flux

equations can be written as:

lt ( ) (4.2)lt OA AB OA AR R R F

(2 ) (4.3)lt OA AB AB OA OB BC OB A BR R R R R F F

(2 ) (4.4)AB OB BC BC OB OC rt OC B CR R R R R F F

( ) (4.5)BC OC rt rt OC CR R R F

ФA

ФB

ФC

Фlt

ФAB

ФBC

Фrt

RAB

RAB RBC

RBC

FA FB FC

ROA ROB ROC

RLt RRt


86

Kirchhoff Current Law (KCL) for magnetic field is applied for the fluxes at the T-joint

of the circuit to derive, the following equations:

(4.6)lt A AB

(4.7)B AB BC

(4.8)rt C BC

From (4.6) to (4.8) under (4.1) condition, we can obtain:

(4.9)lt rt

Knowing lt rtR R due to the structure of the transformer core, and (4.9) indicates that

the flux flowing in the two side yokes is identical.

Based on (4.9), equations (4.2) to (4.5) are added up together, so the solution can be re-

written as:

2 2 0 (4.10)lt lt AB AB BC BC rt rtR R R R

This equation can be used as the Newton-Raphson condition for the calculation and the

calculation method will be presented in the following sections.

By using (4.6) and (4.8) to replace ФAB, and ФBC, (4.10) following (4.11) for calculating

the flux leaked to the tank can be obtained.

2 2(4.11)

2 2

C BC A ABlt

lt AB BC rt

R R

R R R R

Apply Фlt in (4.10) to (4.7), (4.8) and (4.9); we can obtain the equation for calculating

the flux at the main yoke of the core.

(2 )(4.12)

2 2

B BC rt C rt A ltAB

AB BC lt rt

R R R R

R R R R

Equation (4.11) and (4.12) give the basic equations to define the flux distribution in the

tank and the main yoke of the three-limb transformer.


87

The above equations are found to be in the form of reluctance and can be further

expanded using reluctancel

RA

. The expression of ltR , rtR , ABR , BCR can be

rewritten as follows:

2 2; ; ; (4.13)l t l t m m

lt rt AB BC

lt t rt t AB l BC l

L L L L L LR R R R

A A A A

From (4.13), (4.11) and (4.12) can be rewritten as follows:

2 cos( 240 ) cos( )

(4.14)2 2 2 2

om m

BC l AB llt m

l t m m l t

lt t AB l BC l rt t

L Lt t

A A

L L L L L L

A A A A

（）

2 2 2 2cos( 120 )( ) cos( 120 ) cos( )

(4.15)2 2 2 2

o om l t l t l t

BC l rt t rt t lt tAB m

l t m m l t

lt t AB l BC l rt t

L L L L L L Lt t t

A A A A

L L L L L L

A A A A

When (4.14) and (4.15) are obtained, all the flux distribution inside the transformer can

be easily calculated, which means the instantaneous value of the flux at all parts can be

obtained.

From these equations, it seems that the structure parameters of the transformer and the

materials' characteristics are dominating the flux distribution. For the structure, there is

the area of the main limb, yoke and the tank thickness and the length of the yoke, the

length between the core and tank and main limb; for the materials’ characteristics, there

is the varying permeability of the core material and the tank material.

4.1.2 Five-limb transformer core model

For the five-limb transformer core, the equivalent magnetic circuit is shown in Figure

4-5. As for Figure 4-4, R is the reluctance, F is the magneto-motive force (MMF) and Ф

is the magnetic flux in the figure.


88

Figure 4-5 Equivalent magnetic circuit of three-phase five-limb transformer

In the five-limb transformer, there is the low-reluctance return path for the unbalanced

flux to pass through easily. There is no need to build up the extra limb to model the

leaked out flux. The circuit shown in Figure 4-5 is almost the same as the improved

three-limb transformer; however, the difference is that there are two different types of

materials characteristics used in the three-limb transformer model. One of the material

characteristics is the core steel characteristic; and the other one is the transformer tank

material characteristic; in the five-limb transformer, it would be much easier, due to the

fact that all the materials are core steel.

Equation (4.16) is the final equation for the Newton-Raphson condition:

2 2 0 (4.16)ls ls AB AB BC BC rs rsR R R R

The flux can be calculated by using the same method as the previous section; the

equations are shown below, which are (4.17) and (4.18).

2 cos( 240 ) cos( )

(4.17)2 2 2 2

om m

BC l AB llt m

l t m m l t

ls t AB l BC l rs t

L Lt t

A A

L L L L L L

A A A A

（）

2 2 2 2cos( 120 )( ) cos( 120 ) cos( )

(4.18)2 2 2 2

o om l t l t l t

BC l rs t rs t ls tAB m

l t m m l t

ls t AB l BC l rs t

L L L L L L Lt t t

A A A A

L L L L L L

A A A A

ФA

ФB

ФC

Фls

ФAB

ФBC

Фrs

RAB

RAB RBC

RBC

FA FB FC

ROA ROB ROC

RLS RRS


89

4.1.3 Magnetising current calculation

The magnetising current of a transformer is provided by the manufacturer which is

shown in the certification test report of the particular transformer. As we know, the

magnetising current shown in the open circuit test report includes two parts of the

current, which are the current passing through the core resistance and the current

passing through the core inductance.

The open circuit test gives Rc and Xc which are core resistance and core inductance. This

test is performed by applying the rated voltage (Vs) to the low voltage side while leaving

the high voltage side open circuit. Either side may be used, but the voltage is normally

applied to the low voltage side to reduce the requirement for high voltage test

equipment. Assuming that the shunt impedance, which is the core impedance (Rc and

Xc), is much larger than the series impedance which is primary winding impedance (R1

and X1), the equivalent circuit model can be reduced to Figure 4-6.

Figure 4-6 Equivalent circuits with open circuit test

The values of Ir and Im can be calculated using the following formulas (4.19) and (4.20)

from the voltage (Voc), current (Ioc) and power (Poc) measured in the open circuit test.

2 2

m

/ 3 (4.19)

(4.20)

r oc oc

oc r

I P V

I I I

In addition, the open circuit test is normally carried out at the delta winding which is

normally for the lower voltage level in a transmission power transformer. So all the

magnetising currents measured are line currents.

Ir Im


90

4.1.4 Flux density calculation

From the analysis above, it is known that for a three-phase three-limb transformer under

balanced conditions, the computation of flux at the yoke is straightforward. However,

for the improved three-phase three-limb and three-phase five-limb transformer core

model with the non-linearity of core material being considered, the derived flux

formulas show that the magnetic flux calculation are complex. The flux distribution is

dependent on the permeability of the materials and the cross-sectional areas and the

length of the different parts of the transformer. MATLAB simulation will be involved to

calculate the flux density at any part of the three-phase three-limb and five-limb

transformer core structure.

Calculating the instantaneous flux density at any part of the three-phase three-limb and

five-limb transformer core structure is based on the equation BA

. Since the

permeability of the core varies with the flux density, the magnetic material is divided

into sections; it is assumed that each section has a uniform flux density.

If the MMF is set as F R Hl , (4.10) and (4.16) would become:

2 2 0 (4.21)

2 2 0 (4.22)

lt lt AB m BC m rt rt

ls ls AB m BC m rs rs

H l H l H l H l

H l H l H l H l

Significant work has been carried out with the intention to formulate a magnetisation

curve (B-H) representation that is simple and accurate, in order to simplify the

numerical modelling of the transformers. The non-linearity B-H curve can be

represented by a polynomial, which is used to fit the magnetisation characteristic to

provide more flexibility calculations. The magnetisation characteristic can be modelled

by a two-term polynomial relationship between the magnetic field intensity H and the

magnetic field density B:

(4.23)nH aB bB


91

The software called ORIGIN is used to process an array of data and fit it using the

formula as above. Due to the different designs of transformers produced during the

period 1950-today and by different manufacturers, the transformers being picked up in

this investigation used different types of core steels; the following data is supplied by

Japan Nippon Steel Corporation, Japan:

-5 2720.34 (4.55 x 10 ) (4.24)H B B

The curve fitting result is shown in Figure 4-7. Equation (4.24) presents the twenty-

seventh order polynomial representation of the magnetisation curve. This equation is

incorporated into MATLAB script (all the code and data are included in the appendix)

in order to find H that corresponds to the calculated B values. This analytical

representation enables the incorporation of the non-linear effects of the core into the

proposed analytical transformer core model.

Figure 4-7 Curve fitting result for Japan Nippon steel corporation materials

In addition, we need to understand that Figure 4-7 shows the core steel materials

characteristics. The transformer core structure is not only made of core steel material,

but also has air gaps between each lamination in the joint area. Therefore, as we know

the transformer core characteristic would be changed due to the air gap in the magnetic

circuit. Therefore the fitted curve needs to be further refined.

By using MATLAB, the flux density at each part of the transformer core is calculated.

The MATLAB programme is based on the flow chart that is shown in Figure 4-8. First,


92

input the basic parameters of the transformer structure; second, at each time step assume

an initial value for Ф1 and use (4.21) or (4.22) to control it by using the Newton-

Raphson iterative method. The accuracy can be controlled by the tolerance set for the

error and the fine time step.

START

Input transformer design data

The start time as 0

Calculate ФA, ФB,ФC in each time step

Initialisation Фlt value as the maximum flux value in the core

Calculate all the other part Ф value

Check the condition true/false

False

T=0.04s

True

Decrease Фlt value

END

True

False

Calculate the corresponding H value by using Non-linear B-H Curve

Increase time step

Initialize each parameter in the program

Figure 4-8 Flow Chart of the MATLAB programme


93

4.1.5 Curve fitting

There are two methods to model the transformer nonlinearity characteristics. One is to

use the three points of the transformer open circuit test data, and the other one is to use

the core steel material’s characteristics.

Using the three points to fit the transformer core nonlinear characteristic curve, the

accuracy cannot be guaranteed, since the data points are too few to accurately represent

the nonlinearity curve. However, the advantage of this method is that the core loss has

been considered and also the nonlinearity curve shows the characteristics of the

transformer structure.

Using the core steel material’s data to fit the core transformer nonlinearity characteristic

curve, the accuracy is far better than the previous method, because the data sheet of the

steel normally provides at least 10 points. However the disadvantage of this method is

that the core loss cannot be considered, and the transformer structure influence within

the joint area is not included.

The MATLAB mathematical model has not considered the loss of the core material; all

the investigations in terms of curve fitting use the core steel material’s data to fit the

curve.

Once the curve has been fitted, the verification will be carried out by using the

transformer open circuit test data. As mentioned before, since the air gap is included in

the magnetic circuit, the characteristics may change. Therefore further modification of

the nonlinearity curve needs to be done before using the transformer model to carry out

further studies.

In summary, the best way to do the curve fitting in order to simulate the transformer

non-linearity is to combine both of the core material’s characteristics with the

transformer open test data. Use the core material’s characteristics to fit the curve first,

and then use the transformer open circuit test data to modify the fitted curve.


94

4.2 Case 1: Magnetising current investigation

In the last section, there are two transformer models for the three-phase three-limb

transformer and one model for the five-limb transformer. All the models will be used to

investigate the influence of the transformer structure on the magnetising current.

4.2.1 132/33 kV, 90 MVA three-limb transformer

The simulation was carried out using one of the transformers in the distribution

substations in Manchester, UK as part of the case study. The transformer is a 132/33 kV,

90 MVA, three-limb core type transformer. The basic information needed for the

mathematical magnetic circuit model is the basic dimensions of the transformer core

structure. The dimensions of the transformer are shown in Table 4-1, which include the

core dimensions, the max flux density under rated voltage, the winding connection and

turn number, the tank dimension and the air gap between the transformer core and tank.

It is assumed that the leaking flux goes directly to the top/bottom of the tank and

follows this path through the side of tank and finally returns to the core again. Based on

this assumption, the maximum return path length can be calculated by summarising the

tank height and length, two air gaps between the top/bottom of the core and the

top/bottom of the tank length and two parts of the top/bottom tank length. The

maximum return path area can be calculated by summarising the lateral areas of the tank.

Table 4-1 132/33 kV dimensions data

No. Parameters

1 Main limb effective length /m 2.63

2 Main yoke effective length /m 1.48

3 Main limb cross-section area /m2 0.306369

4 Main yoke cross-section area /m2 0.306369

5 Max flux density under rated voltage /T 1.523

6 Primary winding turn number 697

7 Secondary winding turn number 318

8 Connection Y/ delta

9 Tank length /m 4.8

10 Tank width /m 2

11 Tank height /m 3.7

12 Tank thickness /m 0.1

13 Max return path length /m 6.1

14 Max return path area /m2 5.032


95

The three-limb transformer is produced by Alstom in Stafford, UK, and the core steel

material (23M3) characteristics for building up the transformer and the mild steel

material characteristics for building up the tank are shown in Figure 4-9. The blue line

shows the transformer core material characteristics and the red line shows the tank mild

steel material characteristics.

Figure 4-9 Material non-linear characteristics

It can be seen from Figure 4-9, that the materials’ characteristics are quite different. The

transformer core steel material is easier to saturate and the knee point is higher that of

the tank mild steel. Therefore, if the transformer core is working, balanced and lower

than the knee area, all the flux should be passing through the core, negligible flux could

be in the tank.

There are two models proposed for three-limb transformers; then the simulation would

be carried out for comparison purposes between the calculated magnetising currents of

those two models and the test report data.

Normally the transformer manufacturer only provides the open circuit test data for the

supplying voltages at 90%, 100% and 110% of the rated level. Therefore, the

simulations are carried out by following the open circuit test procedure. Figure 4-10 (a),

(b) and (c) shows that when varying the supplying voltage at 90%, 100% and 110%, the

magnetising currents of three phases are calculated by the two different models.


96

(a)

(b)

(c)

Figure 4-10 Three-phase magnetising currents of different supplied voltage level

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40

-30

-20

-10

0

10

20

30

40

0 0.01 0.02 0.03 0.04

Cu

rre

nt(

A)

Vo

ltag

e(k

V)

Time(s)

Magnetising currents in a 3-Limb transformer under 90% rated voltage

Vab Vbc Vca Iab Ibc Ica Iab(Return Path) Ibc(Return Path) Ica(Return Path)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40

-30

-20

-10

0

10

20

30

40

0 0.01 0.02 0.03 0.04C

urr

en

t(A

)

Vo

ltag

e(k

V)

Time(s)



-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40

-30

-20

-10

0

10

20

30

40

0 0.01 0.02 0.03 0.04

Cu

rre

nt(

A)

Vo

ltag

e(k

V)

Time(s)




97

In this figure, the round dot lines represent the supplied voltage; the solid lines represent

the simulation results of the simple three-phase three-limb transformer model and the

dashed lines represent the simulation by the improved three-phase three-limb

transformer results. It can be seen from Figure 4-10 (a), (b) and (c), when the supplied

voltage is 90% and 100% of the rated voltage, the magnetising currents are of the

sinusoidal waveform; when the supplied voltage reaches 110% of the rated voltage, the

magnetising currents are distorted by the harmonics. And the magnitude of the blue

phase of the magnetising current is higher than the other two phases, and this matches

the fundamental theory mentioned earlier in Chapter 2. However, the phase shift

between two adjacent phases does follow the fundamental theory of 120˚ apart; the red

and yellow phases are quite close to each other and away from the blue phase.

There are two different methods that are used to calculate the RMS value of the

magnetising currents. Sometimes they just measure the peak value of the waveform and

then divide it by root two, sometimes they calculate the RMS by using the formula

2

0

1T

RMSI i dtT

, T is the period of the fundamental harmonic, i is the magnitude of

the current.

Table 4-2 shows the comparison between the simulation results with the test results by

using the two different methods to calculate RMS (root mean square) value of the

magnetising currents.

Table 4-2 Comparison the RMS magnetising currents in field test data and simulation results

Supplied voltage (% of rated) Iab(A) Ibc(A) Ica(A)

Test Report

90% 0.55 0.51 0.71

100% 0.69 0.68 0.88

110% 1.01 1.01 1.17

3-Limb Model

90% 0.56 0.56 0.75

100% 0.64 0.64 0.85

110% 0.95 0.95 1.26

3-Limb

(Return Path) Model

90% 0.56 0.56 0.73

100% 0.63 0.63 0.82

110% 0.85 0.85 1.07

It can be seen in Table 4-2 that the RMS value of the phase Iab and Ibc is lower than the

Ica. The simulation results for 90% and 100% voltage supply are very similar to those of

the test report. However, the simulation results for currents do not match well with the

test report under the 110% rated voltage supplied. This is because the magnetising


98

current is distorted during the 110% rated voltage supplied, due to the transformer core

saturation. The test report data is calculated by using the peak value divide root two

method. The simulation results are calculated by using the formula2

0

1T

RMSI i dtT

,

and then the only fundamental frequency is taken into account. This is the reason why

the results of the test data are slightly higher than the simulation results.

Table 4-3 shows the phase angles of the magnetising currents by varying the magnitude

of supplied voltage. Ica is at the 150˚ as the reference. It is easily seen that those three-

phase currents do follow the rule of the 120˚ apart. The red and yellow phases are 12˚

away from the baseline; the phase shift can be influenced by the supplied voltage in the

simple three-limb model.

Table 4-3 Phase angle calculated for magnetising currents for three phases

Supplied voltage (% of rated) Iab(angle) Ibc(angle) Ica(angle)

3-Limb

90% 18 -78 150

100% 18 -78 150

110% 18 -78 150

3-Limb

(Return Path)

90% 19 -79 150

100% 19 -79 150

110% 21 -81 150

4.2.2 400/275/13 kV, 1000 MVA five-limb transformer

In this section, some of the five-limb transformer design data and the open circuit test

data are used to examine the five-limb core model.

Table 4-4 shows the design data of the 400/275/13 kV five-limb transmission

transformer. The core dimensions are used to calculate the flux distribution and the field

intensity as well; once the field intensity is obtained, the magnetising currents can be

calculated by using the winding turn number and the voltage level. Both the line current

and phase current can be calculated as well.


99

Table 4-4 400/275/13 kV five-limb transformer data

No. Parameters



3 Side yoke effective length /m 1.6475



6 Side yoke cross-section area /m2 0.3884



9 Tertiary winding turn number 54

10 Connection Y-Y-Δ

In Figure 4-11, the blue line represents the permeability change by varying the magnetic

field intensity, and the red line represents the materials’ B-H curve. It is easy to see that

when B-H curve reaches the knee area, the permeability starts to reduce; and when B

becomes flat in the deep saturation region, the permeability is reduced near to the level

of µ0(4π×10-7

), which is 2.3×10-5

.

Figure 4-11 Flux density and permeability of the µ0µr by varying magnetic field intensity

Once all the information of the transformer is input into the MATLAB programme, the

Newton-Raphson Method would minimize the error for the solution and solve the

problem within a given tolerance.

Figure 4-12 shows the three-phase magnetising current waveforms and the supplied

voltage waveform. The dotted lines represent the supplied voltage and the solid lines

0

0.01

0.02

0.03

0.04

0.05

0.06

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 20 40 60 80 100 120

Pe

rme

abili

ty µ

0µr

Ma

gne

tic

Fie

ld D

en

sity

(T)

Magnetic Field Intensity (H/m)B Mu


100

represent the magnetising current. The voltage is represented using the left Y-axis, and

magnetising current uses the left Y-axis. The red, yellow and blue lines represent phase

A, B and C respectively.

(a)

(b)

-10

-8

-6

-4

-2

0

2

4

6

8

10

-250

-200

-150

-100

-50

0

50

100

150

200

250

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Vo

ltag

e (

kV)

Time(s)


-20

-15

-10

-5

0

5

10

15

20

-300

-200

-100

0

100

200

300

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Vo

ltag

e (

kV)

Time(s)



101

(c)

Figure 4-12 Three-phase five-limb transformer core magnetising currents of different supplied

voltage level

It can be seen from Figure 4-12, that when the supplied voltage is 90% of the rated

voltage the magnetising current can still follow the sinusoidal waveform; when the

supplied voltage is increased to 100% and 110%, the magnetising currents are distorted

and the magnitudes increase significantly. The phase shifts between each pair of

adjacent phases would also be changed; this is shown in Table 4-5. It is the same reason

as the three-limb transformer; it is due to the part of the transformer core saturated and

the flux re-distribution in the whole magnetic circuit.

Table 4-5 Phase angle for each magnetising current in each phase

Supplied voltage

(% of rated) Iab(Angle) Ibc(Angle) Ica(Angle)

90% 24 -84 150

100% 26 -86 150

110% 29 -89 150

Table 4-6 shows the comparison between open circuit test results with the simulation

results of magnetising currents in RMS value.

Table 4-6 Comparison the RMS magnetising current in simulation results and field test data

Supplied voltage

(% of rated) Iab(A) Ibc(A) Ica(A)

Test data

90% 5.25 6.00 7.28

100% 12.30 12.40 14.75

110% 55.2 54.3 56.8

Simulation results

90% 6.62 6.62 7.84

100% 10.58 10.58 11.95

110% 51.36 51.36 52.78

-80

-60

-40

-20

0

20

40

60

80

-300

-200

-100

0

100

200

300

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Vo

ltag

e (

kV)

Time(s)



102

It can be seen that the simulation results are well matched with the test results for the

five-limb transformer; it has the same trend as the three-limb transformer, which is that

the magnetising currents in the red and yellow phase are lower than that of the blue

phase. However, the unbalanced situation is better than the three-limb transformer. The

unbalanced magnitude ratio of the red phase to blue phase in the three-limb transformer

is around 75%, but in the five-limb transformer it is around 85%.

Comparing the test and simulation data, it can be seen that the test result is larger than

the simulation under 90% supplied voltage, and smaller at 100% and 110%; but the

results are all reasonable.

Table 4-7 shows the phase currents. It can be seen that the magnitude of yellow phase

current is always higher than other two phases, due to the fact that the magnetic circuit

loops for phases are different. The open circuit test data looks like this, because the

transformers do not have a delta winding and the open circuit tests were carried out at

the Y connection side.

Table 4-7 RMS value of phase current

Magnitude Ia(A) Ib(A) Ic(A)

90% 4.02 4.51 4.02

100% 6.37 7.06 6.37

110% 34.54 35.08 34.54

Figure 4-13 shows the sequence component contents of the magnetising currents by

varying the supplied voltage.

Figure 4-13 Current sequence component content of different supplied voltage level

0

10

20

30

40

50

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency (Hz)

Sequence currents content

Zero(90%) Positive(90%) Negative(90%) Zero(100%) Positive(100%)

Negative(100%) Zero(110%) Positive(110%) Negative(110%)


103

It can be seen that the majority of the magnitude is still contributed by the positive

sequence. However, when the voltage supplied is 90% of the rate voltage, the negative

sequence magnetising current has already existed. This means that the negative

sequence component appears because the magnetic circuits of the three-phase are not

balanced.

Figure 4-13 discusses the unbalanced situation of the magnetising current from a three-

phase perspective. Figure 4-14 shows the frequency contents in the line magnetising

currents.

Figure 4-14 Frequency contents of line magnetising currents of different supplied voltage level

It can be seen that when the supplied voltage is increased the harmonics of the

magnetising current are increased, due to transformer nonlinear saturation. The 3rd

harmonic of line current is nearly zero, this is because the delta winding can absorb the

3rd harmonic. Figure 4-15 shows the flux density in the five-limb transformer core by

varying the supplied voltages. There are four groups of flux densities which are at the

yoke between A and B limb (Bab), yoke between B and C limb (Bbc), right side yoke (Brs)

and left side yoke (Bls).

0

10

20

30

40

50

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency (Hz)

Frequency content of line magnetising currents

Iab(90%) Ibc(90%) Ica(90%) Iab(100%) Ibc(100%)Ica(100%) Iab(110%) Ibc(110%) Ica(110%)


104

Figure 4-15 Flux density in 5-limb transformer core

It can be seen that the flux density waveforms are all distorted; the magnitude of the

flux density in the main yoke area do not change much, only the flat top duration of the

waveform with the increase of the supplied voltage. However the magnitudes of the flux

density of the side yoke area are sensitive to the supplied voltages and their magnitudes

have increased from 1 T to 1.5 T for the increase of supplied voltage from 90% to 110%

rated voltage.

Figure 4-16 shows the field intensity in the five-limb transformer core by varying the

supplied voltages. There are four groups of field intensities which are at the yoke

between A and B limb (Bab), the yoke between B and C limb (Bbc), the right side yoke

(Brs) and the left side yoke (Bls).

Figure 4-16 Field intensity in 5-limb transformer core

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

B (

T)

Time (s)

Flux density in 5-Limb transformer core under 90%,100% and 110% rated voltage

Bls(90%) Bab(90%) Bbc(90%) Brs(90%) Bls(100%) Bab(100%)Bbc(100%) Brs(100%) Bls(110%) Bab(110%) Bbc(110%) Brs(110%)

Bab Bbc

BlsBrs

-100

-75

-50

-25

0

25

50

75

100

0 0.01 0.02 0.03 0.04

H (

A/m

)

Time(s)

Field intensity in 5-Limb transformer core under 90%,100% and 110% rated voltage

Hls(90%) Hab(90%) Hbc(90%) Hrs(90%) Hls(100%) Hab(100%)Hbc(100%) Hrs(100%) Hls(110%) Hab(110%) Hbc(110%) Hrs(110%)

Hab Hbc

HlsHrs


105

It can be seen that the field intensity is in an opposite way to the flux density; the field

intensity does not change much in the side yoke area; however the magnitude of field

intensity in the main yoke area is increased gradually with the increase of supplied

voltage.

4.2.3 Comparison of influence between three-limb and five-limb

transformer structure

In the last two sections, the two models of the three-phase three-limb transformer and

the five-limb transformer model have been examined through open circuit test results.

In this section, the core structure influences are discussed and examined by using an

artificial three-phase five-limb transformer which has the same power rating and the

same voltage level as the transformer in section 4.2.1.

Table 4-8 shows the artificial five-limb transformer dimension data based on those in

Table 4-1. Except for the fact that the area is 50% that of the main limb, the main yoke

and the side yoke and the rest of the parameters are the same as those of the three-limb

transformer.

Table 4-8 Artificial five-limb transformer data based on 132/33 kV dimensions data

No. Parameters



3 Side yoke effective length /m 1.055



6 Side yoke cross-section area /m2 0.153184



9 Secondary winding turn number 318

10 Connection Y-Δ

The comparison between these two core structures is carried out with three cases when

the transformers are working at the linear region, the rated voltage and the non-linear

region.


106

4.2.3.1 Comparison in linear region

The comparison is carried out between the magnetising currents of three-limb and five-

limb transformers.

Figure 4-17 shows the comparison between the three-limb and five-limb transformer in

terms of magnetising current when the supplied voltage is at the RMS value. The

supplied voltage is 70% of the rated voltage. The dotted line represents the blue phase

of the three-phase supplied voltage; the solid lines represent the blue phase magnetising

currents of the two different core structures. It can be seen that the magnetising current

nearly follows the pure fundamental sinusoidal waveform for both core structures. The

higher value is for the five-limb core transformer. However the phase angles of the

magnetising currents of the blue phase are the same for three-limb and five-limb core

transformers.

Figure 4-17 Comparison of magnetising currents in three-limb and five-limb transformer

Figure 4-18 shows the sequence component contents of the magnetising currents in the

two different core structures. The positive sequence of the magnetising current in the

five-limb transformer is higher than the three-limb transformer; but the negative

sequence of the magnetising current is lower. This proves that the magnetising current

in a five-limb transformer is more balanced than the three-limb transformer.

-1

-0.5

0

0.5

1

-30

-20

-10

0

10

20

30

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Vo

ltag

e (

kV)

Time(s)

Magnetising currents in a 3&5-Limb transformers (linear region)

Vab Vbc Vca Iab(3-L) Ibc(3-L)

Ica(3-L) Iab(5-L) Ibc(5-L) Ica(5-L)


107

Figure 4-18 Comparison of current sequence component contents in three-limb and five-limb core

transformers

Figure 4-19 shows the comparison of the frequency contents of the magnetising currents

in three-limb and five-limb transformers. The same trend can be seen as in the last

figure. The ratio of the Iab (or Ibc) and Ica is 75% in the three-limb transformer and 81%

in the five-limb transformer.

Figure 4-19 Comparison of frequency contents of magnetising currents in three-limb and five-limb

transformers

Figure 4-20 shows the flux density and field intensity of the yoke between the limb

A&B/B&C (a) and the left/right side of tank (b) in the three-limb transformer. The 70%

of the rated voltage convert to a flux density in the main limb of 1.1 T. When the

supplied voltage is only 70% of the rated voltage, all the flux densities in the three-limb

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency(Hz)

Sequence component contents of magnetising currents (linear region)

Zero(3-L) Positive(3-L) Negative(3-L) Zero(5-L) Positive(5-L) Negative(5-L)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency (Hz)

Frequency contents of line magnetising currents (linear region)

Iab(3-L) Ibc(3-L) Ica(3-L) Iab(5-L) Ibc(5-L) Ica(5-L)


108

core are pure sinusoidal waveforms. The escaped flux into the transformer tank is small;

its magnitude is significantly less than the fluxes cannot in the main flux loop. There are

four groups of flux densities and field intensities which are at the yoke between A and B

limb (Bab, Hab), the yoke between B and C limb (Bbc, Hbc), the right side return path (Brt,

Hrt), the left side return path (Blt, Hlt). The leakage flux is too small compared with the

main flux linkage.

(a)

(b)

Figure 4-20 Flux density and field intensity in three-limb transformer

Figure 4-21 shows the flux density and the field intensity of yokes between limb

A&B/B&C, the left/right side yoke in the five-limb transformer. The magnitude of flux

density at the side yoke in the five-limb core transformer is only 0.6 T peak, in the main

yoke it has already reached 1.54 T which is at the knee point of the material.

-20

-15

-10

-5

0

5

10

15

20

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in 3-limb transformer core

Blt Brt Hlt Hrt

-20

-15

-10

-5

0

5

10

15

20

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in 3-limb transformer core

Bab Bbc Hab Hbc


109

Figure 4-21 Flux density and field intensity in five-limb transformer

There are four groups of flux densities and field intensities which are at the yoke

between A and B limb (Bab, Hab), the yoke between B and C limb (Bbc, Hbc), the right

side yoke (Brs, Hrs), the left side yoke (Bls, Hls). The leakage flux is too small compared

with the main flux linkage.

4.2.3.2 Comparison in rated voltage

In this section, the comparison is carried out between the magnetising currents, flux

distributions of three-limb and five-limb transformer core and field intensities of three-

limb and five-limb transformer core under the rated voltage.

Figure 4-22 shows that the magnetising currents in two different core transformer

structures under the rated voltage which is represented by the dotted lines Vab, Vbc and

Vca. It can be seen that the magnetising current of the three-limb transformer follows the

sinusoidal waveform which is represented by the solid lines Iab(3-L), Ibc(3-L) and Ica(3-L)

and the magnetising current of five-limb transformer is distorted and the magnitude is

higher than that of the three-limb transformer, as shown in Iab(5-L), Ibc(5-L) and Ica(5-L).


110

Figure 4-22 Comparison of magnetising currents in three-limb and five-limb transformers at 100%

rated voltage

Figure 4-23 shows that the sequence component contents of magnetising currents in two

different core structures at 100% rated voltage supplied situation. It is easy to see that

the magnitudes of the fundamental components in the five-limb transformer are higher

than those of the three-limb one. In addition, the negative sequence third harmonic

appears in the five-limb transformer, since a part of the transformer core is saturated.

Figure 4-23 Comparison sequence contents of magnetising currents two different core structures

Figure 4-24 shows the frequency contents of the magnetising currents at 100% rated

voltage. It can be seen that the same trend is shown as Figure 4-23, though the

magnitude of the magnetising current of the fundamental harmonic of the five-limb

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-40

-30

-20

-10

0

10

20

30

40

0 0.01 0.02 0.03 0.04

Cu

rre

nt(

A)

Vo

ltag

e (

kV)

Time(s)

Magnetising currents in 3-limb & 5-limb transformers at 100% rated voltage

Vab Vbc Vca Iab(3-L) Ibc(3-L)

Ica(3-L) Iab(5-L) Ibc(5-L) Ica(5-L)

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency (Hz)

Sequence component contents of magnetising currents (rated voltage)



111

transformer is around 33% higher than that of the three-limb transformer. The third and

fifth harmonic appears in the magnetising current of the five-limb transformer.

Figure 4-24 Comparison frequency contents of line magnetising currents at 100% rated voltage

Figure 4-25 shows the flux density and field intensity in the three-limb core. The flux

density and the field intensity is still a sinusoidal waveform, and the leakage flux is a

hundred times smaller than the flux linkage.

(a)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f cu

rre

nt

(A)

Frequency (Hz)

Frequency contents of line magnetising currents (rated voltage)


-30

-20

-10

0

10

20

30

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 0.01 0.02 0.03 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in 3-limb transformer core(100% rated voltage)

Blt Brt Hlt Hrt


112

(b)

Figure 4-25 Flux density and field intensity in three-limb transformer at 100% rated voltage

Figure 4-26 shows the flux density and field intensity in the five-limb transformer. It

can be seen that the flux density is seriously distorted. The flux at the main yoke is

saturated and the saturated period is around 1/2 cycle in every cycle. The side yoke is

also distorted due to the main yoke saturation. The field intensity is also distorted; the

third and fifth harmonic appears in both of the main yoke and side yoke.

Figure 4-26 Flux density and field intensity in five-limb transformer at 100% rated voltage

4.2.3.3 Comparison in nonlinear region

In this section, the comparison is carried out between the magnetising currents at the

supplied voltage of 120% rated voltage. The flux distributions and filed intensities of

the three-limb and five-limb core transformers.

-30

-20

-10

0

10

20

30

-1.5

-1

-0.5

0

0.5

1

1.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in 3-limb transformer core(100% rated voltage)

Bab Bbc Hab Hbc

-100

-50

0

50

100

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and Field Intensity in 5-limb transformer core(100% rated voltage)

Bls Bab Bbc Brs Hls Hab Hbc Hrs


113

Figure 4-27 shows the magnetising currents of two different core structures and the

supplied voltage waveforms. The peak magnitude of the magnetising current is almost

ten times the rate of the magnetising current. The five-limb core transformer has a larger

magnetising current than the three-limb one.

Figure 4-27 Comparison of magnetising currents in 3 & 5-limb transformers at non-linear region

Figure 4-28 shows the sequence contents of magnetising currents in two different core

structures at the non-linear region. It can be seen that the harmonics of the positive and

negative sequence components appear. There is no zero sequence content for the

supplied voltages are a pure three-phase ideal balanced voltage source. The 3rd order

harmonic is relatively lower than the other harmonics. The fifth negative harmonic is

higher than the positive one; so is the 11th harmonic.

Figure 4-28 Comparison of current sequence contents in 3&5 limb transformer at nonlinear region

-15

-10

-5

0

5

10

15

-60

-40

-20

0

20

40

60

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Vo

ltag

e (

kV)

Time(s)

Magnetising currents in 3-limb and 5-limb transformer (nonlinear region)

Vab Vbc Vca Iab(3-L) Ibc(3-L)Ica(3-L) Iab(5-L) Ibc(5-L) Ica(5-L)

0

1

2

3

4

5

6

0 100 200 300 400 500 600 700 800 900 1000

Mag

nit

ud

e o

f C

urr

en

t (A

)

Frequency (Hz)

Sequence component contents of magnetising currents (nonlinear region)



114

Figure 4-29 shows the frequency content in each phase of the magnetising current at the

nonlinear region. It can be seen that the third harmonic is lower than the fifth and

seventh harmonic due to the delta winding connection. Iab and Ibc are always lower than

Ica in the entire frequency scan range.

Figure 4-29 Comparison of frequency contents of three-limb and five-limb transformers

magnetising currents at nonlinear region

Figure 4-30 shows the flux densities and field intensities in the three-limb transformer

core at the nonlinear region. Figure 4-30 (a) shows the flux densities and field

intensities in the transformer tank, and Figure 4-30 (b) shows the flux densities and field

intensities in the yoke. The highest peak magnitude of the flux density can achieve 1.8T,

and the waveform is distorted. The escaped flux is still low which is 0.0315T; that is the

reason why it cannot be seen in the figure. The field intensity is 30 times higher than the

rated situation.

In addition, the waveform is distorted with the third harmonic and fifth harmonic

content.

0

1

2

3

4

5

6

7

0 100 200 300 400 500 600 700 800 900 1000

Mag

ne

itu

de

of

Cu

rre

nt

(A)

Frequency (Hz)

Frequency contents of line magnetising currents (nonlinear region)



115

(a)

(b)

Figure 4-30 Flux density and field intensity in three-limb transformer at nonlinear region

Figure 4-31 shows the flux densities and field intensities in different parts of the five-

limb transformer at the nonlinear region. The peak value of the flux density in the main

yoke and side yoke are almost the same but achieved the peak value at different times.

The flux density and the field intensity waveforms are distorted. The magnitude of the

field intensity is 10 times that of the rated situation. It is about 8 times higher than the

three-limb one.

-100

-50

0

50

100

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in three-limb transformer core(nonlinear region)

Blt Brt Hlt Hrt

-200

-150

-100

-50

0

50

100

150

200

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H(A

/m)B(T

)

Time(s)

Flux density and field intensity in three-limb transformer core(nonlinear region)

Bab Bbc Hab Hbc


116

Figure 4-31 Flux density and field intensity in five-limb transformer at nonlinear region

4.3 Case 2: Sensitivity study on balance situation

In the balanced situation, it is easy to calculate and understand the flux density

distribution, field intensity and magnetising current. Therefore, in this section a five-

limb core transformer is used as an example to examine the impact of the magnetic flux

density and the impact of the ratio of the main yoke to side yoke.

4.3.1 Impact of magnetic flux density

Due to the fact that the knee point of the B-H curve is about 1.54T as shown in Figure

4-11, based on the knee point definition in the current transformer (CT) standard [83],

more case studies were carried out around the knee point.

4.3.1.1 Main limb B=1.1 T

Using the dimensions of the transformer core and varying the peak value of the flux

density in the main limb from 1.1 T, 1.3 T, 1.5 T, 1.54 T, 1.7 T to 1.9 T, the flux

densities at the side yoke, main yoke and main limb are calculated.

Figure 4-32 shows the results of the magnetic flux density at the side yoke (B1), side

limb (B2), left main yoke (B3) and right main yoke (B4). The supplied maximum value

of flux density of the main limb of phase A is 1.1 T, which is shown as the red thick line.

The maximum magnitude of magnetic flux density at the main yoke is higher than that

-1000

-750

-500

-250

0

250

500

750

1000

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

H(A

/m)

B(T

)

Time(s)

Flux density and field intensity in five-limb transformer core(nonlinear region)

Bls Bab Bbc Brs Hls Hab Hbc Hrs


117

of the main limb, which is about 1.5 T; and the left and right main yokes achieve the

maximum value at different phase angles, with Phase A limb flux acting as the

reference. The side yoke and side limb flux density are in phase and with the same

magnitude, which corresponds to the structure of the transformer core, and which shows

that the cross-section areas of both the left side yoke and the right side yoke are the

same. In this core structure, if the core goes to saturation, it should be the main yoke

that is saturated first.

Figure 4-32 Flux distribution in five-limb transformer at linear region

By using the Fast Fourier Transform Method (FFT) the amplitude-frequency spectra of

the flux density at all parts of the transformer core are obtained and used to check the

harmonic contents as shown in Figure 4-33. All the flux density waveforms are almost

sinusoidal with minimal harmonic content, because the B-H curve is not smoothly linear,

the calculation resolution of the MATLAB software is not enough. The signal is

analysed for two cycles, which is 40 ms, the time step is 55.55 ns. The frequency scan is

from the fundamental frequency until the 19th harmonic. The majority of the frequency

content is at fundamental frequency 50 Hz; which means the waveforms of magnetic

flux density are sinusoidal. From this figure, we can also see that the maximum

magnitude magnetic flux density of the side yoke and side limb is about 0.85 T; and the

maximum magnitude of the flux density of the main yoke is about 1.5 T, which is

almost the same as shown in Figure 4-32.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)B1 B2 B3 B4 PhaseA


118

Figure 4-33 Frequency contents of flux densities in five-limb transformer at linear region

From Figure 4-32 and Figure 4-33, it can be seen that the magnetic flux density of the

left and the right main yoke have the same magnitude and same frequency content with

the only difference of phase shift. In addition, the maximum magnitude of magnetic flux

density in the main yoke is almost twice as high as that of the side yoke and side limb.

Table 4-9 shows the maximum magnetic flux density value at each harmonic frequency.

Table 4-9 Maximum flux density in side yoke and main yoke

Frequency(Hz) Side yoke(T) Main Yoke(T)

50 0.8448 1.4629

150 0.0079 0.0075

250 0.0038 0.0045

350 0.0032 0.0023

450 0.0020 0.0017

4.3.1.2 Main limb B=1.54 T

By increasing the maximum magnetic flux density of the main limb until 1.54 T which

is the knee point of the core material, Figure 4-34 shows the flux distribution at

different parts of the five-limb transformer. The maximum magnitude of flux density at

the main yoke is still higher than that of the main limb, which is about 1.7 T; and the

flux density waveform becomes distorted due to the saturated main yoke. The side yoke

and side yoke flux density are also distorted following the Kirchhoff Current Law (KCL)

in magnetic field circuit; however the magnitude in the main yoke is not as high as that

of the main limb.

0

0.3

0.6

0.9

1.2

1.5

50 150 250 350 450 550 650 750 850 950

Mag

enti

c Fl

ux

Den

sity

(T)

Frquency(Hz)Side Limb Side Yoke Main Yoke(L) Main Yoke(R)

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


119

Figure 4-34 Flux distribution in different parts of five-limb transformer at knee region

Figure 4-35 shows the maximum flux density value of odd harmonic frequency. The

majority of the frequency contents is still in the fundamental frequency; the harmonic

contents especially the third harmonic and fifth harmonic are shown, the magnitude of

third harmonic in the side yoke is higher than that of the main yoke. The fifth harmonics

in the side yoke, side limb and main yoke are almost the same.

Figure 4-35 Frequency contents of flux densities in five-limb transformer at knee region

Table 4-10 shows the maximum flux density value in the side yoke and main yoke of

odd frequency. Comparing with Table 4-9, it can be seen that when the main limb’s flux

density increases to the knee point, the flux density of side yoke increases almost two

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)B1 B2 B3 B4 PhaseA

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

50 150 250 350 450 550 650 750 850 950

Mag

en

tic

Flu

x D

en

sity

(T)

Frquency(Hz)Side Limb Side Yoke Main Yoke(L) Main Yoke(R)

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


120

times as much as the supplied 1.3 T flux density. Meanwhile the side yoke works at the

knee point area and the main yoke is already saturated, and the third harmonic of flux

density also increases about 20 times in both parts.

Table 4-10 Maximum flux density in side yoke and main yoke

Frequency(Hz) Side yoke(T) Main Yoke(T)

50 1.5238 1.8362

150 0.2231 0.2002

250 0.0635 0.0664

350 0.0199 0.0141

450 0.0188 0.0137

4.3.1.3 Main limb change from linear region to non-linear region

When the maximum magnetic flux density of the main limb starts to increase from 1.3

T to 1.9 T with step of 0.1 T, Figure 4-36 shows the change of flux density waveforms

in the side yoke. Along with the increase of maximum magnetic flux density in the main

limb, the flux densities in the side yoke become distorted, even when the main limb

works in the linear region of B-H curve, the flux density in the side yoke is lower than

that of the main limb. The magnitude of B in the side yoke is higher than that of the

main limb, which means the side yoke is easier to be saturated than the main limb, due

to the smaller area.

Figure 4-36 Side yoke flux densities waveforms by varying the maximum main limb flux density

Figure 4-37 also shows that when the magnetic flux density waveforms are distorted,

the third and fifth harmonic appear in the side yoke, in particular the third harmonic is

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)1.3T 1.4T 1.5T 1.6T 1.7T 1.8T 1.9T


121

increased by the increase of supplied magnetic flux density. The fifth harmonic is

increased when the magnetic flux density moves from the B-H linear region to around

the knee point (1.54 T); and then decreases when continuing to increase the magnetic

flux density beyond the knee point.

Figure 4-37 Frequency contents of flux densities in side yoke by varying the maximum main limb

flux density

The increase of maximum magnitude of flux density in the side yoke at fundamental

frequency has a different increasing slope from that of the third harmonic frequency;

Table 4-11 shows the step change of the odd harmonic in the side yoke with the supply

flux density step increase by each 0.1 T. The fundamental frequency and third harmonic

frequency components increase faster at the linear region than at the non-linear region,

which is after the knee point.

Table 4-11 Maximum flux density at fundamental and third harmonic frequency in side yoke

Supplied Flux Density(T) Fundamental(T) Third Harmonic(T)

1.3 1.0814 0.0711

1.4 1.2495 0.1303

1.5 1.4404 0.1947

1.6 1.6441 0.2598

1.7 1.8344 0.3267

1.8 1.9927 0.3923

1.9 2.1277 0.4475

Figure 4-38 shows that the phase angles of harmonics, the fundamental frequency and

third harmonic frequency phase angles are almost unchanged for varying flux densities

0

0.5

1

1.5

2

2.5

50 150 250 350 450 550 650 750 850 950

Mag

en

tic

Flu

x D

en

sity

(T)

Frquency(Hz)1.3T 1.4T 1.5T 1.6T 1.7T 1.8T 1.9T

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


122

in the main limb. The phase angles of the fifth harmonic frequency stay nearly the same

until the core goes into deep saturation.

Figure 4-38 Phase angle contents of flux densities in side yoke by varying the maximum main limb

flux density

The waveform distortion also happens on the main yoke core with the increase of the

magnetic flux density, as shown in Figure 4-39. When the peak flux density in the main

limb is 1.3 T, the peak magnitude of flux density in the main yoke is near to 1.6 T.

Furthermore, when increasing the supplied flux density in the main limb, there is not

much increase of peak flux density in the main yoke. This is because when the main

yoke is near to saturation and cannot allow more flux through; the flux might go

through the side yoke which is an easier route. Therefore, the magnitude of magnetic

flux density of the side yoke is catching up with that of the main yoke.

Figure 4-39 Main yoke flux densities waveforms by varying the maximum main limb flux density

-180

-120

-60

0

60

120

180

50 150 250

An

gle

(De

gre

e)


Frequency (Hz)

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)1.3T 1.4T 1.5T 1.6T 1.7T 1.8T 1.9T


123

Figure 4-40 shows the change of harmonic content of Bm in the main yoke with the

variation of the flux density in the main limb. The magnitudes of fundamental

frequency are higher than those of the side yoke. The third harmonic content is slightly

lower than those of the side yoke. Compared with the side yoke of Figure 4-37, the

magnitudes of the fundamental frequency flux densities in the side yoke are changing

faster than those of the main yoke. Furthermore, when the supplied magnetic field

densities become higher, the side yoke has more potential to be saturated due to the

higher increasing slope.

Figure 4-40 Frequency contents of flux densities in main yoke by varying the maximum main limb

flux density

The maximum magnitude of flux density in fundamental frequency also has a different

slope from that of the third harmonic frequency; Table 4-12 shows the step change of

the odd harmonic in the main yoke with the supply flux density step increase by each

0.1 T. The same as in the side yoke, the fundamental frequency and third harmonic

frequency increase faster at the linear region than that at the non-linear region, which is

after the knee point.

Table 4-12 Maximum flux density at fundamental and third harmonic frequency in main yoke

Supplied Flux Density(T) Fundamental(T) Third Harmonic(T)

1.3T 1.6655 0.0633

1.4T 1.7427 0.1161

1.5T 1.8086 0.1734

1.6T 1.8699 0.2316

1.7T 1.9410 0.2912

1.8T 2.0297 0.3497

1.9T 2.1304 0.3989

0

0.5

1

1.5

2

2.5

50 150 250 350 450 550 650 750 850 950

Mag

en

tic

Flu

x D

en

sity

(T)


Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


124

Figure 4-41 shows the phase angles of harmonics in the main yoke area. The

fundamental and 3rd

harmonic frequency phase angles have decreased which can also be

seen in Figure 4-39 for varying flux densities in the main limb. The phase angles of the

fifth harmonic frequency stay nearly the same until the core goes into deep saturation.

Figure 4-41 Phase angle contents of flux densities in main yoke by varying the maximum main limb

flux density

4.3.2 Impact of area

From the equation to calculate the side yoke flux of a three-phase five-limb transformer,

it can be seen that the magnetic flux density is associated with the maximum supplying

flux density, the permeability, the length, the cross-section area of each part of the

three-phase five-limb transformer core, which are the side yoke, the main yoke and the

main limb. The maximum supplying flux density will also influence the permeability, in

other words, these two conditions are coupled. The length of the main limb, the main

yoke and the side yoke is due to the winding length, the winding radius and the

insulation level. Moreover, it is now easy to understand that not only the permeability of

each part of transformer core contributes to the flux distribution, the cross-sections of

side yoke and main yoke also play an important role for the flux distribution.

Identifying the cross-section area of main limb 0.71805 m2

as 1 per unit, in order to let

all the flux have the return path, the cross-section areas of the side yoke and the main

yoke should be added together to be at least the same as that of the main limb. However,

the basic principle design is to make the transformer work reliably in normal conditions

-180

-120

-60

0

60

120

180

50 150 250

An

gle

(De

gre

e)


Frequency (Hz)


125

by using the least materials; normally the manufacturers use the ratio of 1:1 for the main

limb: (side yoke + main yoke).

Comparisons between the three groups are carried out by changing the supply magnetic

flux density, which is 1.1T at the liner region, 1.54T at the knee point and 1.9T at the

saturation region. In each group, the supply magnetic flux density is fixed by varying

the ratio of cross-section areas of the side yoke and the main yoke. The design rule is to

maximally use the materials characteristics; the core should work use near the knee area

under normal operating voltage. In this case, the knee area of the material is around 1.54

T. Varying the ratio of the cross-section area between the side yoke and the main yoke,

the sensitivity study on the impact of area ratio is carried out. Table 4-13 shows the ratio

variations of the cross-section area between the side yoke and the main yoke.

Table 4-13 Ratio variations of the cross section

Ratio Area of side yoke(m2) Area of main yoke(m

2)

0.5:0.5 0.359025 0.359025

0.45:0.55 0.3231225 0.3949275

0.4:0.6 0.28722 0.43083

0.35:0.65 0.2513175 0.4667325

0.3:0.7 21.5415 50.2635

Figure 4-42 and Figure 4-43 show that the flux density in the side yoke and main yoke

are at different area ratios and the supplying maximum flux density is 1.1 T. The

waveforms are all sinusoidal only when the amplitudes are different in both areas. The

amplitudes of the flux density are decreased with the increase of the ratio of the cross-

section area between the side yoke and the main yoke. The maximum magnitudes of Bm

in the side yoke are always lower than the supplied value of 1.1 T, on the other hand the

maximum magnitudes Bm of the main yoke are always higher than the supplied value of

1.1 T. For different area ratios, the Bm of the side yoke does not exhibit phase shifts

while the Bm of the main yoke shows some degree of phase shifts.


126

Figure 4-42 Side yoke flux densities waveforms at different area ratios at the supplying maximum

flux density of 1.1 T

Figure 4-43 Main yoke flux densities waveforms at different area ratios at the supplying maximum


Table 4-14 shows the maximum magnitude of flux density at the side yoke and the main

yoke for different cross-section area ratios. From this table, it can also be seen that the

amplitudes of the magnetic flux density are decreased with the ratio of the cross-section

area between the side yoke and the main yoke.

Table 4-14 Maximum magnitude of flux density

Ratio Side yoke(T) Main yoke(T)

0.5:0.5 0.8522 1.4962

0.45:0.55 0.8433 1.4364

0.4:0.6 0.8346 1.3776

0.35:0.65 0.8261 1.3252

0.3:0.7 0.8177 1.2798

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7


127

When increasing the supply magnetic flux density to the knee point of 1.54 T, the

magnetic flux density waveform of the side yoke and the main yoke are shown in Figure

4-44 and Figure 4-45. The waveforms are all distorted. The amplitude of the flux

density is decreased with the ratio of the cross-section area between the side yoke and

the main yoke. From Figure 4-45 it can be seen that the time for the flux density

waveform to be flat is increased with the decrease of the ratio of the cross-section area

between the side yoke and the main yoke. This also means that the total harmonic

content in the waveform is also increased.





-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7


128

Figure 4-46 and Figure 4-47, show that the magnitudes of fundamental frequency and

third harmonic in both the side yoke and the main yoke are decreased with the decrease

of the percentage ratio of the cross-section area between the side yoke and the main

yoke. This is because the increase of the main yoke area allows more flux to pass

through. In addition, both of the magnetic flux densities in the side yoke and main yoke

are decreased, due to the increase of percentage ratio of the cross-section area between

the side yoke and the main yoke. From this point of view, the higher the ratio between

the main yoke and the side yoke, the less likely the transformer will saturate. However,

the main yoke length is almost 2 times that of the side yoke; if the area of the main yoke

were increased, more materials would be required. It also increases the transformation

height and makes it harder to transport.

Figure 4-46 Frequency contents of flux densities in side yoke by varying ratio of cross-section at

knee region

Figure 4-47 Frequency contents of flux densities in main yoke by varying ratio of cross-section at

knee region

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

50 150 250 350 450 550 650 750 850 950

Mag

en

tic

Flu

x D

en

sity

(T)

Frquency(Hz)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

50 150 250 350 450 550 650 750 850 950

Ma

gen

tic

Flu

x D

en

sity

(T

)

Frquency(Hz)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


129

Continuing to increase the supply magnetic flux density into saturation region as 1.9 T,

the flux density waveform of the side yoke and the main yoke are shown in Figure 4-48

and Figure 4-49. The waveforms of the magnetic flux density are all distorted. The

change in the flux density in the side yoke is not much; however the flux density in the

main yoke is changed to a better sinusoidal waveform by decreasing the ratio of the

cross-section between the side yoke and the main yoke.





Figure 4-50 shows that the maximum magnitudes of fundamental frequency and third

harmonic in the side yoke do not change much by decreasing the percentage ratio of the

cross-section area between the side yoke and the main yoke. In addition, the fifth,

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T

)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Ma

gne

tic

Flu

x D

en

sity

(T)

Time(s)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7


130

seventh and ninth harmonics appear. This is because the side yoke has already been

deep saturated; this is why we cannot see too much difference between them.

Figure 4-50 Frequency contents of flux densities in side yoke by varying ratio of cross-section at

nonlinear region

Figure 4-51 shows that the maximum magnitudes of fundamental frequency and third

harmonic are decreased with the increase of ratio of the cross-section area between the

side yoke and the main yoke.

Figure 4-51 Frequency contents of flux densities in main yoke by varying ratio of cross-section at

nonlinear region

0

0.5

1

1.5

2

2.5

50 150 250 350 450 550 650 750 850 950

Ma

gen

tic

Flu

x D

en

sity

(T

)

Frquency(Hz)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)

0

0.5

1

1.5

2

2.5

50 150 250 350 450 550 650 750 850 950

Ma

gen

tic

Flu

x D

en

sity

(T

)

Frquency(Hz)0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Frequency (Hz)

Ma

gn

eti

c F

lux

De

ns

ity (

T)


131

4.4 Case 3: GIC Study---sensitivity on unbalanced

situation

As mentioned in the literature review, the cycle of solar wind is around eleven years.

The last famous one (which led the Canadian power system to black out) is 22 years old,

and this year solar wind is active again. Consequently, the risks of transformer failure

need to be considered.

The solar winds will disturb the geomagnetic field, and then shift the potential of the

surface voltage up. The frequency of the created voltage is around 0.1 Hz, which will

look like DC supplied into the power system grid.

4.4.1 Impact of DC supply level

Taking the three-limb core transformer as an example, the investigation is carried out on

the impact of the DC supply level on transformer saturation by varying the peak value

of the flux density in the main limb as at the linear region, knee point and non-linear

region; the magnetising current and the flux density at the main yoke and the tank are

calculated.

4.4.1.1 Sensitivity study on linear region with DC situation

The supplied three-phase AC voltage is 70% of the rated voltage, which can warrant the

transformer working under the linear region. The DC supply, which is in the unit of flux,

Wb, varies at 0.1 Wb, 0.15 Wb or 0.2 Wb.

Figure 4-52 shows the line magnetising current waveforms varying by the DC supply

level. The round dotted lines represent the magnetising currents under the DC supply

level as zero, the dash lines represent the magnetising currents under the DC supply

level as 0.1 Wb, the dash dotted lines represent the magnetising currents under the DC

supply level as 0.15 Wb, the dash long lines represent the magnetising currents under

the DC supply level as 0.2 Wb. It can be seen that the line magnetising currents are

follow the sinusoidal waveform until the DC supply level reaches 0.15Wb. When the

DC supply level is increased to 0.2 Wb, the current waveforms are distorted.


132

Figure 4-52 Line magnetising currents in three-limb transformer at linear region by varying DC

supply level

Figure 4-53 shows the phase magnetising currents for the three-limb transformer. It is

clear that when increasing the DC supply level, the currents shift up and change from

the pure sinusoidal waveform into half cycle saturation. The magnitude of the waveform

does not go to the negative any more when supplying enough level of DC.

Figure 4-53 Phase magnetising currents in three-limb transformer at linear region by varying the

DC supply level

Figure 4-54 and Figure 4-55 show the flux density and the field intensity distribution

inside the three-limb transformer. The left side Y-axis in Figure 4-54 and Figure 4-55

represent the flux density and the flux density in the yoke of the three-limb core. The

right side Y-axis in Figure 4-54 and Figure 4-55 represent the flux density that leaked

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Time(s)

Line magnetising currents in a 3-Limb transformer (linear region with DC)

Iab(No DC) Ibc(No DC) Ica(No DC) Iab(0.1Wb) Ibc(0.1Wb) Ica(0.1Wb)

Iab(0.15Wb) Ibc(0.15Wb) Ica(0.15Wb) Iab(0.2Wb) Ibc(0.2Wb) Ica(0.2Wb)

-1

0

1

2

3

4

5

0 0.01 0.02 0.03 0.04

Cu

rre

nt(

A)

Time(s)

Phase magnetizing currents in three-limb transformer (linear region with DC)

Ia(No DC) Ib(No DC) Ic(No DC) Ia(0.1Wb) Ib(0.1Wb) Ic(0.1Wb)

Ia(0.15Wb) Ib(0.15Wb) Ic(0.15Wb) Ia(0.2Wb) Ib(0.2Wb) Ic(0.2Wb)


133

out of the three-limb core. The flux density and filed intensity would be increased at the

yoke area as the DC supply level increases, but not too much. The positive magnitude of

the flux density is changed from 1.2 T to 1.4 T, and the positive magnitude of the field

intensity is changed from 22 A/m to 25 A/m. However, the leak out flux density and

field intensity suddenly increased about twice the rate.

Figure 4-54 Flux densities distributions in three-limb transformer at linear region by varying the

DC supply level

Figure 4-55 Field intensities distributions in three-limb transformer at linear region by varying the

DC supply level


134

4.4.1.2 Sensitivity study on knee area with DC situation

The supplied three-phase AC voltage is the rated voltage, which can warrant the

transformer working under the linear region similar to the linear region one, the DC

supply, which is in the unit of flux, Wb, varies at 0.1 Wb, 0.15 Wb and 0.2 Wb.

The same experience can be obtained in the last section, the magnitude of the line

current can change and there is no magnitude offset shift, the three-phase currents still

follow the balanced situation. As a result, only the phase currents are calculated.

Figure 4-56 and Figure 4-57 show phase current waveforms. The magnetising current is

much more sensitive towards DC supply compared with the linear region. When the DC

supply is 0.15 Wb, the current has already shown transformer half cycle saturation, and

furthermore increasing the DC supply results in the dramatic increase of the magnitude

of the current.

Figure 4-56 Phase magnetising currents in three-limb transformer (No DC, 0.1 Wb)

-2

0

2

4

6

8

10

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Time(s)

Phase magnetising currents in a 3-Limb transformer (Knee region with DC)

Ia(No DC) Ib(No DC) Ic(No DC) Ia(0.1Wb) Ib(0.1Wb) Ic(0.1Wb)


135

Figure 4-57 Phase magnetising currents in three-limb transformer (0.15 Wb, 0.2 Wb)

Figure 4-58 and Figure 4-59 show that the flux density and the filed intensity. The X-

axis and the Y-axis styles are all the same as the previous figures. It can be seen that the

flux density waveforms start to become distorted and the flat part of the saturation

period becomes longer when increasing the DC supply level. In addition, the flux

density escaped to the tank is increased to 0.14 T. The field intensity is much more

distorted compared with the flux density waveform.

Figure 4-58 Flux density distributions in three-limb transformer by varying the DC supply level

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.01 0.02 0.03 0.04

Cu

rre

nt

(A)

Time(s)

Phase magnetising currents in a 3-Limb transformer (Knee region with DC)

Ia(0.15Wb) Ib(0.15Wb) Ic(0.15Wb) Ia(0.2Wb) Ib(0.2Wb) Ic(0.2Wb)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

B(T

)

B(T

)

Time(s)

Flux Distribution in three-limb transformer(Knee region with DC)

Bbc(0.1Wb) Bab(0.1Wb) Bab(0.15Wb) Bbc(0.15Wb) Bab(0.2Wb) Bbc(0.2Wb)

Blt(0.1Wb) Brt(0.1Wb) Blt(0.15Wb) Brt(0.15Wb) Blt(0.2Wb) Brt(0.2Wb)


136

Figure 4-59 Field intensity distributions in three-limb transformer by varying the DC supply level

4.4.1.3 Sensitivity study on non-linear region with DC situation

The supplied three-phase AC voltage is 120% of rated voltage, which can warrant the

transformer working under the non-linear region. The same as the previous two cases,

the DC supply which is in the unit of flux, Wb, varies at 0.1 Wb, 0.15 Wb and 0.2 Wb.

Instead of showing the phase current waveforms, Table 4-15 shows the peak value

results of the phase current in all the three simulation cases. It can be seen that, the

higher the working point of the transformer, the more sensitive it is towards the DC

supply.

Table 4-15 Peak values of the phase currents for different cases

DC(Wb) Ia(A) Ib(A) Ic(A)

Linear

0.1 2.564749 2.614067 2.564751

0.15 3.841559 3.919921 3.841561

0.2 5.373061 5.477727 5.373062

Knee

0.1 4.653478 4.687275 4.653488

0.15 48.48069 48.51229 48.4807

0.2 624.8655 624.9169 624.8655

Non-Linear

0.1 4021.98 4022.017 4021.98

0.15 39118.42 39118.55 39118.42

0.2 329004.1 329004.3 329004.1

Figure 4-60 and Figure 4-61 show the flux density and field intensity distribution.

Compared with the case of rated voltage supplied, the magnitudes of both parameters

are increased and the harmonic contents are more serious. The saturation period is

longer which can be seen from the flat part of the of flux density yoke in Figure 4-60.

0

50

100

150

200

250

-40

-20

0

20

40

60

80

100

0 0.01 0.02 0.03 0.04

H(A

/m)

H(A

/m)

Time(s)

Field intensity in three-limb transformer(Knee region with DC)

Hab(0.1Wb) Hbc(0.1Wb) Hab(0.15Wb) Hbc(0.15Wb) Hab(0.2Wb) Hbc(0.2Wb)

Hlt(0.1Wb) Hrt(0.1Wb) Hlt(0.15Wb) Hrt(0.15Wb) Hlt(0.2Wb) Hrt(0.2Wb)


137

Figure 4-60 Flux density distribution in the three-limb transformer

Figure 4-61 Field intensity distribution in the three-limb transformer

From the investigation above, it can be seen that the higher the working point of the

transformer, the higher the risk of saturation the transformer would have when it meets

the DC supply. The five-limb transformer has the similar trend as the three-limb core

transformer.

4.5 Summary

In this chapter, the transformer core structure influence on the magnetising current and

the transformers response to DC bias or GIC events has been successfully identified.

0

0.05

0.1

0.15

0.2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.01 0.02 0.03 0.04

B(T

)

B(T

)

Time(s)

Flux distribution in three-limb transformer(Nonlinear region with DC)

Bbc(0.1Wb) Bab(0.1Wb) Bab(0.15Wb) Bbc(0.15Wb) Bab(0.2Wb) Bbc(0.2Wb)

Blt(0.1Wb) Brt(0.1Wb) Blt(0.15Wb) Brt(0.15Wb) Blt(0.2Wb) Brt(0.2Wb)

0

50

100

150

200

250

300

-100

-50

0

50

100

150

200

250

300

350

0 0.01 0.02 0.03 0.04

H(A

/m)

H(A

/m)

Time(s)

Field intensity in three-limb transformer(Nonlinear region with DC)

Hab(0.1Wb) Hbc(0.1Wb) Hab(0.15Wb) Hbc(0.15Wb) Hab(0.2Wb) Hbc(0.2Wb)

Hlt(0.1Wb) Hrt(0.1Wb) Hlt(0.15Wb) Hrt(0.15Wb) Hlt(0.2Wb) Hrt(0.2Wb)


138

Besides investigating the corresponding magnetising current in relation to the core

structure, the flux distribution in the transformer core has also been determined.

Based on the knowledge developed and the analysis of the simulation cases, the core

structure influence on the magnetising current and flux distribution of the transformers

can be summarised as follows:

1. From the statistical analysis of data from the open circuit tests, it can be seen

that for the magnetising current of the transformer, it was found that the

improvement in the core materials would reduce the magnitude of the

magnetising currents, and the two types of core structures influence the balance

of three-phase currents.

2. The magnetising currents are not only related to B-H curve of the core material,

but also the length and the cross-section area of the transformer yoke and limb.

3. Based on case study one, the three-phase magnetising currents of the five-limb

transformer are much better balanced than those of three-limb transformers; this

is proved by the statistical data provided by the National Grid database.

4. From case study two, it can be seen that during the five-limb transformer

simulation analysis, by varying the magnitude of the magnetic flux density, the

waveform of the magnetic flux density would be distorted with the increase of

the flux density, and the magnitude of the main yoke is higher than that of the

main limb and side yoke. Nevertheless, the magnitude of the fundamental

frequency magnetic flux density in the side yoke changes faster than the main

yoke. By varying the ratio of the cross-section between the main yoke and the

side yoke, the magnitude of the fundamental frequency and the third harmonic

decreased as the main yoke cross-section area is increased. In addition, both of

the magnetic flux densities are decreased in the side yoke and main yoke, due to

the increase of the main yoke area.

5. From case study three, it can be seen that fixing the DC supply flux at 0.1Wb, by

varying the magnitude of supplied AC voltage, the waveform of the magnetic

flux density in the side yoke and main yoke would be distorted with the increase

of supplied AC voltage, and they have the same trend as under the balanced

situation. This means the magnitude of the main yoke is higher than that of the

main limb and side yoke.


139

Although the manufacturer provides the RMS values of the magnetising currents, the

information is not sufficient to understand the flux distribution and the core situation.

The recommendation is made for the manufacturer to provide more detailed

magnetising current waveforms.

However, all the analyses above are based on some assumptions, the losses and the

joints of the transformer core are not considered, the model is good for analysis of

individual transformer flux distributions and magnetising currents; however it is not

appropriate to investigate the GIC or other core saturation events of the whole network

influence. Therefore, the next chapter will look at the influences regarding the network.

Chapter 5 GIC magnetic and electrical circuit modelling

140

Chapter 5 GIC magnetic and

electrical circuit modelling

5.1 Introduction

In Chapter 4, the influence of the transformer core structure on magnetising currents and

flux distributions was discussed. In addition, the investigation is conducted on both the

balanced and unbalanced situations in order to understand parameters which influence

the flux distribution.

In reality, a three single-phase transformers bank is normally used as generator

transformers, three-phase five-limb transformers are extensively used as interconnection

transformers to connect two transmission voltage levels; three-phase three-limb

transformers are the most frequent form, which are extensively used in transmission

systems and distribution systems. Therefore, it is necessary to model the individual

system under study in order to understand the influences of system parameters and the

transformer structure.

This chapter will set out to evaluate the power system and transformer factors that may

affect the magnetising current level and its risk when a transformer meets the DC bias

situations or GIC events. The transformer structures and the system parameters will be

examined for their influences on GIC. Both cases of the DC only and AC plus DC

voltage supply are studied. The DC only case is used to illustrate the core saturation

process, which clearly shows the stages of the growing process of primary current

during a GIC event. However, in reality, the system works under the AC source, and the

AC plus DC voltage supply case is more realistic, since the core works in the knee area

so it quickly saturates and the envelope of the current is more realistic.

5.2 Case 1: GIC effect on single phase transformer

5.2.1 Single-phase model

The transformer data used are from an existing three-limb distribution transformer,

because no single phase transformer data are provided. The voltage level of the single


141

phase transformer is assumed to be the same as the real three-phase transformer which

is 132/33 kV. The data used for the transformer modelling are shown in previous

chapter Table 4-1.

According to the open circuit and short circuit test report data in Table 5-1, the

equivalent resistance and inductance of the core and the winding can be obtained. The

short circuit test is carried out on the high voltage side i.e. 132 kV for a rated current

with low magnitude; while the open circuit test is carried out on the low voltage side i.e.

33 kV for a rated voltage with low magnitude.

Table 5-1 132/33 kV transformer test report data

Short circuit test Open circuit test

Voltage

(V)

Current

(A)

Losses

(kW)

No load

voltage(V)

Average

current(A)

No load

loss(kW)

29628 378.1 279.9 29702 0. 643 23.61

/ / / 33005 0.977 29.64

/ / / 36296 1.8133 37.62

From experience, if there is no specific value provided by the manufacturer, then the

distribution of the winding impedance at primary and secondary sides will be the same,

50% of the impedance. The calculation equations are the following:

. .

1* * (5.1)

2s

p w s w bb

PR R Z

S

2 2

. . .

1* ( ) (5.2)

2H

p w s w p ws

VX X R

I

.. . (5.3)

2p w

p w s w

XL L

f

2

(5.4)Hb

b

VZ

S

21* (5.5)

3o

co

VR

P

All the symbols of the equations are shown in Table 5-2.


142

Table 5-2 Symbol explanations for the calculation of transformer parameters

Winding resistance per phase on the

primary side Short circuit test losses

Winding resistance per phase on the

secondary side Power base

Winding reactance per phase on the

primary side Primary side voltage

Winding reactance per phase on the

secondary side Short circuit test current

Winding inductance per phase on the

primary side f Frequency of the system

Winding inductance per phase on the

secondary side Impedance base on the primary side

Core resistance per phase 100% voltage in open circuit test

100% voltage open circuit test losses

Then all the parameters which are used in the lumped-element transformer model can be

calculated. And the calculated parameter values are shown in Table 5-3.

Table 5-3 Values of transformer model parameters

To represent the single-phase transformer core characteristics, for the purpose of

illustration only, the three-limb transformer core characteristics are used. Figure 5-1

shows the core characteristics λ-I curve, where the λ is the flux linkage of the

transformer in Wb, and I is the magnetising current in Amp.

Figure 5-1 Core λ-I curve from the three-phase transformer


143

The curve shown in Figure 5-1 is fitted by using the open circuit test which is based on

the 90%, 100% and 110% supplied voltages and corresponding magnetising currents.

Then a three single-phase transformer model can be built in ATPDraw for investigating

the DC bias or GIC events. The model is built as a lumped parameters model which

includes the resistances and inductances of primary winding and secondary winding

(Rp.w, Lp.w, Rs.w, Ls.w), the resistance and non-linear inductance of the transformer core

(Rc, Lc). One of single-phase transformer models is shown in Figure 5-2.

Figure 5-2 Single phase transformer model

The difference between the YNd connected transformers and YNy connected

transformers of the no load situation is due to the fact that the zero sequence induced

current can pass through the delta windings but not the star-connected open circuit

windings. So the transformer winding connections as YNd and YNy should have

different responses when both of them meet the GIC or DC bias situation.

To investigate the influences of two different winding connections three single-phase

transformer models are built and the simulation results are presented and discussed in

the following sections.

5.2.2 Simulation of DC only supply

The simulation is designed in such a way that a step-by-step approach is used. The first

step is conducted to supply a DC voltage into the primary side of the single phase

transformer to investigate the influence of DC bias or GIC. As the typical range of GIC

value is from 10 to 15 V [70], a 10 V DC voltage source is used. There are two key

geophysical factors controlling the earth surface potential level, which are: ground

conductivity structure and geomagnetic latitude [84].

The single phase transformer model connected with DC voltage source is shown in

Figure 5-3.


144

Figure 5-3 Single phase transformer simulation model in ATP

The three single-phase transformers are connected together by using delta connected

secondary windings under an open circuited situation which is shown in Figure 5-4. The

supplied voltage is a DC source, and then the DC current or zero sequence current

would be circulating in the transformer delta connected windings. The results are shown

in Figure 5-5.

Figure 5-4 Three single-phase transformer bank simulation model in ATP


145

(a)

(b)

Figure 5-5 (a) Primary side current and flux under DC excitation-full waveforms

(b) Primary side current under DC excitation-zoomed in waveform

Figure 5-5 shows the primary side current and the flux waveform, the red line represents

the primary side current and the green line represents the flux linkage. It can be seen

that the primary current has a 'two-step function' waveform, and the flux has a 'one-step

function' waveform. In order to conveniently explain its behaviour, the waveform of the

current is divided into three stages as indicated in Figure 5-5.

Figure 5-5 (b) shows that the primary side current waveform of Figure 5-5 (a) is

separated into three parts and each part is zoomed. Each stage is named in accordance

with its own property. However, it is not quantificational defined so there are no

definite boundaries between the two adjacent stages.

It can be seen in Figure 5-5 (b) that, the step-response stage is the first stage that the

primary current has experienced under the GIC. Because the circuit is structured as the

inductance and resistance, from the fundamentals of electric circuits; it is known that the

behaviour of the primary current would start as the step-response-like. The pseudo-flat

stage comes after the step-response stage; and the waveform looks flat in Figure 5-5 (a),

but when it is zoomed in, it is in fact not flat. The saturation stage comes after the

pseudo-flat stage; and the current is increased quickly and then stabilised at this stage.

This is mainly due to the saturation characteristics of the non-linear inductance of the

transformer core.

Flux(W

b)C

urr

en

t(A

)

Time(s)

Stage I

Stage IIIStage II

Step-response stage Pseudo-flat stage Saturation stage

Cu

rre

nt(

A)


146

The equivalent circuit of the whole circuit can be represented in Figure 5-6 which can

help to understand the “two-step function” waveform of the primary current.

Figure 5-6 Equivalent circuit of the simulation model

The secondary delta winding impedance is referred to the primary side and paralleled

with Rc and Lc.

The equivalent circuit works as long as the transformer is working properly. It means

that the current flowing into the transformer core, i.e. the non-linear inductance in this

case must vary with real time to make sure the secondary winding impedance can be

seen by the whole circuit.

The beginning of the supply DC only voltage which is the step-response stage; a current

is produced and tends to approach the first stable DC current value in the transformer

core non-saturated situation. However, due to the effect of the inductance, it takes time

for the current to grow from zero to a stable value. During this stage, the transformer

core is working at the linear region and the inductance and resistance of the core both

have with large values compared with the winding inductance and resistance, and also

as the core impedance is parallel with the secondary winding impedance, the core

impedance can then be omitted. The equivalent circuit can therefore be simplified as

shown in Figure 5-7.

Figure 5-7 Simplified equivalent circuit at step-response stage in YNd connection

Once the circuit is determined, the time constant and the final value for the step

response can be calculated by using (5.6).


147

. . . .( )* ( ) (5.6)o p w s w p w s wdiV R R i L L

dt

By solving the differential equation above, the current can be obtained as,

. .

. .

*

. .

*(1 ) (5.7)

p w s w

p w s w

R Rt

L Lo

p w s w

Vi e

R R

Then the time constant and the final stable value are calculated as,

. .

. .

0.0720.2371 (5.8)

0.301

p w s w

p w s w

L L Ht s

R R

. .

1016.6 (5.9)

2*0.301

oo

p w s w

V Vi A

R R

A comparison between the theoretical calculations with the simulation results is shown

in Figure 5-8. The simulation results show that the final stable value is 16.6 A and the

time constant is 0.2371 s, which coincides with the calculation values. As a final point

during the step-response stage, only the winding resistances would influence the results,

and the transformer core impedance can be ignored.

Figure 5-8 Time constant and the final value of the step response current

For the second stage which is the pseudo-flat stage, it can be seen that the primary side

current has changed slightly. As long as there is some voltage drop in the core, there

will be a current flowing through the core resistance and inductance, the secondary delta

T=0.2371sI=(1 - e-1)Io=10.49A

Io=16.6A

Time(s)

Cu

rre

nt(

A)


148

connected winding impedance still needs to be taken into account as the transformer

still works and follows the fundamental theory.

Due to the DC voltage drop on the transformer core which is around a half of the source

voltage, the flux is accumulated in the transformer core. As we know, for the single

phase transformer all the DC flux would be circulated inside of the core. In addition,

with the DC flux growing, the working point of the non-linearity of the inductance

gradually shifts up and approaches the knee area.

In this process, the value of the non-linear inductance decreases slowly and the current

increases slightly. Consequently, the primary current, as the sum of the secondary

current, the core resistance current and core inductance current, increases slightly.

Figure 5-9 indicates the variation of the current of the non-linear inductance and the

primary current under its influence.

Figure 5-9 Primary current and core current at the pseudo-flat stage

It can be seen that during this stage both the primary and non-linear inductance currents

have changed. Therefore, the change makes sure that the transformer is still working

properly; because the flux in the core also varies by the time the induced voltage

appears in the secondary side of the transformer. At the end of pseudo-flat stage, the

flux reaches the knee area and the value of the non-inductance starts to change swiftly.

Primary current

Core current

Cu

rre

nt(

A)

Time(s)

Cu

rre

nt(

A)


149

Following the pseudo-flat stage is the saturation stage. It starts at the flux just stepping

into the knee area. As the value of the non-linear inductance changes very swiftly from

a large value to a very small value, the distribution of the DC source voltage between

the primary winding and the core also changes very fast. Even though the voltage drop

on the core decreases with the decrease of the value of the non-linear inductance, the

core flux keeps accumulating until the flux leaves the knee area and goes into the

saturation region, where the value of the non-linear inductance can be considered as

zero and the voltage drop on the core falls to zero.

As a result, the transformer does not transform voltage anymore and tends to be short

circuited in an ideal situation. From then on, the system becomes stabile and the

primary current does not change anymore. The stabilised primary current is only

controlled by the primary winding resistance as it is the only component that the DC

source is able to see. So the final current can be calculated as

.

1033.22 (5.10)

0.301

ostable

p w

V Vi A

R

The simulation result which is shown in Figure 5-10 is well matched with the

calculation result in (4-10).

Figure 5-10 Final stable value of the primary current

I = 33.217A

Cu

rre

nt(

A)

Time(s)


150

As the flux is totally contributed by the DC voltage source, it can be calculated by using

the formula: 0dE

dt

, E is the voltage drop on the transformer core which results in the

total flux accumulated by the DC source.

Assuming that the 110% rated voltage can saturate the transformer core, and then the

saturation flux can be calculated as0

110%* ( 2 sin )3

rateds

Vt dt

.

The time for the saturation of the core and also for the primary current to become stabile

can be approximately calculated as stE

. In this case the saturation time is 75.5 s.

The simulation results are shown in Figure 5-11 which include the flux linkage and the

primary current waveforms. It can be seen that the saturation time is 82.4 s which is a

little bit greater than the theoretically calculated result.

Figure 5-11 Core flux and primary current

The difference between the simulation results and the calculation results are mainly due

to two reasons; the first is that the knee area is simplified as the cross point of the two

straight lines, one represents the linear region and the other saturation region; and the

second is that the voltage drop on the transformer core is assumed as a constant value

before the transformer is saturated. In the calculation, the flux is approximated to

accumulate a consistent speed even in the knee area, but the growing speed of flux in

the knee area is actually slower.

Primary current

Core flux

t = 82.4s

Cu

rre

nt(

A)

Time(s)

Flux(W

b)


151

5.2.3 Winding connection influence

For three single-phase transformers which are connected as YNy, it can be seen that

there is no mutual coupling between any of them, and the zero sequence current cannot

be passed to the secondary side windings. So a single phase model can be used to

represent the situation of the three single-phase transformers (transformers bank).

Therefore the simulation of DC voltage supply is carried out by using the model which

is shown in Figure 5-12.

Figure 5-12 Simplified three single-phase transformers model in ATPDraw

The simulation result is shown in Figure 5-13. It can be seen that the step-response

stage disappears and the other two stages remain. The primary current stabilises when

the core flux stops growing and reaches saturation. The saturation time is around 42 s

which is half the saturation time of the YNd three single-phase transformers bank (82.4

s).

Figure 5-13 Core flux and primary current in the simulation for YNy three single-phase

transformers bank

Since the primary winding impedance in series with the core impedance is smaller than

the core impedance, almost all of the DC voltage would drop onto the core impedance

until the core is saturated and behaves as short-circuited. In addition, the step response

Cu

rre

nt(

A)

Time(s)

Flux(W

b)Primary current

Core flux

t = 42s


152

should still exist but the total system inductance is the winding plus the core

inductances which are equal to a large value, then the increasing time of the current is

too long to be seen. Figure 5-14 shows the simplified equivalent circuit at the step-

response stage in YNy connection.

Figure 5-14 Simplified equivalent circuit at step-response stage for YNy connection

Before the first stabile point appears, the core has already been saturated and the current

would rise again to reach the final stabile point; so the step response would not be

observed in this case. Also, almost all of the supplied voltage drops onto the core

inductance instead of half the voltage as in the YNd case, the flux accumulating speed

doubles and the time for saturation is halved compared with the YNd connected

transformer.

To conclude, the primary current presents a ‘single-step function’ waveform in the YNy

connection situation instead of a ‘two-step function’ waveform as in the YNd

connection. Since the step-response stage is not observed, the pseudo-flat stage and the

saturation stage show up; however the saturation time will be approximately half that in

the simulation for the YNd three single-phase transformers bank.

For the three single-phase transformers bank, the key parameters which influence the

transformer behaviour under the GIC events include the level of DC voltage supply, the

value of winding resistance, the value of winding inductance and the non-linear

characteristics of the core.

5.2.4 Transformer core characteristic influence

From the previous section, it can be seen that the core characteristics can influence the

results. Therefore the core characteristics, which are the non-linear inductance of the

core, are varied so that we can understand its influence. The single phase transformer

model in Figure 5-3 has been used for the simulation studies. The resistance of 0.5 Ω

and inductance of 100 mH added at the primary side, which is between the DC voltage


153

source and the transformer, represent the system’s resistance and inductance. The 10 V

DC voltage is supplied as the source.

5.2.4.1 Forward and backward shifting

The λ-I curve of the non-linear inductance is modified by changing the non-linear

characteristics settings. The λ-I curve is defined by 31 flux/current points, and it can be

modified by changing the current value of each point with the corresponding flux value

maintained. In this way, the maximum flux that the core inductance can reach is

maintained while the curve is shifted backward by reducing the current values or shifted

forwards by increasing them. This modification is to simulate different materials which

are used to build the transformer core.

In the simulations, two extra λ-I curves are generated based on the original one. Figure

5-15 shows two generated curves and the original λ-I curve.

Figure 5-15 λ-I curves (a): Three curves in one figure (b): Knee areas of three curves

The original one is given as the green line, the backward shifted one is given as the red

line and the forward shifted one is given as the blue line. The modifications attempt to

represent different situations; i.e. the backward shifted curve represents the easiest case

for the core to saturate, because it needs the least current to reach the maximum flux. By

contrast the forward shifted curve is the hardest to go into saturation since it requires the

most current. Also, the backward shifted core curve has the sharpest knee area and the

forward shifted curve has the flattest knee area.

(a) (b)

Flu

x(W

b)

Current(A)


154

Figure 5-16 shows the simulation results for three identical models with three different

core curves.

Figure 5-16 Simulation results for models with different core curves

Simulation results show that the modification of the core curve, in the form of forward

and backward shifting, does not influence the step-response stage and the early part of

the pseudo-flat stage. The only influence made by the core curve is in the later part of

the pseudo-flat and the step changing. This is mainly because during the time when the

transformer core is working at the knee area, the knee areas of these three curves are

different. It can be seen that the steeper the knee area, the more quickly the primary

current rises. Due to the fact that the maximum flux is not changed, the saturation times

in different cases are the same.

5.2.4.2 Changing of slope of the saturation part

The purpose of the modification of the characteristics of the λ-I curve is to simulate the

effects of different materials. By fixing the linear and the knee region of the curve, and

only varying the final slope of the saturation region, it can be considered that this is to

simulate the different core structures. The final slope of the characteristics represents air

core inductance, which is mainly determined by the structure inside the transformer.

For the 120% curve, the maximum value of flux is set as 120% of the max value in the

original curve, thus the slope of its saturation region is roughly 8.15 Wb per ampere.

For the 110% curve, the maximum value of flux is set as 110% of the max value in the

original curve, and the resultant slope of the saturation region is around 4.2 Wb per

ampere. Figure 5-17 shows two generated curves and the original λ-I curves. The

original one is given as the blue line; the upward shifted 110% one is given as the green

line and the upward shifted 120% one is given as the red line.

Cu

rre

nt(

A)

Time(s)


155

Figure 5-17 Three curves for upward and downward shifting

In Figure 5-18, it can be seen that the saturation time of each result is different from one

another. The more the saturation region of the core curve shifts upwards, the longer time

it takes the transformer to be saturated; and the longer the rising time of the second step

is maintained. By changing the slope of the saturation region of the core curve, not only

the maximum flux at a certain level of current is changed, the way of the change of core

inductance is also changed. After the core gets into saturation, the voltage dropping on

the core depends on the core inductance. If the core inductance turns zero ideally after

saturation, it can be considered that no voltage is dropped on the core and the flux

accumulation is stopped. In this case, the saturation time is the total time taken by the

DC flux accumulation to reach the saturated core flux.

Figure 5-18 Simulation results for models with different core curves (a): Primary current (b): Flux

However, with the change of the slope of the saturation region of the core curve, the

voltage drop on the core is no longer zero but a very small value, which leads to a very

slow rise of the flux accumulation after saturation.

Flu

x(W

b)

Current(A)

146.8s 286.9s182.5s

Cu

rre

nt(

A)

Time(s)

Flu

x(W

b)


156

For the investigation above, it can be known that the non-linear slope and the knee area

of the B-H curve would influence the second step response for the YNd, and the

saturation time for both the YNd and YNy connection transformers.

5.2.5 Network parameter influence

In terms of the influences of network parameters for GIC events or DC bias, the single

phase transformer model displayed in Figure 5-3 is used for the simulation investigation.

The simulations are carried out as the DC voltage supplying the whole circuit, like

before only varies the system resistance and inductance.

Resistance is added in series between the DC source and the impedance of the primary

winding of the transformer. The DC supplied voltage is still set as 10 V.

Figure 5-19 A system resistance added in circuit with transformer model

The simulation and calculation results are recorded and presented in Table 5-4. In the

table, Sim means the simulation results, and the Cal means the calculation results by

using the equations introduced in the early part of the chapter. The ‘two-step function’

waveform can be determined by the time constant of the rise at the step-response stage,

the stable value after the step response, the saturation time and the final stabilised

current.

Table 5-4 Impacts of system resistances on transformer performance under GIC or DC bias

Branch

Resistance (Ω)

Time constant

(s)

First stable

value (A)

Final stable

value (A)

Saturation time

(s)

Sim Cal Sim Cal Sim Cal Sim Cal

0.1 0.204 0.203 14.25 14.25 24.94 24.94 94.77 88.06

0.5 0.13 0.13 9.08 9.07 12.48 12.48 144.4 138.3

1 0.089 0.089 6.242 6.242 7.686 7.686 209.8 201.1


157

As the system resistance is increased, the time constant of the step-response is decreased;

the first stable value of current after the step-response stage; and then the final stable

value of current is decreased as well. Only the saturation time is increased.

Equation (5-8) shows that the time constant is determined by the inductance and

resistance of the system. So the time constant becomes shorter when the branch

resistance is increased. In addition, from (5-9) and (5-10), it can be seen that the primary

side current is determined by the supplied DC voltage level and the total resistance in

the system. When the total resistance in the system is increased, the supplied voltage is

not changed, and then the current must be decreased. The saturation time is mainly

determined by the voltage drop on the core. When adding a resistance connected with

the core in series, then it will re-distribute the ratio of the voltage. The voltage on the

core will be decreased, and then the saturation time will become longer.

Similar to adding system resistance, a system inductance is added in series between the

DC source and the impedance of the primary winding of the transformer. The DC

voltage level is still set as 10 V. A fixed system resistance of 0.5 Ω is connected in order

to accompany the system inductance in the simulation.

Figure 5-20 A system inductance added in circuit with transformer model

Table 5-5 shows the simulation results and calculation results.

Table 5-5 Impacts of system inductances on transformer performance under GIC or DC bias

Branch

Inductance

(mH)

Time constant

(s)

First stable

value (A)

Final stable

value (A)

Saturation time

(s)

Sim Cal Sim Cal Sim Cal Sim Cal

50 0.175 0.175 9.078 9.076 12.48 12.48 144.4 138.3

100 0.221 0.220 9.078 9.076 12.48 12.48 144.4 138.3

200 0.311 0.311 9.078 9.076 12.48 12.48 144.4 138.3

From the results, it can be seen that the system inductance only affects the time constant

of the step response which is mentioned in (5-8).


158

In the same way as before, with two parameters added to the circuit, the shunt

capacitance is added to the circuit. In the circuit, 0.5 Ω system resistance and 100 mH

system inductance are added at the primary side and a shunt capacitance with a value of

100 µF is added between the system impedance and the winding impedance. The

waveforms of the primary current and flux linkage are displayed in Figure 5-21.

Figure 5-21 Impacts of the shunt capacitance

The overall shapes of the primary current and flux linkage waveform are the same as

those simulated without the shunt capacitance. Even the key features including the step-

response time constant, the step-response stable value, the saturation time and the final

stable value do not change with or without the shunt capacitance. However, the

existence of the shunt capacitance produces some high frequency components due to its

resonance with the system inductance.

5.2.6 Simulation of AC & DC supply

From the last section, it can be seen that the three single-phase transformers bank can be

represented as a single phase transformer in the case of DC supply only. However, a

single-phase model cannot represent three single-phase transformers bank in the AC and

DC mixed supplied situation.

A YNd connected transformer bank is constructed by using a three single-phase

transformer model. There are two sources in the model, one is the AC supplied voltage

at 132 kV and the other is a 10 V DC voltage which is supplied from the neutral of the

primary side Y connection winding to simulate GIC event or DC bias. Large resistances

are connected as load to simulate the no load condition. The simulation model is shown

in Figure 5-22.

Cu

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b)

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Figure 5-22 Three single-phase transformers bank in YNd connection

System resistance and inductance are set as 1.376 Ohms and 24.968 mH which are

obtained from one of the 132 kV busbar database provided by Electrical Northwest

(ENW).

As mentioned before, the DC voltage supplied to the single phase transformer model is

to simulate the YNd three single-phase transformers bank and results show that the

primary current displays a ‘two-step function’ waveform, which includes the step-

response stage, pseudo-flat stage and the saturation stage. When the DC voltage is

supplied in the neutral of the primary star in the AC powered YNd single-phase

transformers bank, the primary current has the same pattern of waveform, with the

sinusoidal waveform integrated. This is shown in Figure 5-23.


160

Figure 5-23 Simulation results for Phase A (a): Primary current (b): Step-response of primary

current (c): Magnetising current (d): Current referred from secondary winding

It can be seen that the waveforms are following the supplied AC source, and the

oscillation content in the waveforms is of 50 Hz.

Figure 5-24 compares the saturated part of the primary current, magnetising current and

secondary winding current referred to the primary side. It can be seen that the delta

connected secondary windings influence the primary current because the third order

harmonic current flows into the delta connected loop. Due to the symmetry of the three

phase system, the current of each phase behaves similarly; therefore only phase A is

displayed.

Figure 5-24 Saturated part of primary current, magnetising current and secondary delta connected

winding current referred to primary side

(a) (b)

(c) (d)

Cu

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Time(s)

Cu

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Time(s)

Primary Current

Magnetizing current

Delta winding current referred to primary side

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At the very beginning, before the core is saturated, as the secondary delta winding

impedance can be seen from the primary side, the magnetising current is relatively small

because of the large core impedance and therefore the primary current is in sine wave.

With the flux accumulating, the core working point goes into the knee region and the

magnetising current roars up to a large value, so does the primary current. Then the core

is saturated and the magnetising current stabilises. At this moment, the primary current

contains bi-polar pulses contributed by the magnetising current and the third harmonic

current from the secondary delta connected windings as shown in Figure 5-24.

When an AC source is present, the saturation time is shortened. Comparing the supplied

DC only case and this case where GIC effects on the AC system are simulated, although

the accumulating speed of the flux remains the same, the additional AC voltage peak

pushes the flux closer to the saturation region, so the time spent on reaching the

saturation is much shorter in the real case of GIC effect.

The AC voltage source also brings the over-current in the saturation stage due to the

saturation of the core. As in the power system, the voltage level of the system is almost

fixed around the rated voltage but the GIC can be varied within a wide range from a few

volts to hundreds of volts, how different levels of GIC affect the value of the stable peak

of the saturation current becomes an interesting and important topic. A series of

simulations have been done to explore the relationship between the DC supply level and

the final stable peak value of the primary current after saturation. The results are shown

in Table 5-6.

Table 5-6 Relationship between the supplied DC level and the final peak current value

Supplied DC voltage (V) 1 5 10 20

Final peak primary current (A) 12.644 46.172 75.387 121.83

Final peak magnetising current (A) 15.198 55.057 89 142.11

Larger DC levels lead to larger final values for the primary current drawn from the

system. Also, the final peak value difference between the primary current and the

magnetising current increases with the DC supply level. This can be explained as the

larger the DC voltage supply, the larger the current will flow in the secondary delta

connected loop.

In reality, a transformer or a system grid is often connected with the load, which is the

function of the grid to transfer the energy. Consequently, whether the load would

influence the GIC effects would become an interesting and important topic to study. RL


162

loads (with the power factor of 0.8 lagging) are added onto the YNd three single-phase

transformers bank to investigate the effects of load on the GIC effect of transformer

with DC supply at the neutral of the primary-side star connected windings. The

simulation model displayed in Figure 5-22 is used by varying the load. Simulations with

100%, 70%, 50%, 30% and 10% loads respectively are conducted. Key parameters of

the primary current including the stable value of the step response, the saturation time

and the final peak value are recorded which are shown in Table 5-7.

Table 5-7 Load effects on GIC performance of the YNd single phase transformer banks

Load (%)

Stable value

of the step

response (A)

Saturation

time (s)

Saturated magnetising

current peak value (A)

Saturated

primary current

peak value(A)

100 5 59 88.64 184.70

70 5.02 58 88.73 149.03

50 5.02 58 88.70 127.59

30 5.02 57 88.86 107.82

10 5.02 56 88.97 86.14

No load 5.02 55 88.90 75.40

From the data in Table 5-7, the stable current value of the step response is

approximately the same as 5 A, which is independent of the load. Loads have little

influence on the saturation time, although the saturation time increases slightly with the

increase of load. The saturation time is mainly decided by the DC supply level.

The YNy connected three single-phase transformers bank is built for the comparison

with the YNd connection. There are two sources of the model, one is the AC supplied

voltage at 132 kV; and the other is a 10 V DC voltage which is supplied from the

neutral of the primary side Y connection winding to simulate GIC event or DC bias.

Large resistances are connected as load to simulate the no load condition. The

simulation model is shown in Figure 5-25.


163

Figure 5-25 YNy single phase transformer bank under no load condition

According to the previous simulations, when a DC source supplies a single phase

transformer, the primary current presents a ‘one-step function’ waveform, which

contains only the pseudo-flat stage and saturation stage. When an AC source is plugged

in, although the current turns sinusoidal, the envelope of the waveform will still exhibit

the ‘one-step function’ shape which is the same as the case where only DC is supplied.

However, the saturation of the core will result in overcurrent, thus the stabilised peak

value of the current can be very large. The simulation results are shown in Figure 5-26.


164

Figure 5-26 Simulation results for Phase A (a): Primary current (b): Magnetising current (c):

Starting moment (d): Saturation moment

Similar to the case of DC supply only, the primary current presents a ‘one-step function’

envelope. The primary current is comprised of the magnetising current and the current

flowing through the core resistance. At the very beginning, the primary current is so

small and it is a sine wave. With the flux accumulating, the working point of the core

biases and goes into knee area and the magnetising current roars up to a large value, so

does the primary current. Then the core is saturated and the magnetising current is

stabilised.

The saturation time of the primary current is shortened for the case of GIC effect. It is

because the AC peak brings the flux closer to saturation and so less time is needed for

the accumulation of DC flux to bias the working point of the core reach saturation.

Simulations investigating the relationship between the DC levels and the peaks of final

current are performed and the results are shown in Table 5-8.

Table 5-8 Relationship between the supplied DC level and the final peak current value

Supplied DC voltage (V) 1 5 10 20

Final peak primary current (A) 14.79 52.79 86.28 137.64

Final peak magnetising current (A) 14.79 52.79 86.26 137.64

(a) (b)

(c) (d)

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It can be seen that, the stabilised peak value of the primary current is equal to the

saturated magnetising current peak value, which indicates that the primary current peak

values are decided by the magnetising current after saturation. This result is different

from that of the case of the YNd three single-phase transformers bank, since no current

flows in the secondary side. The peak value of the magnetising current increases with

the growth of the supplied DC level, as a larger supplied DC may bring the core into

deeper saturation.

For the load influence, Table 5-9 shows the simulation results by varying the load

percentage. Due to the fact that there is no step-response in the YNy connection, then

there are only three parameters recorded, i.e. saturation time, saturated magnetising

current peak value and saturated primary current peak value.

Table 5-9 Load effects for the YNy single phase transformers bank

Load (%) Saturation

time (s)

Saturated magnetising current

peak value (A)

Saturated primary

current peak value(A)

100 16 84.65 467.19

70 15 84.64 344.78

50 14 85.28 255.58

30 14 85.87 185.72

10 14 84.87 118.61

No load 15 86.23 86.26

Both the saturation time and the magnetising current peak value can be considered to be

independent of the load.

5.3 Case 2: Sensitivity of transformer core structure

In the last section, the influence of the winding connection, core characteristic and

network parameters were discussed by using three single-phase lumped-parameter

transformer models. Supply the DC only and DC mixed with AC are both used for the

simulation studies.

In this section, the influences of core structures or transformer GIC performance will be

discussed which include three-limb and five-limb transformers with the three single-

phase transformers bank acting as the reference.


166

5.3.1 Comparison between YNd connected three single-phase

transformers bank and three-phase three-limb transformer

As far as the transformer structure is concerned, the main difference between the three

single-phase transformers bank and the three-phase three-limb transformer is that there

is flux coupling among phases by yoke in a three-limb transformer. In addition, there’s

no DC flux passing path in a three-limb transformer.

The simulation was carried out by using the same condition as before which is the

supply DC voltage as 10 V. The comparison of the primary side current waveforms

between a three-limb transformer and three single-phase transformers bank are shown in

Figure 5-27.

Figure 5-27 Comparison between YNd connected 3 single phase transformers bank and three-phase

three-limb transformer

The top figure shows the whole waveforms of primary side current of the two different

core structure transformers; and the bottom two figures show the step-response stage

and the final stage. It can be seen that at the step-response stage and the final stage these

two different core structure transformers have slightly different responses.

Transformers bank

3-leg transformerCu

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Table 5-10 shows the key parameters of the comparison between the transformers bank

and the three-phase three-limb transformer.

Table 5-10 Comparison between YNd connected transformers bank and three-phase three-limb

transformer

Parameters Time

Constant (s)

Stable value of

the step response

(A)

Saturation

Time (s)

Saturated

primary current

peak value(A)

Phases A B C A B C A B C A B C

Transformers

bank 0.24 0.24 0.24 16.6 16.6 16.6 32 32 32 259 259 259

Three-limb

transformer 0.15 0.15 0.15 20.2 20.2 20.2 75 75 75 220 220 220

It can be seen from Figure 5-27 and Table 5-10, the time constant of the step-response

part is different; the three-phase transformer has a shorter time constant, a higher stable

value of current of the step-response; also the saturation time is longer; and the final

current value is higher than the three single-phase transformers bank.

The zero sequence core impedances of the two transformers are different, and the zero

sequence core impedance is connected in parallel with the positive sequence core

impedance and the impedance of secondary delta connected windings. The system

equivalent resistance and inductance at the step response stage and pseudo flat stage is

decreased; as a result, in the case of three-limb transformer, the step response stable

value is increased and the time constant of the step response is decreased.

As far as the magnetic field is concerned, in the three single-phase transformers bank,

each phase has its own core which has high permeability and provides low reluctance

path for the flux passing through, including positive, negative and zero sequence flux.

Thus there is no flux coupling among phases, the magnetic flux of each single phase

transformer is considered to be inside the core only. However, for the three-phase three-

limb transformer, there is no low reluctance path for DC flux to pass, the only way for

the DC flux to pass through is to leak out of the core and go through the winding, oil,

tank and so on. However, those materials have low permeability and thus high

reluctance.

When the same level of DC voltage is supplied into the transformer via neutral, the high

reluctance loop is harder for the DC flux to be accumulated in the transformer core; then

it is harder for the three-limb transformer to be saturated therefore the three single-phase

transformers bank.


168

As far as the electrical circuit is concerned, the zero sequence impedance is the main

parameter which influences the DC bias or GIC events. The zero sequence impedance is

varied so that its influence on the no-load primary current can be investigated. The DC

only voltage is supplied into the transformer model. Figure 5-28 shows the comparative

results for different levels of zero-sequence impedances.

Figure 5-28 Zero sequence effects on the no load primary current of the YNd three-limb

transformer (a) infinity zero sequence impedance (b) default zero sequence impedance

It can be seen that, when the zero sequence is set as infinity, the zero sequence branch

parallel with core branch turns to be open circuit. Then the time constant, the stable

value of the step response stage, the saturation time and the stable value of saturated

current are determined by the supply DC level and the transformer winding impedance.

The default setting of zero sequence impedance gives and

. As the zero sequence impedance is paralleled with the core branch, its value

would influence the voltage drop on the core and therefore the saturation time is

changed by the zero sequence impedance. After the core is saturated, zero sequence

core impedance is short circuited as a result; its existence makes no difference to the

final value of the current.

As no DC flux leaks out of the core in the single phase transformer banks, zero

sequence core impedance is the same as the core impedance for the single phase

transformers bank before the core is saturated, which is exactly the same as setting the

zero sequence impedance as infinity in the three-phase three-limb transformer. Zero

sequence impedance is set as the default value in the three-limb transformer. The

comparison between the simulation results for the transformers bank and the three-limb

transformer with the same AC and DC supply agrees with the prediction.

Cu

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nt(

A) 16.6 A

20.2 A33.2 A 33.2 A

88.2 s 114 s

Time(s)

(a) (b)


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5.3.2 Comparison between YNy connected three single-phase

transformers bank and three-phase three-limb transformer

The same simulation investigation is carried out on the YNy connected transformer

model. Figure 5-29 shows the comparison results between the transformer banks and the

three-limb transformer. The Y-axis on the left side is for the transformer banks; and the

Y-axis on the right side is for the three-limb transformer.

Figure 5-29 Comparison between YNy connected 3 single phase transformers bank and three-phase

three-limb transformer

It can be seen that a ‘one-step function’ waveform occurs for the primary current of the

transformer banks, while the current of three-limb transformer has a ‘two-step function’

waveform due to the zero sequence core impedance in parallel with the transformer core.

The current rises much sooner for the transformers bank because more DC voltage

would be dropped on the core which means the accumulating speed of the flux is higher

than that in the three-limb transformer. The stable step response current value for the

three-limb transformer is 11.7 A. Table 5-11 shows almost all of the key parameter

values.

Transformers bank

3-leg transformer

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Cu

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Table 5-11 Comparison between YNd connected transformers bank and three-phase three-limb

transformer

Parameters Time

Constant (s)

Stable value of

the step response

(A)

Saturation

Time (s)

Saturated

primary current

peak value(A)

Phases A B C A B C A B C A B C

Transformer

bank / / / / / / 16 16 16 286 286 286

Three-limb

transformer 0.15 0.15 0.15 11.7 11.7 11.7 55 55 55 176 176 176

It can be seen that both of the two transformers under YNy connection are saturated

earlier as compared with the YNd connection.

To understand the influence of the zero sequence core impedance in the YNy three-limb

transformer, the DC only voltage is supplied and the zero sequence core impedances of

the transformer are varied. The simulation results are shown in Figure 5-30.

Figure 5-30 Zero sequence effects on the no load primary current of the YNy three-phase three-

limb transformer (a) infinity zero sequence impedance (b) zero sequence impedance between

infinity and default value (c) default zero sequence impedance

It can be seen that the step response stage cannot be observed as the time constant turns

to be infinity when zero sequence core impedance is set as infinity, due to the fact that

the transformer core impedance is in series with the primary winding impedance in the

circuit. The pseudo-flat stage and the saturation stage still exist and the saturation time

and the final current value can be calculated.

33.2 A

45 s

33.2 A

60 s

33.2 A

70 s

(a) (b)

(c)

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With the zero sequence core impedance is decreased from the infinity to a definite value,

the time constant of the step response stage gradually drops, thus the beginning part of

the waveform of the primary current rises gradually as shown in Figure 5-30 (b). And

the waveform is similar to one of the experimental results published by P.Price [70].

Decreasing the zero sequence core impedance down to the default value, the simulation

results are shown in Figure 5-30 (c). The ‘two-step function’ waveform is shown again.

As the zero sequence core impedance is decreased, the saturation time is increased.

5.3.3 Five-limb transformer

The five-limb transformer core is different from the three-limb transformer core and the

single phase transformer core as well. First, there is a loop on the core for DC flux

passing through which is similar to the single phase transformer core; second, there is

coupling among phases via the yoke of core which is similar to the three-limb

transformer core. So the five-limb transformer has some combined features of the other

two transformer core structures.

The response of the five-limb transformer to GIC is investigated in the following by

using one of several existing transformers working in the National Grid network. The

transformer is a 400/275/13 kV, 1000 MVA, YNad winding connection. Table 5-12

shows the basic information of the transformer model applied in this simulation.

Table 5-12 Basic information and test data of the three-phase five-limb transformer

Short Circuit Test Data Open Circuit Test Data

Voltage

Level Power Base

Impedance

(%)

Losses

(kW)

No Load

Voltage

(%)

Average

Current

(A)

No Load

Losses

(kW)

Primary:

400 kV

HV/LV

@1000MVA 16.78 1383 90 6.177 96.3

Secondary:

275kV

HV/T

@60MVA 7.29 71.9 100 13.15 127.9

Tertiary:

13kV

LV/T

@60MVA 5.97 77.3 110 55.433 175.3

In accordance with the test data and the basic information, a five-limb hybrid

transformer model is built for the simulation studies. In the circuit, there is a three-phase

400 kV AC source connected with the transformer and 100 V DC voltage supplied from

the neutral point of the primary side star connected windings into the transformer. No


172

loads are connected at the secondary side. The simulation results of the primary side

current are shown in Figure 5-31.

Figure 5-31 Primary side current with AC and DC supply

It can be seen that the waveform is neither ‘one-step function’ nor a ‘two-step function’

waveform. It is shown as a ‘three-step function’ waveform. Then the simulations of DC

supply only are carried out to try so that we can understand the response of the five-

limb transformer. The simulation results are shown in Figure 5-32.

Figure 5-32 Primary side current with pure DC supply only

Cu

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It can be seen that the primary side current is a ‘three-step function’ waveform. For the

first two steps, their flat parts are not truly flat, since the current still actually increases

but in a very slow slope. For the last step, the current is finally stabilised and is

maintained at the same level.

Compared with the ‘two-step function’ waveform of the primary side current of the

YNd connected three-limb transformer, the ‘three-step function’ waveform of the YNad

five-limb transformer has an extra step, and this is because the extra component forms

the core structure, the side yoke.

For the first step, it is as the same as the step-response controlled by delta winding, as

was previously explained. However, in this step, the DC flux accumulates inside the

core through the side yoke, which then has a different reluctance from the positive

sequence core reluctance.

For the second step, the whole DC flux continues to accumulate and flow through the

side yoke, until the side yoke is saturated. The saturation of the side yoke causes the

second rise of the primary current. After the side yoke is saturated, the DC flux cannot

be absorbed any more into the side yoke so the only way for them is to leak out of the

core and go into the oil and tank. In other words, the five-limb transformer tends to

become a three-limb transformer after the side yoke is saturated.

For the last step, DC flux further increases in the transformer core; the entire core goes

into saturation. Then the total non-linear core inductance starts to decrease and the

primary side current rises swiftly, which can be observed as the rise in the third step.

After the entire core is fully saturated, the core inductance drops to a very small value

which indicates that the short circuit and primary side current are finally stabilised.

All the key parameters can be calculated by using the same method as previously done

in this chapter. The calculation results are shown in Table 5-13.

Table 5-13 Key parameters of the primary side current with pure DC voltage supply

31.3 A 54.3 A 200.78 A 0.195s 15.6s 44s 90s

: The time constant of the step response

: The time instant when the second rise starts

: The time instant when the third rise starts

: The time instant when the entire core is fully saturated

: The stable value of the step response

: The stable value after the side yoke is saturated

: The stable value after the entire core is fully saturated


174

Compared with the simulation results, the calculated , and match the simulation

results very well; this verifies the explanation of the ‘three-step function’ waveform of

the primary side current with pure DC voltage only for the three-winding YNad five-

limb transformer. The explanation is also suitable for the case of AC supply and

Supplied DC as well. The waveform still follows the ‘three-step function’ as shown in

Figure 5-31. The key parameters of the primary side current waveform are shown in

Table 5-14.

Table 5-14 Key parameters of the primary side current with AC&DC voltage supplied

(A) (A) (A) (s) (s) (s) (s)

Phase A 31.3 54.3 571.79 0.195 15.6 25.6 78

Phase B 31.3 54.3 571.79 0.195 15.6 25.6 78

Phase C 31.3 54.3 571.79 0.195 15.6 25.6 78

, , , , , , symbols follow the definition as in Table 5-13. Ipeak is the

stable peak value after the entire core is fully saturated. and values are the RMS

value in this table. Compared with the case of DC supply only, , , and have

the same values as the DC level remains the same. It reflects that those parameters are

really determined by the DC supply level in the five-limb transformer core. , and

are determined by both of the levels of AC and DC supply.

5.3.3.1 Winding connection

As we know, winding connections have several common types used for power

transformers. There are two windings and three windings connection transformers. The

original transformer used in the simulation is the YNad connection transformer. The

investigation is carried out by varying the winding connection types which include

YNyd (three-winding connection), YNy (two-winding) and YNd (two-winding). All

other configurations remain the same, e. g. voltage level, power rating, short circuit test

data, open circuit data and core structure. Pure DC voltage source is supplied in this

simulation.

Figure 5-33 shows the primary side current waveform for three types of connection. It

can be seen that the ‘three-step function’ waveform is shown for the Yyd and YNd

connection, except the YNy connection. The waveform of the YNy connection is only a

‘two-step function’; since there is no secondary side delta connected winding in the

circuit in YNy connection. Therefore, the transformer core impedance needs to be taken


175

into account from the beginning; it increases the time constant of the step-response then

causes the current value to keep a low value. It also shortens the time allowed for

saturation. In addition, the final saturated stable value of the current is the lowest in the

Yyd connection due to the extra winding impedance.

Figure 5-33 Primary side current of Yyd, YNd and YNy connection transformer

Comparing all the four types of winding connection, the final saturated current value of

the YNad connected transformer is the lowest one, and the saturation time is the longest

one. Table 5-15 shows the key parameters of the primary currents for all the four types

of transformer winding connection.

Table 5-15 Simulation results for the primary side current in all four type of connection

(A) (A) (A) (s) (s) (s) (s)

YNad 31.3 54.3 200.8 0.195 15.6 44 90

Yyd 29.3 212.4 433.6 0.18 4.5 17 36

Yd 45.2 530.8 903.8 0.39 8.1 23.8 70

Yy / 270 903.8 / 4.2 13.3 44

‘Three-step function’ waveform still appears on the YNd connected transformer; while

the primary side current of the YNy connected five-limb transformer has a ‘two-step

function’ waveform. The first step response is missing in the YNy connection, also in

the YNd connection, the stable value of the step response is half the final stable value.

Yyd connection

YNd connection YNy connection

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A)

Time(s)


176

In these YNd and YNy connected cases, the winding impedance is identical, the only

difference is that the secondary winding impedance cannot be seen from the primary

side when it is open circuited in the YNy connection; on the other hand it can be seen in

the YNd connection due to the zero sequence component loop provided by the delta

winding. The final values of the current are the same in both YNd and YNy connections

as it is decided by the DC voltage level and the primary winding resistance.

5.3.3.2 Five-limb area ratio influence

It can be seen that the ratio of the side yoke and main yoke would influence the flux

distribution of the five-limb transformer core at the steady state which is mentioned in

Chapter 4. In this section, the transient influence of the area-ratio on GIC performance

will be discussed.

The simulation was carried out by varying the ratio of the main yoke area and the side

yoke area from 0.7/0.3 to 0.5/0.5, each 0.05 as a step and using the original connection

of YNad as the transformer winding connection. The DC supply voltage is fixed as 100

V to investigate the different reactions for different area ratio. The simulation results are

shown in Table 5-16.

Table 5-16 Simulation results for main-side yoke area ratio modified

Area Ratio

Main /Side yoke (A)

(A)

(A)

(s)

(s)

(s)

(s) A B C

0.7/0.3 31.3 40.3 200.78 0.195 7.1 40 130 130 130

0.65/0.35 31.3 40.3 200.78 0.195 8.9 40 130 130 130

0.6/0.4 31.3 39.7 200.78 0.195 9.9 40 130 130 130

0.55/0.45 31.3 38.7 200.78 0.195 10.7 40 140 140 140

0.5/0.5 31.3 37 200.78 0.195 12.5 40 165 165 165

It can be seen that by reducing the main yoke area and side yoke area ratio to the area of

the core limb, the side yoke becomes easier to saturate; thus the second rise of the

primary side current comes earlier. In addition, the final saturation time is also reduced.

Since the modification to the side yoke area may also affect the λ-I curve of each part of

the core, the third step of the ‘three-step function’ waveform may be changed. The

simulation results of the primary current waveforms are shown in Figure 5-34.


177

Figure 5-34 Primary side current waveform with main-side yoke area ratio modified

It can be seen that the ‘three-step function’ waveform remains. Modifying the areas of

the main yoke and side yoke has no impact on the primary side current of step-response

and the final stabilised current value. They are decided by the DC voltage level and the

transformer winding impedance.

However, as mentioned before, reducing the side yoke area, would make it easier for the

side yoke to be saturated, the second rise of the primary side current waveform would

come earlier which is shown in Figure 5-34.

Meanwhile, the zero sequence core impedance, which is parallel with the delta

connected tertiary winding impedance, is increased; therefore the stable current value

after the saturation of the side yoke is decreased since the overall resistance is increased.

Figure 5-35 shows the side yoke and main limb λ-I curves with different main yoke/side

yoke area ratio.

Figure 5-35 Side yoke and main limb λ-I curves with different main-side yoke area ratio

Cu

rre

nt(

A)

Time(s)

Flu

x(W

b)

Current(A)

Outer leg λ-I curve Inner leg λ-I curve


178

It can be seen that the change of the ratio of the main yoke and side yoke area would

influence both of the side yoke and main limb λ-I curves. The left side figure represents

the side yoke characteristics and the right side figure represents the main limb

characteristic. As a result, the saturation characteristics would be changed as well. It

would bring the difference to the second and third step waveforms. In addition,

significant change on the main limb λ-I curve is observed when the main yoke/side yoke

area ratio changes from 0.55/0.45 to 0.5/0.5. From the right side of the figure, it can be

seen that, when it is further reduced, the maximum flux of the main limb increases and

the knee area gets smoother and smoother. This is why the saturation time increases and

the third rise of the waveform does not appear that steep.

5.3.3.3 Effects of the system impedance R & L

Since the ‘three-step function’ waveform of the five-limb transformer is different from

the other two types of transformer core structures, the system R and L are added at the

primary side of the transformer so that the influence on the primary current or

magnetising current of the transformer can be investigated. The simulation was carried

out by only supplying 100 V DC voltage; no load is connected to the transformer, the

primary side current is observed to investigate the effects of additional system R and L.

The simulation was carried out by discussing the influence of the resistance and

inductance separately. The first step is to vary the resistance value from 0.5 Ohm, 1

Ohm to 2 Ohm, and then the second step is to fix the resistance value as 0.5 Ohm and to

vary the inductance value from 100 mH, 200 mH to 400 mH. The key parameter values

of the simulation results are shown in Table 5-17 and Table 5-18.

Table 5-17 Simulation results for the key parameters by varying system R

R (Ω) (A) (A) (A) (s) (s) (s) (s) 0.5 27 42.8 100.2 0.17 18 54 93

1 23.9 35.3 66.75 0.15 20.5 64.3 98

2 19.3 26 40 0.12 25.1 83.8 103

It can be seen that when the total primary side resistance is increased, the time constant

of the step-response, the stable value after the step response and the final stable value of

the ‘three-step function’ primary side current waveform are decreased. In addition,

because of the growth of the equivalent primary side resistance, the DC voltage

dropping on the core would be decreased, and then the DC flux would accumulate more

slowly and would take more time for the side yoke and the entire core to saturate. As a


179

result, the time taken for the second and third rise to occur is lengthened and the total

saturation time for the entire core is longer.

Table 5-18 Simulation results for the key parameters by varying system L

L(mH) (A) (A) (A) (s) (s) (s) (s)

100 27 42.8 100.2 0.197 18 54 93

200 27 42.8 100.2 0.22 18 54 93

400 27 42.8 100.2 0.27 18 54 93

It can be seen that by varying the system L it would only influence the time constant of

the step response. The time constant of the step-response is increased with the increase

of the system L value, and the slower rising speed of the current after the DC supply is

seen.

5.4 Summary

In this chapter, the transformer core structure influence on the primary current or

magnetising current under the DC bias or GIC events has been successfully identified

by using simulation case studies. Based on the results analysis of the simulation cases,

the effects of the winding connection, the core structure, and the network parameters on

the magnetising currents of the transformers can be summarised as follows:

1. For the waveform of the primary side of the current, its step times are influenced

by the winding connection, the core structure and the zero sequence core

impedance. In short, the ‘one-step function’ waveform only appears for a single

phase transformer with the YNy winding connection; the ‘two-step function’

waveform appears for a single phase transformer and a three-limb transformer

and a five-limb transformer with a YNd winding connection; the ‘three-step

function’ waveform appears for a five-limb transformer with three windings

YNad or two windings YNd connection.

2. The three stages are defined in a ‘two-step function’ waveform, which are the

step-response stage, the pseudo-flat stage and the saturation stage. The step-

response stage only appears when there is low value impedance connected in

parallel with the core impedance in the equivalent circuit. The durations of the

pseudo-flat stage and the final saturation are controlled by the accumulating

speed of the zero sequence DC flux which the DC voltage dropped on the core.


180

3. Transformer winding impedance controls the behaviour of the primary side

current. Winding impedance combined with DC supply level decides the time

constant and the stable value of the step response. The system impedance gives

the same effect as the winding impedance. Core saturation characteristics mainly

control the saturation stage, including the speed of the rise and the time for the

saturation.

4. The zero sequence impedance of the three-phase three-limb transformer is more

complex than that of the three single-phase transformers bank. In a three-limb

transformer, DC flux cannot find a return path inside of the core and has to leak

out of the core and circulate through the oil and tank. The zero sequence

impedance in the three-limb transformer affects the step response time constant

and the stable value and also it impacts the saturation time by influencing the

DC voltage drop on the transformer core. The experiments done by Tokyo

Electrical Power show the same pattern as the simulation results in this chapter

hence it confirms the above conclusion. [71]

5. Three-step waveform appears on the primary side current of the five-limb

transformer. The cause of the first step function is the same as explained before

the step response, the second step function is due to the saturation of side yoke,

and the third step function is caused by the saturation of the entire core.

6. Reducing the side yoke area ratio makes the side yoke easier to saturate in a

five-limb transformer. As a result, the second rise in the three-step function

waveform becomes earlier and the stable value of the current is decreased.

Modifying the side yoke area ratio also has some impact on the third rise of the

waveform.

7. R, L loads connected at the secondary winding side have no influence on the

severity of the GIC response of the transformers.

Chapter 6 Low frequency switching transient magnetic and electrical modelling

181

Chapter 6 Low frequency switching

transient magnetic and electrical

modelling

6.1 Introduction

In Chapter 5, the DC bias or GIC event has been simulated by using ATP/EMTP

software; and the results have been discussed. All the parameters in the circuit have

been examined including the network parameters, the winding connection and the core

structure of transformer.

In the UK distribution networks, a grid transformer tends to be operated by the circuit

breaker in the upstream substation and a fair length of cable or overhead line is

connected in between the upstream and the downstream substations. De-energising a

transformer with a long cable connected to it can induce the occurrence of ferroresonant

transients due to the interaction between the cable and the transformer.

In this chapter, one of the low frequency transients will be discussed and the effects of

parameters in circuit will be studied via ATP/EMTP simulation. Normally, the low

frequency phenomena include inrush and ferroresonance as mentioned in the literature

review; only the ferroresonant transient phenomenon associated with de-energisation

operation in a UK distribution network will be investigated.

6.2 Distribution network layout

In the UK, when the network was initially built in the 1960s, the cost of the circuit

breaker was exceedingly high; and to save the capital cost of the power system network,

a typical network is configured in such a way that a grid transformer in the downstream

substation is to be operated by the circuit breaker in the upstream substation via a fair

length of cable or overhead line. The typical network is shown in Figure 6-1.


182

Upstream

Substation

Busbar

Upstream Circuit

Breaker

Long Distance

Cable/Overhead

Line

Disconnector

Grid

Transformer

VT

Downstream

Busbar

Grounding

Transformer

Short

Distance

Cable

Downstream Circuit

Breaker

Figure 6-1 Typical UK distribution network diagram

However, this kind of circuit configuration would usually be susceptible to

ferroresonance occurrence, during the switching operations in distribution networks.

When maintenance, system re-configuration or fault clearance on the network is needed,

switching operations are carried out; switching a transformer with a long cable

connected to it can be problematic due to the interaction between the cable capacitance

and the transformer non-linear core; upon de-energising operations switching

ferroresonant transients would occur. This type of transient was not specified in

standard factory tests and therefore transformers cannot be tested before acceptance and

commissioning. Depending on individual transformer design, some transformers may be

able to withstand the ferroresonant transient and the associated energy dumped into

them without causing localised overheating, whereas the others might not. [45]

It is therefore of interests for a utility to understand the causes, the impacts and the

mitigation measures of switching ferroresonant transients when de-energising a

transformer, in order to maintain failure-free network operations or at least with a

minimum rate of failure.

The utility of Electricity North West first noticed the ferroresonant transients when de-

energising one of the transformers in Preston East Substation during a system

reinforcement project. During commissioning Preston East substation, a so called

'switching transient ferroresonance' problem was experienced when de-energising two

132/33 kV, 45/90 MVA grid transformers. The transformers are configured to be

energised /de-energised by circuit breakers at Penwortham East substation via 11.5 km

long 132 kV polymeric cables and an audible "clunk" noise can be heard from one of

the transformers when it was de-energised.

The same phenomenon happened on the Bloom Street Substation as well. This

confirmed that ferroresonant transients are commonly associated with transformers in

such a network configuration. Field experimental investigations were carried out, as


183

well as recording voltage and current waveforms, acoustic sensors designed for partial

discharge detection and location were used to pick up the audible noise in an attempt to

pin-point the source location. During this investigative field test oil samples were taken

before and after the tests for DGA analysis [12].

6.3 Case 1: Bloom street substation circuit

6.3.1 Introduction of the circuit

There are two transformers--GT1 and GT2 at Bloom Street Substation (BSS) which the

layout of which is shown in Figure 6-2. Both are 132/33 kV, 45/90 MVA, 3 phases 50

Hz, ONAN/OFAF, YNd1 connection, transformers made by GEC Alstom Stafford in

1997 and installed in 1999. The upstream substation is South Manchester Substation

(SMS); the 132 kV circuit breakers (CB) are installed in SMS and between SMS and

BSS there are 9.5 km single-core XLPE cables connecting the transformers and circuit

breakers. The red circles mark the circuit under study in Figure 6-2, which includes the

CB and 132kV XLPE cable going out from SMS to BSS.

Figure 6-2 South Manchester Substation (SMS) and Bloom Street Substation (BSS) layout

The relevant part of distribution network for de-energising a 132/33kV grid transformer

includes: in the upstream substation busbar, circuit breaker, isolator and the cable and in

9.5 km single-core XLPE cables

Bloom Street Substation (BSS)South Manchester Substation (SMS)

Ground


184

the downstream substation isolator, grid transformer, auxiliary transformer, a short

length cable, voltage transformer and circuit breaker. The circuit arrangement is given

in Figure 6-3.

Figure 6-3 Single line diagram of the circuit

6.3.2 Recorded transformer de-energisation voltage and current data

The voltages and currents of the transformer were recorded via the protection VTs and

CTs using a transient recorder, when the tests were carried out in Bloom Street

Substation. The three-phase 132 kV line currents and 33 kV line voltages were recorded.

The transient recorder has a sampling frequency fs = 12.8 kS/s which means that each

cycle of the power frequency contains 256 sampling points.

After de-energisation, the transformer voltage and current waveforms recorded were

seen as oscillatory and transient in nature. The whole transient process lasts for less than

0.62 s. The voltage has a square like waveform, and the current oscillates between

positive and negative spiky high magnitudes.

6.3.2.1 Type 1---Results of GT1 first switch-off operation

The 33 kV CB was first opened to shed the load and after one to two minutes the 132

kV CB was opened to de-energise the no-load grid transformer, GT1. To aid

comparisons among all the voltage and current waveforms, the same number of 50 Hz

cycles prior to the voltage change is taken for plotting in all figures.

Figure 6-4 shows the three line voltages at the 33 kV side of the transformer which are

in phase with 132 kV side phase voltages (A phase, B phase and C phase). The whole

process of switching ferroresonant transients lasts for less than 1 s.

BSSSMS

AUX T2

Grid Transformer T2


185

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5-5x10

4

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

lta

ge

(V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage

Figure 6-4 Line voltages at transformer 33 kV terminals

It can be seen that Figure 6-4 shows voltage waveforms change from a sin wave to a

square wave after the CB is opened; the voltage waveform levels off as dc-like for 2-3

ms and due to flux linkage which is the integral of voltage by time, the flux linkage

increases to the level of saturation, owing to the non-linear inductance characteristics of

the core inductance would become small at the saturation region and the dc-like voltage

will drop quickly to zero and then go to negative, the core reverses to the linear region

and the voltage waveform levels off dc-like for some more milliseconds. It also shows

that all three-phase voltages decay within a short time period around 0.62 s. Given the

equivalent capacitance of the 9.5 km cable is 1.096 uF (see appendix) and the time

constant for paralleled resistance and capacitance is given as RC , the estimated

resistance value of the parallel resistor is around 100 kOhms.

Figure 6-5 shows the 3-phase line currents at transformer 132 kV side. It shows that

after CB opening the currents of three phases oscillate between positive and negative

polarities and high magnitude spiky currents occur simultaneously with the rapid

change of voltage polarities. When the core of the grid transformer works at the

saturation region the currents suddenly increase in magnitude. Overall the currents also

gradually decay due to the effect of resistive loss.


186

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

-150

-100

-50

0

50

100

150

Cu

rre

nt

(A)

Time (s)

Phase A

Phase B

Phase C

Figure 6-5 Line currents at transformer 132 kV terminals

Figure 6-6 and Figure 6-7 focus further on the short initiation period of ferroresonant

transients and plot three-phase voltages and three-phase currents. On the current and

voltage waveforms around t = 0.60 s, the changes of currents and voltages seem to

happening simultaneously. Some high frequency components on the voltage waveforms

near to t = 0.60 s can be vaguely seen and since the voltage waveforms were measured

at the 33 kV side, and high frequencies are not easily transferred between HV and LV

windings, this indicates that high frequency oscillations with stronger magnitudes may

exist at 132 kV side phase voltages.


187

Figure 6-6 Line voltages at transformer 33 kV terminals – zoomed waveforms for 40 ms

In Figure 6-6 when three-phase voltages are distorted from sin waves, they stay flat for

around 3 ms before changing simultaneously. The yellow (green line) phase is near to

the positive peak when ferroresonance occurs and the other two phases, red and blue are

at/near to the half magnitude of the negative peak. When the voltages are in the rapid

changing region, there are five gradients of slopes which can be seen in Figure 6-6 by

circles. Since the voltage rapid changing region is the time when the core goes into

saturation, the gradients mean that the core works at different parts of the B-H curve of

the core.

Figure 6-7 shows that before CB opening the current measured at the 132 kV side are

magnetising currents with magnitude near to zero, not measurable by the protection CTs.

After CB opening the currents of three-phase increase at the same time and with the

same magnitude: the peak values are around 10 A and the frequencies are around 400

Hz, at or near to the time t =0.60 s. They behaved like zero sequence currents since

secondary windings are delta connected. The large magnitude ferroresonant currents

then follow and they start to move to different polarities for three phases. The currents

take complicated patterns. It is assumed that this is due to mixing the components of

zero sequence current and high magnitude spiky ferroresonant current. On each phase

the maximum value of current can reach 90 A.

0.584 0.588 0.592 0.596 0.600 0.604 0.608 0.612 0.616 0.620 0.624-5x10

4

-4x104

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-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

lta

ge

(V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage


188

0.584 0.588 0.592 0.596 0.600 0.604 0.608 0.612 0.616 0.620 0.624

-150

-100

-50

0

50

100

150

Cu

rre

nt

(A)

Time (s)

Phase A

Phase B

Phase C

Figure 6-7 Currents at transformer 132kV terminals – zoomed waveforms for 40 ms

Figure 6-8 shows the voltages/currents of the transformer plotted in the same graph. The

corresponding relationship between the current and voltage waveforms is shown: a

higher magnitude current corresponds to the rapidly changing voltage; and the flat dc-

like voltage corresponds with the zero sequence current.

0.584 0.588 0.592 0.596 0.600 0.604 0.608 0.612 0.616 0.620 0.624

-5x104

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

A-B Voltage

B-C Voltage

C-A Voltage

Vo

lta

ge

(V

)

Time (s)

-150

-100

-50

0

50

100

150

Phase A

Phase B

Phase C

Cu

rre

nt

(A)

Figure 6-8 Voltages/currents of the transformer near to the initiation of ferroresonance


189

Figure 6-9 Voltages/integrated fluxes of the transformer

Figure 6-9 shows the relationship between the flux leakage in the core limb by

integrating the 33 kV line voltage with the time and voltage of the 33 kV winding.

When the transformer works at a steady state the flux is a pure sin wave. However after

the CB is opened, the flux waveform is distorted and becomes larger than the maximum

value of the steady state flux. This means that, after the switching operation, the core

limb goes into saturation. The plotted flux linkage indicates that each limb will take its

turn to go into saturation.

6.3.2.2 Type 2---Results of GT2 second switch-off operation

The second type of ferroresonant voltage and current waveforms was obtained during

the second switching operation of GT2. The ferroresonance voltages and currents last

for less than 1 s, in the same way as type one before they are completely decayed to

zero; the ferroresonant voltage is in the shape of a square wave and the ferroresonant

current oscillates between positive and negative polarities with high spiky during the

core saturation. Three ferroresonant currents are all in similar shapes and their

magnitudes follow 1:-0.5:-0.5 proportionate to one another. The maximum magnitude

of the three-phase currents can be achieved around 130 A.

Figure 6-10 shows the three-phase voltages near to the initiation of ferroresonance. In

this case, the blue phase voltage is near to the negative peak value when ferroresonance

0.58 0.59 0.60 0.61 0.62 0.63 0.64-5x10

4

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

lta

ge

(V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage

-4.0x106

-2.0x106

0.0

2.0x106

4.0x106

A-B Flux

B-C Flux

C-A Flux

Flu

x (

Wb

)


190

occurs, while the red phase and yellow phase are at positive magnitude but their

magnitudes are quite different from each other. When the voltages are in the rapid

changing area, there are three gradients of slopes, rather than five gradients for the first

type.

0.59 0.60 0.61 0.62 0.63 0.64 0.65-5x10

4

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

lta

ge

(V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage

-150

-100

-50

0

50

100

150

Phase A

Phase B

Phase C

Cu

rre

nt(

A)

Figure 6-10 Voltages/currents of the transformer plotted in the same graph

It can also be seen that the three phases line currents near to the initiation of

ferroresonance, at t = 0.61 s where the voltage waveforms show the starting of

ferroresonance, have no significant increase around this time. The currents follow 1:-

0.5:-0.5 magnitude ratio and the waveforms are quite similar. When the core is in the

linear region the currents of three phases are zero sequence currents and the peak value

is around 10 A and the frequency is around 400 Hz. Higher magnitude currents

correspond with rapid changing voltages, which occurs when the core goes into

saturation.

Figure 6-11 shows the corresponding relationship of the voltage and the flux for each

individual phase.


191

0.59 0.60 0.61 0.62 0.63 0.64 0.65-5x10

4

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

lta

ge

(V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage

-4.0x106

-2.0x106

0.0

2.0x106

4.0x106

A-B Flux

B-C Flux

C-A Flux

Flu

x(W

b)

Figure 6-11 Voltages/integrated fluxes of the transformer plotted in the same graph

Figure 6-11 shows the relationship between the flux lineage in the core limb by

integrating the 33 kV line voltage with the time and voltage of the 33 kV winding. It is

the same as type one; when the transformer works at a steady state the flux is a pure sin

wave and after the CB is opened, the flux waveform is distorted and becomes larger

than the maximum value of the steady state flux. Among the four records of the test

results, three of them belong to Type 2.

The switching tests made on a distribution network were described and the test results

were given with some preliminary analysis. However, these analyses are basic and we

need to carry out more modelling and simulation analysis. The ATP transient analysis

software package was used to build the model and to carry out sensitivity studies in

order to understand how each parameter influences the results.

6.3.3 Simulation model

The simulation model has been developed in ATPDraw as shown in Figure 6-12. At the

132 kV side, there is the 132 kV bus bar, 132 kV SF6 circuit breaker, 9.5 km XLPE

single core cable and current transformers included in the simulation model. The current

transformers are three 1:1200 current measuring devices. The burden rating of the

current transformer is normally lower than 60 VA. This value of burden impedance

converting to 132 kV side can be ignored, so if the current transformer is working in


192

normal conditions, it can be ignored in the simulation model and be replaced a line

current probe.

At the 33 kV side, there is the ground transformer, the short XLPE cable, the voltage

transformer and the 33 kV CB included in the circuit. The sizes of the ground

transformer and the voltage transformer are much smaller than the grid transformer, so

the impedances of them are much higher than that of the grid transformer. Because they

are connected in parallel with the grid transformer, these two transformers can also be

ignored in the model. Equally, the short cable has very limited capacitive impedance

and also before the ferroresonance event the 33 kV CB has been opened already, so the

33 kV circuit breaker and the short distance cable can both be ignored in the simulation

model. Therefore, the simulation model network can simply include the 132 kV voltage

source, the 132 kV CB, the 132 kV cable and the 132/33 kV distribution transformer

which is shown in Figure 6-12.

Figure 6-12 132/33 kV network simulation model in ATPDraw

When building the simulation model, the 132 kV substation is modelled by a 3-phase

voltage source with R = 0.79 % and X = 4.5 % based on the fault level provided ENW.

The circuit breaker is represented by a 3-phase time-controlled switch with external

connected grading capacitors. The 9.5 km length cable is modelled as PI representation

based on cable geometry dimensions and dielectric property. The 132/33 kV

transformer is represented by a HYBRID model, [61][2] which is based on open-/short-

circuited test report and core dimensions which are available from GEC Alstom. The 3-

phase current probe is connected at the primary side of the transformer and the line

voltages are measured at the secondary side.


193

6.3.4 Simulation results and analysis

6.3.4.1 Simulation results

The three-phase voltages and currents for the de-energisation event can be reproduced

by controlling the circuit breaker’s switching time, the magnitude of the current

chopping, the parallel resistance value and the λ-I curve of transformer core. The

detailed simulation results of the secondary side line voltages and the primary side line

current for type one ferroresonant transient are shown in Figure 6-13 and Figure 6-14.

They are compared with the corresponding field test waveforms which are shown in

Figure 6-4 and Figure 6-5.

Figure 6-13 Simulation results of secondary side line voltages

Time(s)

Vo

ltag

e(k

V)


194

Figure 6-14 Simulation results of primary side line currents

The details of the waveforms are shown in Figure 6-15 for the 40 ms zoomed-in detail

which is the same time scale in Figure 6-8. It can be seen that the simulation and test

results are well matched with each other.

Figure 6-15 Simulation results of voltages/currents near to the initiation of ferroresonance

Time(s)

Cu

rre

nt(

A)

Time(ms)

Cu

rren

t(A)

Vo

ltag

e(k

V)


195

For type two, waveforms are also well matched with test results by changing the circuit

breaker’s opening time. The detail of the match between the results would be discussed

in the following section.

6.3.4.2 Modelling analysis

A) Selecting and building up the model

The voltage source at 132 kV busbar in SMS substation can be modelled as an ideal

source with internal impedance. The ground capacitor of the bus bar should also be

included. The information of 132kV three phase fault level for SMS substation from the

ENW yearly report, are shown in Table 6-1.

Table 6-1 132kV three-phase fault level information in South Manchester Substation

Base on this, the calculation of the impedance is as follows:

2 2(132 )174.24( )

100

174.24*0.79% 1.376496( )

174.24*4.5%24.968041( )

2 2*3.1415926*50

basebase

base

base per unit

base per unit

U kVZ

S MVA

R Z R

Z LL mH

f

Generally, the ground capacitance of a 132kV busbar is about 0.1 pF/m. The busbar

length is normally within the range of hundreds of metres. To model the circuit breaker,

the ground capacitor and grading capacitor connected with the circuit breaker need to be

considered. Typical grading capacitance applied across each break is 30 to 800 pF for

an air blast breaker, 800 to 1350 pF for a minimum oil breaker and 1500 to 1600 pF for

a SF6 breaker [7]. The ground capacitance value can be estimated to be in the range of a

few hundred pF when considering the bushing of the circuit breaker. The ATP model of

the source bus bar and the time controlled circuit breaker, and the parameters for these

components are shown in Figure 6-16.


196

Figure 6-16 Model of source and circuit breaker

For the cable modelling, there are several different types of cable models which are PI

model, Bergeron model, JMarti model and NODA model, and it is necessary to know

the cable length, and the highest frequency desired to be simulated because an accurate

cable model must take frequency-dependent parameters into consideration. However,

the effects of frequency dependent parameters may not be significant when it comes to

the modelling of a ferroresonance phenomenon due to its low frequency transient

characteristic. Therefore, the PI model is selected which is a nominal PI-equivalent

circuit for short lines. For the transient analysis both inductance and capacitance

distributed parameters need to be considered in modelling. The resistivity and relative

permittivity values of typical materials used by cables are shown in Table 6-2 and Table

6-3 [85].

Table 6-2 Resistivity of conductive materials used in cables

Material Copper Aluminium Lead Steel

ρ[Ω.m] 1.72E-8 2.83E-8 22E-8 18E-8

Table 6-3 Relative permittivity of insulating materials used in cables

Material XLPE Mass-impregnated Fluid-filled

Relative Permittivity 2.3 4.2 3.5

For the copper conductor and XLPE insulating materials, their relative permeability is

nearly the same as they are diamagnetic. The information about the diameter of the

conductor and the thickness of the semi-conductor, the main insulation and the outer

sheath are illustrated in Table 6-4.

R=1.38 ohm

L= 24.97mH

Grading Capacitance = 1600pF

Grounding Capacitance = 100pFSource

Vpeak=107.78 kV

Busbar


197

Table 6-4 Dimension of single core cable

Parameter Value

(mm) Calculation of cable diameter (mm)

Diameter of conductor 21.5 21.5+0=21.5

Thickness of Conductor screen 0.8 21.5+0.8*2=23.1

Thickness of insulation 19.0 23.1+19*2=61.1

Thickness of core screen 1.0 61.1+1.0*2=63.1

Thickness of Semicon WST 1.0 63.1+1.0*2=65.1

Thickness of lead sheath 3.5 65.1+3.5*2=72.1

Thickness of Bitumen 0.5 72.1+0.5*2=73.1

Thickness of MDPE sheath 3.65 73.1+3.65*2=80.4

Based all the information above, the data of the 132 kV cable in ATP is shown in Table

6-5.

Table 6-5 Input data of the 132kV cable

Paramete

rs

Value Explanation

Conductor Sheath

Rin 0 0.03255 Inner radius of conductor (m)

Rout 0.01075 0.03605 Outer radius of conductor (m)

Rho 1.72E-8 22E-8 Resistivity of the conductor material

Mu 1 1 Relative permeability of the conductor

material

mu(ins) 1 1 Relative permeability of the insulator

material outside the conductor

eps(ins) 2.3 2.3 Relative permittivity of the insulator

material outside the conductor

The total radius of the cable (outer insulator) [m] and the position of cable relative to

ground surface for single core cables are also specified. It can be assumed that the bury

depth is 1 m, in the flat arrangement, with 0.1 m space between each single cable central

[86]. The model view is shown in Figure 6-17.

Figure 6-17 Cable model views

For the transformer model, the hybrid model is selected which is a duality-based model,

taking into account the frequency dependent resistive effect, capacitive effect and

saturation effects with topologically correct core modelling. The data needed in the


198

ATPDraw are the open circuit, the short circuit test data, the structure of the core and

windings. In the model, the 3-limb core is spilt into five parts which are three limbs and

two yokes. Figure 6-18 shows the equivalent circuit of the core which uses a resistance

and nonlinear inductance to represent each part.

Figure 6-18 Equivalent circuit of three-limb core

B) Validation and analysis of the model

Based on the literature reviews in Chapter 2, the influencing parameters of the

ferroresonance in the circuit are the circuit breaker characteristics, transformer

characteristics and cable characteristics. For the circuit breaker, there are two main

parameters which would influence the ferroresonance phenomena; the opening time and

chopping current; for the transformer characteristic they are the core nonlinearity and

the losses of the transformer; for the cable characteristics they are the capacitance value

and the losses as well. Those parameters will be discussed below.

Since the circuit breaker is modelled as a time controlled switch, when no current

chopping is considered, the switch opening time is always at the moment of current zero

no matter when the opening signals are sent to the CB. As can be seen in Figure 6-19,

six zones are defined between the 50 Hz zero crossing within one cycle. These six zones

can be defined here as pre-zero crossing ranges, which takes 3.33 ms. If switching is

ordered at zone 1, the contact of phase C breaker will open first and will then be

followed by phase B and phase A respectively. Actually, each phase has two chances to

reach current zero earlier than the other two phases within one cycle.


199

Figure 6-19 Six zones within one cycle

These six zones can be further separated into negative zones (including zone 1, zone 3

and zone 5) and positive zones (including zone 2, zone 4 and zone 6). Given the CB is

modelled as an ideal switch to clear the current at zero of a 50 Hz current, zone 1

switching response would be the same as zero 3 and zero 5, the first phase being the

only difference. The same principle is valid for zone 2, zone 4 and zone 6. Simulations

studies are conducted in these two typical positive and negative zones. The results

shown in Figure 6-20 and Figure 6-21 are almost identical except opposite polarities. It

is further suspected that using the ideal switching CB model, the simulation responses

are probably going to be identical, only with phase and polarity differences, if a system

is full transposed and de-coupled.

Figure 6-20 Switching at positive zones

(a) three phase current waveforms of circuit breaker

(b) three-phase transformer secondary line voltage global and zoomed waveforms

(c) three-phase transformer primary line current globe and zoomed waveforms

(file Baseline.pl4; x-var t) c:X0014A-X0012A c:X0014B-X0012B c:X0014C-X0012C

2.020 2.024 2.028 2.032 2.036 2.040[s]-50.0

-37.5

-25.0

-12.5

0.0

12.5

25.0

37.5

50.0[A]

Time(ms)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

Time(s)

Cu

rre

nt(

A)

(a)

(b) (c)


200

Figure 6-21 Switching at negative zones

(a) three phase current waveforms of circuit breaker

(b) three-phase transformer secondary line voltage global and zoomed waveforms

(c) three-phase transformer primary line current globe and zoomed waveforms

In Figure 6-20 and Figure 6-21, the first phase’s current is cleared at the 50 Hz zero

crossing, and the second phase current is slightly affected and its zero crossing comes

before the supposed 3.33 ms later; once the second phase is also cleared the third phase

experiences a large overcurrent and is cleared when the zero crossing is reached, which

is before the supposed time delay of 6.67 ms. There are overvoltages after switching

operations.

Compared with the recorded test data, there are two major differences: first the

resonance decay time is longer, the resonant frequency is higher and the current

magnitude is higher in the simulation results than the test ones, indicating that less

damping effect has been represented by the model; second, overvoltages appear in the

simulation results after the switching operation whereas no overvoltage is observed in

the recorded test data.

The resonance period is maintained for quite a long time which means the loss used in

the simulation circuit is not enough to damp the energy. Therefore, the following

simulations are carried out to add the parallel resistor. The following results show for

one zone only when the switching off time = 0.02 s, with the resistance value added step

by step in order to match the time constant (τ), the resistance value is modified from

90 kOhms to 140 kOhms.

Time(ms)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

Time(s)

Cu

rre

nt(

A)

(a)

(b) (c)


201

Table 6-6 illustrates the relationship between the resistance value and the damping time

for the ferroresonant transient.

Table 6-6 Relationship between resistance value and time constant

R(kOhms) 90 100 110 120 130 140

Damping time(s) 0.38 0.45 0.51 0.55 0.59 0.62

The best suitable value of resistance equals to 140 kOhms.

Although the simulation result matches the test result reasonably well, using a linear

resistor to represent core losses is rather over-simplified. This is due to the fact that

core-losses are non-linear as described in chapter 2. However the ATP software does

not have a non-linear resistor representation, therefore a linear resistor was used instead.

Indeed, the results with the added resistance value of 140 kOhms still have some

differences from the recorded test data. Firstly the number of the oscillations is more

than the recorded test data, secondly after the switching operation three-phase currents

are cleared at different points of time and overvoltages are also created for three phases.

To further match the simulation results with the recorded test results, the inclusion of

clearing times and the level of current chopping as the model parameters are effective.

In the test results from Figure 6-6 and Figure 6-10, the voltages of the three phases and

currents are shown to change together, almost simultaneously. This can be only realised

in simulation by controlling current chopping or adding in a very short time difference

between the openings of different phases of CB.

The basic operational principle for CB under the AC voltage and current is to clear the

fault current and extinguish the arc in the arc chamber at the zero crossing. However,

the SF6 and vacuum circuit breakers could clear the arc current at a low non-zero

current value, and this phenomenon is normally called ‘current chopping’. Current

chopping happens with individual circuit breakers at various non-zero values, which are

controlled by multiple parameters and they are hard to determine unless measurements

are done on each circuit breaker and for each occasion. In general, the typical value of

the current chopping for a SF6 circuit breaker is around 10 A [87].

Comparing the chopping current level, the SF6 circuit breaker is the lowest among all

types including the air blast, the oil and the vacuum circuit breakers. As we know, the

hazard of generating a large overvoltage is mainly due to the chopping current level.


202

The following investigations were carried out by varying the values of the chopping

current from 10 A to 40 A. Table 6-7 illustrates the relationship between the resistance

value and the time constant for ferroresonant transient to damp.

Table 6-7 Relationship between chopping current value and first peak voltage

Chopping current value(A) 10 20 30 40

First peak voltage value(kV) 59.78 56.58 50.27 44.57

Damping time(s) 0.52 0.45 0.42 0.41

It can be seen from the simulation results that, by increasing the current chopping value

step by step, the overvoltage becomes smaller, the number of oscillations becomes less

and the magnitude of the current becomes lower. When the current chopping value

equals the optimal value of 30 A, the voltage waveforms in the initial part are quite

similar to the recorded test data and also the maximum magnitudes of the three-phase

currents are also similar.

From the recorded test data, three phase currents seem to be cleared simultaneously at

the switching operation time and the change in voltages seems to be constant with time

(dc like). Therefore, the three-phase circuit breaker was set to open simultaneously; only

the opening time was varied. However, the results cannot be well matched. In a 132 kV

circuit breaker, the three phases were unable able to open simultaneously. By varying

the opening sequences and the opening time difference between each phase, the results

show a good match.

Figure 6-22 (a) shows the initial λ-I curve which is built based on open circuit test

results, and (b) shows the modified λ-I curve by varying the 110% rated voltage of the

open circuit test data.


203

Figure 6-22 λ-I curve before and after modification

(a) Before modification (b) After modification

Combining all the parameters including the circuit breaker opening time, the circuit

breaker current chopping value and the modified λ-I curve, there are two results which

are quite similar to the recorded test data.

Figure 6-23 (a) shows the recorded data voltage/current results; (b) shows the

simulation results using the test report data to build the transformer core characteristics;

(c) shows the one that used the modification best matches with the test results.

0.1 4.4 8.7 13.1 17.4

Ipeak [A]71.1

96.1

121.1

146.1

171.1 Fluxlinkage [Wb]

0.1 5.3 10.5 15.8 21.0

Ipeak [A]85.6

105.0

124.3

143.7

163.1 Fluxlinkage [Wb]

(a) (b)


204

Figure 6-23 Results comparison: (a) recorded test data for the voltage and current waveform (a) for

the voltage and current waveform before modified, (b) for the voltage and current waveform after

modified

It can be seen that at the beginning, the peak of each phase voltage has a spike because

the core goes into saturation and forces the voltage to increase further. Before

modifying the λ-I curve, the spike waveforms only display in the red and the yellow

phase; after modifying the λ-I curve; the results are almost the same as the record test

data. The reason is that the modification lowers the saturation part of the λ-I curve and

the core is easier to go into saturation.

However the current waveforms still have some issues; at the beginning the current

magnitude is higher than the record data and between two high magnitude saturation

currents the magnitude of the current in the linear region is lower than the recorded data.

Time(s)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

Time(s)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

(a)

(b)

0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78

-150

-100

-50

0

50

100

150

Cu

rren

t (A

)

Time (s)

Phase A

Phase B

Phase C

0.58 0.62 0.66 0.70 0.74 0.78-5x10

4

-4x104

-3x104

-2x104

-1x104

0

1x104

2x104

3x104

4x104

5x104

Vo

ltag

e (V

)

Time (s)

A-B Voltage

B-C Voltage

C-A Voltage

(c)


205

During the exercise of matching the simulation results with the recorded results of the

field tests, we found that there are several parameters which control waveforms. The

circuit breaker opening time controls the initial parts of the current and voltage

waveforms; the chopping current controls the magnitudes of the overcurrents and

overvoltages; if there is no chopping current, the overvoltage would occur. The parallel

resistance value would influence the decay time of the ferroresonance, if there is no

parallel resistance, the oscillation would remain for a longer time; the slope of the

excitation curve of the transformer core would not only influence the magnitude of the

current waveform, but also the oscillation period. Overall, the ferroresonance in this

particular circuit is a combined effect of the multi-parameter controlled phenomenon.

6.3.5 Sensitivity study and mitigation

As we know, the produced ferroresonance phenomena are caused by the stored energy

in grounding capacitances in the cables that are discharged through the core impedance.

When the circuit breaker is opened and the voltage source is disconnected, the circuit of

the cable and the transformer core become a free-source RLC resonance circuit;

therefore non-linear resonance occurs.

6.3.5.1 Worst scenario

The worst scenario is when the damping resistance is not included and the circuit

breaker is opened at the point of current zero crossing. The simulation results are shown

in Figure 6-24.


206

Figure 6-24 Simulation results: (a) secondary side voltage; (b) primary side current

It can be seen that the transient overvoltages occur and the magnitudes are about 137%

of the rated voltage, the currents are increased by about 40% more than the field test

results and the lasting time of the ferroresonance is also maintained for longer, which is

around 2 s.

6.3.5.2 Cable length study

It is known that the ground capacitance of the cable is mainly due to the length of the

cable. The sensitivity study was carried out by reducing the cable length from 7 km to 1

km by 2 km in one step. The simulation results are shown in Figure 6-25.

Time(s)

Vo

lta

ge

(kV

)C

urr

en

t(A

)

Time(s)

(a)

(b)


207

Figure 6-25 Simulation results by varying the cable length

It can be seen that the shorter the cable length, the less severe the switching

ferroresonance is, for the ground capacitance value and the stored energy are decreased.

6.3.5.3 Mitigation

6.3.5.3.1 Adding a second circuit breaker in system

A second circuit breaker could be installed in the front of the grid transformer in the

BSS substation to disassociate the cable and the grid transformer, if necessary to solve

the problem of switching ferroresonant transients. The cable would not be able to

discharge its energy to the transformer. Instead it will take the shunt resistance to

discharge itself and in the present configuration the shunt resistance is huge and

therefore the discharge time can be significant. The distribution network model and the

simulation results are given in Figure 6-26 and Figure 6-27.

Figure 6-26 Adding a second circuit breaker for distribution network

Vo

lta

ge

(kV

)

Cu

rre

nt(

A)

Time(s)

3-phase line secondary side voltage 3-phase primary side current

1km

3km

5km

7km

3-phase secondary side line voltage 3-phase primary side line current


208

Figure 6-26 shows the circuit diagram with the added circuit breaker at the front of the

grid transformer. If the transformer goes through the routine maintenance, the first step

of the operation should be to open the 33 kV circuit breaker; the second step should be

to open the 132kV CB in front of the grid transformer.

Figure 6-27 shows the simulation results including the cable voltages, the secondary

side voltages of the transformer, the second circuit breaker currents and the primary side

currents of the transformer. The transformer has not oscillated and there is no

overvoltage and overcurrent occurring in the system.

Figure 6-27 Simulation results: (a) three-phase cable voltages; (b) three-phase secondary side line

voltages; (c) three-phase circuit breaker currents; (d) three-phase primary side currents

6.3.5.3.2 Adding a parallel resistor bank at secondary side of system

The previous solution using the second circuit breaker is not economic, due to the cost

of the circuit breaker. Another solution is to add a parallel resistance load at the

secondary side of the transformer [16]. The resistance bank can be only switched in

whenever the grid transformer needs to be disconnected. Prior to switching operation,

the resistance bank is switched into the circuit to prepare for the operation, the circuit of

the modified model after shedding the load is shown in Figure 6-28.

Time(ms)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

Time(ms)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

(a) (b)

(c) (d)


209

Figure 6-28 Adding parallel resistor for distribution network

It can be seen from Figure 6-29 that the voltages and the currents damped quickly and

there are slight overvoltages lasting for less than a cycle here. The magnitude of the

current reaches 50 A, but it is still lower than the ferroresonance current and also lowers

than the full load current. The voltage damped within one cycle, the current is sin wave

which means that the transformer works at the linear and is not caused by

ferroresonance.

Figure 6-29 Simulation results: (a) three-phase line voltages at secondary side; (b) primary side

currents

The suitable resistance bank has a resistance value of 200 Ohm.

6.4 Case 2: Red bank substation circuit

6.4.1 Introduction

Base on the modelling experience for the Bloom Street Substation, the Red Bank

Substation model has been built in order to predict the ferroresonant transient

phenomenon in this circuit system.

The Red Bank circuit has the same configuration as the Bloom Street Substation case;

however there is a long cable connected between the transformer and the circuit breaker.

The cable used is the oil-fed cable.

Time(ms)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)

(a) (b)


210

Figure 6-30 Whitegate Substation and Red Bank Substation layout

Figure 6-31 shows the comparison between the Bloom Street circuit and the Red Bank

circuit.

Figure 6-31 Comparison of single line diagram of the Bloom Street and Red Bank circuit

It can be seen that both of them are built with a 132 kV busbar, 132 kV SF6 circuit

breaker, a long distance 132 kV cable a 132/33 kV YNd connected transformer, an

earthing transformer and a voltage transformer.

The likelihood of inducing the same phenomenon as in Bloom Street Substation and

Preston East Substation is quite high, so simulation studies were conducted and the

comparison is made.

substationRed Bank

Underground cable

Whitegate(132 kV)

(33 kV)

Ground

Preston East

Bloom Street

Red Bank

System Configuration:

- same

Voltage level:

- same


211

6.4.2 Simulation and comparison

This circuit can be simplified by ignoring closed isolators and opened earth switches so

that it consists of the main components such as a 132 kV voltage source, CB, cable and

grid transformer. The connected auxiliary transformer, 33kV cable and 33kV VT are

further neglected since they bear negligible consequences. The model is shown in

Figure 6-32.

Figure 6-32 ATP simulation model of Red Bank circuit

Table 6-8 shows the source impedance at the busbar in the 132 kV substations. It can be

seen that both of the resistances are the same in those two circuits, and the inductances

are slightly different.

Table 6-8 132 kV three-phase fault level comparison between Bloom Street case and Red Bank case

Figure 6-33 shows the comparison between the two transformers operating in the two

different circuits, i.e. the transformer test reports for the open circuit test and short

circuit test. It can be seen that although the two transformers are manufactured by two

different manufacturers, the open circuit and short circuit test results are similar to each

other.


212

Figure 6-33 Comparison of two transformers’ data

Figure 6-34 shows the comparison between the XLPE cable used to connect with

Bloom Street Substation and the oil-fed cable used to connect with Red Bank Substation.

Figure 6-34 Comparison of the data of two cables

It can be seen that the capacitance value of the oil-feed cable is almost twice as high as

the XLEP one. The cable length in the Red Bank circuit is slightly longer than the

Bloom Street circuit. It can be expected that the magnitude of ferroresonant transients

would be higher in the Red Bank one and the resonance period would be longer than the

Bloom Street Substation.

Since both of the circuits use 132 kV circuit breakers from the same manufacturer, the

simulation is carried out by using the same opening time (phase A=0.0292, phase

B=0.0301, phase C=0.0301) and chopping current (30 Amp)as those used in the Bloom

Street case. The simulation results are shown in Figure 6-35. Figure 6-35 (a) is the

secondary side line voltages and (b) is the primary side currents.

Bloom Street

Red Bank

Type Length ConfigurationSubstation Capacitance

173 pF/m XLPE 9.55 km

335 pF/m Oil-Feed 11.5 km

3 single core cable

3-core cable in a pipe


213

Figure 6-35 Simulation results of Red Bank (a) secondary side line voltages (b) primary side

currents

It can be seen that the comparison suggests that between the two types of cable singe-

core XLPE cable and the three-core oil-fed cable, the oil-fed cable has more energy

(higher capacitance) and takes longer for the transient ferroresonance to damp than the

XLPE cable.

The currents approximately follow a 1:-0.5:-0.5 magnitude ratio and the waveforms are

quite similar. When the core is in the linear region, the currents of three phases are zero

sequence currents and the peak value is around 6 A and the frequency is around 400 Hz.

The current takes around 0.8 s to be damped.

Figure 6-36 shows that varying the cable length the ferroresonance of the secondary

side voltage waveforms and the primary side current waveforms. Compared with the

Bloom Street case, the transient ferroresonance takes longer to damp than the XLPE

cable for the same length cable. 1 km of oil-fed cable can create a three cycle

ferroresonance.

Time(s)

Cu

rre

nt(

A)

Time(s)

Vo

ltag

e(k

V)


214

Figure 6-36 Simulation results by varying the cable length

6.5 Summary

In this chapter, each main component of the distribution network has been modelled

using test report data and design data. In order to have a valid model which produces

matching results to the field recorded data, parameters have been trailed with slight

modifications such as the current chopping of circuit breaker, transformer λ-I curves

and resistive losses. Although ATP simulation eventually presented reasonable results

which matched with the recorded test data, ferroresonant transient phenomena are

complex multi-parameter controlled and we cannot be certain that the simulation

conditions which produced matching results are realistic situations when the tests were

performed.

However, general knowledge can be obtained on the switching ferroresonant transient

phenomena. During normal de-energisation events, interaction between the circuit

breaker, the cable and the transformer in this distribution network configuration results

in a ferroresonant transient phenomenon. In nature, the transient ferroresonance is due

to the fact that the energy stored in the cable capacitance discharges itself via the

transformer core inductance and causes core saturation. Since the energy source (cable

capacitance) is a limited one, the ferroresonance will not be sustained. Depending on the

5km

2km

1km

Vo

lta

ge

(kV

)

Cu

rre

nt(

A)

Time(s)

3km

3-phase line secondary side voltages 3-phase primary side currents


215

coordination of the three-phase switching time of the circuit breaker, fine differences

can exist between ferroresonant voltage and current waveforms.

From the previous field recorded results and simulation analysis, it is clear that the

unusual noise heard when de-energising the off-load transformer is due to core

saturation and ferroresonance. However, detailed analysis indicates that there is no

overvoltage on the transformer terminals and the highest saturation magnetising current

is about 130 A in peak, which is much higher than the normal magnetising current (Im =

0.98 A) but less than the full load current (IL = 396 A).

The potential damage of this ferroresonant transient phenomenon is therefore not caused

by overvoltage or overcurrent; instead it can be due to the fact that the flux was forced

to go through other paths as well as the core. Overfluxing and its side effects of

producing induced eddy currents and local heat concentration can be a long-term ageing

factor. However the total energy dumped into the transformer during the short lasting

time of transient (t = 0.62 s) is only 50 kJ, which is higher than the no-load loss but

much lower than the load-loss. From this comparison it seems reasonable to conclude

that the heating effect may not be significant due to the transient nature of

ferroresonance upon de-energisation.

In terms of the overfluxing and the flux leak, they are likely to occur near to the core

joints. During the investigative field tests acoustic sensors from Physical Acoustics Ltd

were used in an attempt to locate the source of the audible noise. However the acoustic

emission from the de-energisation event is relatively low and the acoustic emission did

not hit enough sensors to allow a 3D location. The DGA analysis on the oil samples was

normal, and there was no trace increase of any overheating gases in the oil samples

taken before and after the tests.

Transient interaction among transformers and other system components during

energisation and de-energisation are becoming increasingly important, due to the

increased generation connection and the reinforcing network activities.

Although computer simulation can be successfully employed to investigate the root

cause of the switching transient ferroresonance, it is recommended that the following is

necessary in order to develop a simulation model more accurately: (1) Measuring the

current and voltage at the primary side: high frequencies cannot pass through windings


216

without distortion, (2) Making synchronised time control: record exactly the circuit

opening time, the “cluck” noise appearing time, (3) Measuring current passing through

the circuit breaker since CB behavior to break small capacitive and inductive currents

are unknown and worth studying.

Chapter 7 Conclusion and further work

217

Chapter 7 Conclusion and further

work

7.1 Conclusion

7.1.1 General

This thesis described extensive simulation studies carried out on GIC and low frequency

switching transient phenomena where the effects of the transformer design and the

network parameters were identified. The main objective of this thesis is to investigate

the sensitivity of transformer structure design when it meets the GIC events and the

switching transient’s phenomena. The key technical challenge is associated with the

transformer core saturation.

The overall thesis work consists of the following parts:

1. To build a mathematical magnetic circuit model based on the principle of duality;

in particular to develop and validate a three-limb transformer core model having

zero-sequence flux return path, so it can be used to simulate the flux distribution

inside the transformer under the unbalanced situation;

2. To build a model in ATPDraw which is able to describe the system network

including transformers and other system components under GIC events;

3. To perform sensitivity studies on different network circuit parameters with

different transformer structures in order to investigate their influences on the

transformer saturation level, the saturation currents, the saturation time and the

sustained current waveforms;

4. To build a network model in ATPDraw based on the general distribution

network configuration, and validate the model with the field test results; and to

conduct the sensitivity study.

7.1.2 Summary of results and main findings

The influence of transformer core structure on the magnetising current under DC bias or

GIC events have been successfully identified. Starting with a statistical analysis of the


218

National Grid database of the transformer open circuit test results, it was found that core

material improvement has reduced the magnitude of the magnetising current over the

last few decades. There are two common types of transformer core structures: three-

limb and five-limb cores influence the balance of three-phase magnetising currents. In

addition, the winding connection; Y or D would influence the magnetising currents.

The simulation cases show that for the five-limb transformer, three-phase magnetising

currents are much better balanced than those of the three-limb transformer; and the

magnitude of the magnetic flux density of the main yoke is higher than in the main limb

and side yoke in the five-limb transformer core. The magnitude of the fundamental

frequency magnetic flux density in the side yoke is changing faster than that in the main

yoke with the change of the supplied voltage; the ratio of the cross-section between the

main yoke and the side yoke would influence the magnitude of fundamental frequency

and third harmonic flux distribution in the five-limb transformer core. The higher the

ratio between the main yoke and the side yoke, the more difficult it would take the

transformer to become saturated. However, the main yoke length is almost twice that of

the side yoke; so if the area of the main yoke is increased, it would cost more to buy

core materials and become harder for the transformer to transport.

Although the transformer manufacturers provide the RMS values of the magnetising

currents, without the detailed waveform, the information is not sufficient to understand

the flux distribution in the core. The recommendation is then made in this research that

the manufacturers should provide the detail of the magnetising current waveforms for

90%, 100% and 110% voltage levels during the open circuit tests.

By using the EMTP-ATPDraw transient calculation software, a network system was

built to analyse GIC events and it can be seen that the step time of the primary side

current is influenced by the winding connection, the core structure and the transformer

zero sequence impedance. It can be summarised that the ‘one-step function’ waveform

only appears for a single phase transformer with the YNy winding connection; the ‘two-

step function’ waveform appears for a single phase transformer and a three-phase three-

limb transformer with the YNd winding connection and a five-limb transformer with the

YNy winding connection; the ‘three-step function’ waveform appears for a five-limb

transformer with a three winding YNad or a two winding YNd connection.

Transformer winding impedance controls the behaviour of the primary side current.

Winding impedance combined with DC supply level decides the time constant and the


219

stable value of the step response. The system impedance gives the same effect as the

winding impedance. The core saturation characteristics mainly control the saturation

stage, including the speed of the rise and the time for the saturation.

The zero sequence impedance also plays an important role in this phenomenon.

Different structures of transformers have different characteristics from the zero

sequence impedance. The three-phase three-limb transformer is more complex than that

of the three single-phase transformers bank, i.e. the DC flux cannot find a return path

inside of the core and has to leak out of the core and circulate through the oil and tank.

The zero sequence impedance in the three-limb transformer affects the step response

time constant and the stable value and it also impacts the saturation time by influencing

the DC voltage drop on the transformer core.

For a three-phase five-limb transformer, the ‘three-step function’ waveform appears

with a YNd winding connection. For the first step, the DC flux is accumulated inside

the core through the side yoke, which then has a different reluctance from the positive

sequence core reluctance. For the second step, all DC flux continues the accumulation

and flows through the side yoke until the side yoke is saturated. The saturation of the

side yoke causes the second rise of the primary current. After the side yoke is saturated,

the five-limb transformer tends to behave like a three-limb transformer. For the last step,

DC flux increases further in the transformer core; the entire core goes into saturation.

As a result, the total non-linear core inductance starts to decrease and the primary side

current grows swiftly.

As for another core saturation problem named ferroresonance, it was found that

ferroresonant transients are complex multi-parameter controlled phenomena which

include the circuit breaker chopping current, its opening time and the grading

capacitance, the cable length and the transformer core characteristics. During normal

de-energisation events, interaction between the circuit breaker, the cable and the

transformer in the typical distribution network configuration results in a ferroresonant

transient phenomenon. In nature, the transient ferroresonance is due to the fact that the

energy stored in the cable capacitance discharges itself via the transformer core

inductance and causes core saturation. Since the energy source (cable capacitance) is a

limited one, the ferroresonance will not be sustained. Depending on the coordination of

the three-phase switching times of the circuit breaker, fine differences can exist on

ferroresonant voltage and current waveforms.


220

Based on the field recorded results and simulation analysis, it is clear that the unusual

noise heard when de-energising the off-load transformer is due to core saturation and

ferroresonance. However detailed analysis indicates that there is no overvoltage on the

transformer terminals and the highest saturation magnetising current is about 130 A in

peak, which is much higher than the normal magnetising current (Im = 0.98 A) but less

than the full load current (IL = 396 A). The potential damage of this ferroresonant

transient phenomenon is therefore not caused by overvoltage or overcurrent; instead it

can be due to the fact that the flux was forced to go through other paths as well as the

core.

Overfluxing and its side effects of producing induced eddy currents and local heat

concentration can be a long-term ageing factor. However the total energy dumped into

the transformer during the short lasting time of transient (t = 0.62 s) is only 50 kJ, which

is higher than no-load loss but much lower than the load-loss. From this comparison it

seems reasonable to conclude that the heating effect may not be significant due to the

transient nature of ferroresonance upon de-energisation.

More importantly, in terms of overfluxing and flux leak, they are likely to occur near to

the core joints. During the investigative field tests acoustic sensors from Physical

Acoustics Ltd were used in an attempt to locate the source of the audible noise.

However the acoustic emission from the de-energisation event is relatively low and the

acoustic emission did not hit enough sensors to allow a 3D location. The DGA analysis

of the oil samples was normal, and there was no trace increase of any overheating gases

in the oil samples taken before and after the tests.

7.2 Further work

The work presented in this thesis indicates that the overall approach of modelling

transformer core has helped the interpretation of core saturation problems; however

further work could be carried out on the following points:

As mentioned in Chapter 3, the transformer core model used in this thesis neglected the

losses of the transformer core material and also the building/structuring effect of core,

i.e. at the core joint areas. This model is a pure magnetic circuit model for the moment,

so the electrical part should be added into the model in the future. Once the model is


221

combined with both of the electrical and magnetic circuits, it can be used to calculate

both the balanced and the unbalanced studies.

When the manufacturer does the open circuit test for a transformer, only the RMS

values of the supplied voltages and the RMS values of the magnetising currents are

recorded. If the transformer core is working in the knee area or the saturation region,

only recording the RMS values is not accurate enough for the data to be used or

extrapolated to represent the transformer core characteristic which is a necessity for the

simulation model especially when studying the behaviours of transformer under

saturation. Unless the manufacturers can provide those data, the transformer model and

the simulation results could not be further improved.

The benefit of the mathematical model introduced in Chapter 3 can show the flux

distribution in the transformer and the ATPDraw could not do this at the moment. If the

mathematical model can be applied into ATPDraw as an external coded model, it would

massively improve the ATPDraw software.

The present models built up in the ATPDraw do not consider the non-linear core losses

in the transformer; instead it uses a linear resistor to represent the core losses. And a

parallel resistor is connected with the transformer core. In the future work the

transformer model should be further improved using the dynamic value of core losses.

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Appendix

227

Appendix

1 Matlab Code

clc clear all

%Inputing transformer basic parameters % 400/275/13kV, 1000MVA Transformer, working on Bm = 1.694T % Base on E=4.44*f*Bm*A1*N % Ibase=1000MVA/(400kV*1.732) % 400kv=4.44*50*1.694*0.70138*N*¡Ì3 % Calculation of Turn NO. for total winding together=965(real=960) % 965/(400/¡Ì3/13)=54 % Calculation of Turn NO. for tertariy winding = 54 % Core Material 27M4 % Original data of transfomrer % Main limb cross-section area/m2 0.6438 % Main yoke cross-section area /m2 0.3884 % Side limb cross-section area /m2 0.3884 % leg length (l1) = 2.79 m % Main yoke length (l2) = 2.57 m % Side yoke length (l3) = 1.6475 m

% Ratio Area of side limb(A3) Area of main yoke(A2) % 0.5:0.5 0.3219 0.3219 % 0.45:0.55 0.28971 0.35409 % 0.4:0.6 0.25752 0.38628 % 0.35:0.65 0.22533 0.41847 % 0.3:0.7 0.19314 0.45066

l1 = 2.79; l2 = 2.57; l3 = 1.6475; A1 = 0.6438; A2 = 0.3219; A3 = 0.3219; %initializing the intial condition a=1; x=1; z=1; m=1; k=1; Bm = 1.3; f = Bm*A1; flux(z,1)=f; e = 1e-10; t = 0; w=2*pi*50; np=965; nt=54;

%Inserting the B-H curve parameter 27M4 material A = 20; B = 6.46919e-5;

Appendix

228

while t<=0.04 %Checking the intial condition

fa(a,1) = f*cos (w*t)+0.2; fb(a,1) = f*cos (w*t - 2.0944)+0.2; fc(a,1) = f*cos (w*t + 2.0944)+0.2;

f1(x,1) = f-20; B1(x,1) = f1(x,1)/A3; B2(x,1) = ( f1(x,1) - fa(a,1))/A2; B3(x,1) = ( -f1(x,1) + fa(a,1) + fb(a,1))/A2; B4(x,1) = ( -f1(x,1) + fa(a,1) + fb(a,1) + fc(a,1))/A3;

H1(x,1) = A*(B1(x,1)) + B*((B1(x,1))^27); H2(x,1) = A*(B2(x,1)) + B*((B2(x,1))^27); H3(x,1) = A*(B3(x,1)) + B*((B3(x,1))^27); H4(x,1) = A*(B4(x,1)) + B*((B4(x,1))^27);

Ba(a,1) = fa(a,1)/A1; Bb(a,1) = fb(a,1)/A1; Bc(a,1) = fc(a,1)/A1;

Ha(a,1) = A*(Ba(a,1)) + B*((Ba(a,1))^27); Hb(a,1) = A*(Bb(a,1)) + B*((Bb(a,1))^27); Hc(a,1) = A*(Bc(a,1)) + B*((Bc(a,1))^27);

y(x,1)= H1(x,1)*(l1+2*l3) + H2(x,1)*2*l2 - H3(x,1)*2*l2 -

H4(x,1)*(2*l3+l1);

% Calculate few points for Newton-Raphson method initial value for x=1:4 f1(x+1,1)= f1(x,1) - 20; B1(x+1,1) = f1(x+1,1)/A3; B2(x+1,1) = ( f1(x+1,1) - fa(a,1))/A2; B3(x+1,1) = ( -f1(x+1,1) + fa(a,1) + fb(a,1))/A2; B4(x+1,1) = ( -f1(x+1,1) + fa(a,1) + fb(a,1) + fc(a,1))/A3;

H1(x+1,1)= A*(B1(x+1,1)) + B*((B1(x+1,1))^27); H2(x+1,1)= A*(B2(x+1,1)) + B*((B2(x+1,1))^27); H3(x+1,1)= A*(B3(x+1,1)) + B*((B3(x+1,1))^27); H4(x+1,1)= A*(B4(x+1,1)) + B*((B4(x+1,1))^27);

y(x+1,1)= H1(x+1,1)*(l1+2*l3) + H2(x+1,1)*2*l2 -

H3(x+1,1)*2*l2 - H4(x+1,1)*(2*l3+l1); x=x+1; end

while abs(y(x,1)) >= e % Newton-Raphson method to do the iteration f1(x+1,1)= f1(x,1) - (y(x,1)*(f1(x,1)-f1(x-1,1))/(y(x,1)-y(x-

1,1)));

B1(x+1,1) = f1(x+1,1)/A3;

Appendix

229

B2(x+1,1) = ( f1(x+1,1) - fa(a,1))/A2; B3(x+1,1) = ( -f1(x+1,1) + fa(a,1) + fb(a,1))/A2; B4(x+1,1) = ( -f1(x+1,1) + fa(a,1) + fb(a,1) + fc(a,1))/A3;

H1(x+1,1)= A*(B1(x+1,1)) + B*((B1(x+1,1))^27); H2(x+1,1)= A*(B2(x+1,1)) + B*((B2(x+1,1))^27); H3(x+1,1)= A*(B3(x+1,1)) + B*((B3(x+1,1))^27); H4(x+1,1)= A*(B4(x+1,1)) + B*((B4(x+1,1))^27);

y(x+1,1)= H1(x+1,1)*(l1+2*l3) + H2(x+1,1)*2*l2 -

H3(x+1,1)*2*l2 - H4(x+1,1)*(2*l3+l1); x=x+1

end

%Pick up the suitable value from the circle and pun into new array Bfit1(m,1)=B1(x-1,1); Hfit1(m,1)=H1(x-1,1); Bfit2(m,1)=B2(x-1,1); Hfit2(m,1)=H2(x-1,1); Bfit3(m,1)=B3(x-1,1); Hfit3(m,1)=H3(x-1,1); Bfit4(m,1)=B4(x-1,1); Hfit4(m,1)=H4(x-1,1);

Hfita(m,1)= Ha(a,1)*l1 + Hfit1(m,1)*(2*l3+l1); Hfitc(m,1)= Hc(a,1)*l1 + Hfit4(m,1)*(2*l3+l1); Hfitb(m,1)= Hb(a,1)*l1 + 2*Hfit2(m,1)*l2 + Hfit1(m,1)*(2*l3+l1);

Ia(m,1)=Hfita(m,1)/np; Ib(m,1)=Hfitb(m,1)/np; Ic(m,1)=Hfitc(m,1)/np;

Hmin(m,1)= (Hfit2(m,1)+ Hfit3(m,1))* l2; Haa(m,1)= Ha(a,1)*l1; tt(a,1)=t; a=a+1; t=t+0.0001; m=m+1;

end % plot the flux density for each part of transformer Current= [Ia Ib Ic]; figure(1) plot(tt, Hfit1,'--r',tt, Hfit2,'y',tt, Hfit3,'b',tt,Hfit4,'--

g','LineWidth',3.5) grid % Labels are erased, so generate them manually title('Mangetic field intensity(No-Delta)','FontSize',13) xlabel('Time(s)','FontSize',13) ylabel('H(A/m)','FontSize',13) % Add a legend in the upper left legend('H1','H2','H3','H4','Location','northeast')

figure(2) plot(Hfita,Ba,'r',Hfitb,Bb,'y',Hfitc,Bc,'b','LineWidth',3.5) grid % Labels are erased, so generate them manually

Appendix

230

title('B-H Characteristic in each phase(No-Delta)','FontSize',13) xlabel('H(A/m)','FontSize',13) ylabel('B(T)','FontSize',13) % Add a legend in the upper left legend('PhaseA','PhaseB','PhaseC','Location','northwest')

figure(3) plot(tt,Hfita,'r',tt,Hfitb,'y',tt,Hfitc,'b',tt,200*Ba,'--

r',tt,200*Bb,'--y',tt,200*Bc,'--b','LineWidth',3.5); grid % Labels are erased, so generate them manually title('Mangetic field intensity and Mangetic flux density(No-

Delta)','FontSize',13) xlabel('Time(s)','FontSize',13) ylabel('Ni(A) or B(200*T)','FontSize',13) % Add a legend in the upper left legend('Nia','Nib','Nic','Ba','Bb','Bc','Location','northeast')

% calculate FFT FFTA=fft(Ia); M1=abs(FFTA)*2/400; % obtain the magnitude value of each frequency Phase1=angle(FFTA)*180/pi; % obtain the angle value of each frequency % Pick the fundanmental frequency and harmorinic for i=1:21 MP1(i) = FFTA(1+2*(i-1)); Mhar1(i) = M1(1+2*(i-1)); % 1/(total time) is the fundamental

harmonic frequency, collecting the 50 Hz and Odd harmonics Phar1(i) = Phase1(1+2*(i-1)); end % plot magnitude value of fundanmental frequency and harmorinic

f1=0:50:1000; figure(4) stem(f1,Mhar1,'r','LineWidth',3.5); grid; % Labels are erased, so generate them manually title('Mangetizing Current Frequency Contain in Phase A(No-

Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude of Current(A)','FontSize',13) %figure(5) %stem(f1,Phar1); %grid;

FFTB=fft(Ib); M2=abs(FFTB)*2/400; % obtain the magnitude value of each frequency Phase2=angle(FFTB)*180/pi; % obtain the angle value of each frequency % Pick the fundanmental frequency and harmorinic for i=1:21 MP2(i) = FFTB(1+2*(i-1)); Mhar2(i) = M2(1+2*(i-1)); Phar2(i) = Phase2(1+2*(i-1)); end

figure(5) stem(f1,Mhar2,'y','LineWidth',3.5); grid;

Appendix

231

% Labels are erased, so generate them manually title('Mangetizing Current Frequency Contain in Phase B(No-

Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude','FontSize',13)

FFTC=fft(Ic); M3=abs(FFTC)*2/400; % obtain the magnitude value of each frequency Phase3=angle(FFTC)*180/pi; % obtain the angle value of each frequency % Pick the fundanmental frequency and harmorinic for i=1:21 MP3(i) = FFTC(1+2*(i-1)); Mhar3(i) = M3(1+2*(i-1)); Phar3(i) = Phase3(1+2*(i-1)); end

PhaseABC= [Phar1' Phar2' Phar3'];

figure(6) stem(f1,Mhar3,'b','LineWidth',3.5); grid; title('Mangetizing Current Frequency Contain in Phase C(No-

Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude','FontSize',13)

%Calculate the Zero, Positive and Nagative sequence

for i=1:21 III=[MP1(1,i);MP2(1,i);MP3(1,i)]; AA=[1,1,1;1,complex(-0.5,0.866),complex(-0.5,-0.866);1,complex(-

0.5,-0.866),complex(-0.5,0.866)]; Izpn = AA*III/3; Izero (1,i)= Izpn(1,1); Iposi (1,i)= Izpn(2,1); Inaga (1,i)= Izpn(3,1); MIzero(1,i)=abs(Izero(1,i))*2/400; MIposi(1,i)=abs(Iposi(1,i))*2/400; MInaga(1,i)=abs(Inaga(1,i))*2/400; end

hba= [Hfita Ba]; hbb= [Hfitb Bb]; hbc= [Hfitc Bc]; hb= [Hfita Ba Hfitb Bb Hfitc Bc];

HarmonicA= Mhar1'; HarmonicB= Mhar2'; HarmonicC= Mhar3'; Harmonic= [HarmonicA HarmonicB HarmonicC];

figure(7) plot(tt, Bfit1,'r',tt,Bfit2,'y',tt,Bfit3, 'b',tt,Bfit4, 'g',

'LineWidth',3.5) grid title('Flux Density in Transformer Core(No-Delta)','FontSize',13) xlabel('Time(s)','FontSize',13) ylabel('Flux Density(T)','FontSize',13)

Appendix

232

legend('Left Outer Yoke','Left Main Yoke','Right Main Yoke','Right

Outer Yoke','Location','northeast')

figure(8) plot(tt, Ia,'r',tt,Ib,'y',tt,Ic, 'b', 'LineWidth',3.5) grid title('Mangetizing current in Each Winding(No-Delta)','FontSize',13) xlabel('Time(s)','FontSize',13) ylabel('Current in primary side','FontSize',13) legend('PhaseA','PhaseB','PhaseC','Location','northeast')

figure(9) plot(Hfit1,Bfit1,'r',Hfit2,Bfit2,'y',Hfit3,Bfit3,'b',Hfit4,Bfit4,'g','

LineWidth',3.5) grid title('Transformer Core Characteristic in each part(No-

Delta)','FontSize',13) xlabel('Magetic Field Intensity(A/m)','FontSize',13) ylabel('Flux Density(T)','FontSize',13) legend('Left Outer Yoke','Left Main Yoke','Right Main Yoke','Right

Outer Yoke','Location','northeast')

figure(10) stem(f1,MIzero,'LineWidth',3.5); grid; title('Zero sequence mangetizing current (No-Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude(A)','FontSize',13)

figure(11) stem(f1,MIposi,'LineWidth',3.5); grid; title('Positive sequence mangetizing current (No-Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude(A)','FontSize',13)

figure(12) stem(f1,MInaga,'LineWidth',3.5); grid; title('Nagative sequence mangetizing current (No-Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude(A)','FontSize',13)

HarmonicZ= MIzero'; HarmonicP= MIposi'; HarmonicN= MInaga'; HarmonicS= [HarmonicZ HarmonicP HarmonicN];

% calculate FFT of the Magnetic density

FFTB1=fft(Bfit1);

MB1=abs(FFTB1)*2/400; % obtain the magnitude value of each frequency PhaseB1=angle(FFTB1)*180/pi; % obtain the angle value of each

frequency % Pick the fundanmental frequency and harmorinic

Appendix

233

for i=1:21 MPB1(i)=FFTB1(1+2*(i-1)); MharB1(i)=MB1(1+2*(i-1)); % 1/(total time) is the fundamental

harmonic frequency, collecting the 50 Hz and Odd harmonics PharB1(i)=PhaseB1(1+2*(i-1)); end % plot magnitude value of fundanmental frequency and harmorinic

f1=0:50:1000; figure(13) stem(f1,MharB1,'LineWidth',3.5); grid; % Labels are erased, so generate them manually title('Mangetic density Frequency Contain in Side yoke(No-

Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude(T)','FontSize',13) %figure(5) %stem(f1,Phar1); %grid;

FFTB2=fft(Bfit2);

MB2=abs(FFTB2)*2/400; % obtain the magnitude value of each frequency PhaseB2=angle(FFTB2)*180/pi; % obtain the angle value of each

frequency % Pick the fundanmental frequency and harmorinic for i=1:21 MPB2(i)=FFTB2(1+2*(i-1)); MharB2(i)=MB2(1+2*(i-1)); % 1/(total time) is the fundamental

harmonic frequency, collecting the 50 Hz and Odd harmonics PharB2(i)=PhaseB2(1+2*(i-1)); end % plot magnitude value of fundanmental frequency and harmorinic

f1=0:50:1000; figure(14) stem(f1,MharB2,'LineWidth',3.5); grid; % Labels are erased, so generate them manually title('Mangetic density Frequency Contain in Main yoke(No-

Delta)','FontSize',13) xlabel('Frequency(Hz)','FontSize',13) ylabel('Magnitude(T)','FontSize',13) %figure(5) %stem(f1,Phar1); %grid;

HarmonicB1= MharB1'; HarmonicB2= MharB2'; HarmonicBB= [HarmonicB1 HarmonicB2];

Appendix

234

2 Impact of Area under GIC situation

2.1 Sensitivity study on linear region with GIC situation

From the investigation, it can be seen that the ratio of the main yoke and side yoke

would influence the magnetising current and flux density distribution. The ratio varying

is still following Table 4-13 and the results and discussion will be represented in the

following.

Three groups are carried out by changing the supplied voltage, which are 70% of the

rated voltage at liner region, rated voltage at knee point and 115% of the rated voltage at

saturation region. In each group, the supplied AC voltage and DC supply as 0.1 Wb are

fixed by varying the cross-section area ratio of side yoke and main yoke.

Figure 1 and Figure 2 show that magnetic flux density in the side yoke and main yoke at

the different area ratios at the supplying 70% rated voltage. The waveforms are not

following sinusoidal waveform and the peak value is increased with the ratio of the

cross-section area between side yoke and main yoke, but the amplitudes are decreased.

The amplitudes of the magnetic flux density are decreased in the main yoke area with

the ratio of the cross-section area between side yoke and main yoke which is opposite

with side yoke. The maximum magnitudes of Bm in the side yoke is increasing, but the

main yoke is decreasing. The maximum magnitude of the flux density keeping longer

time as flat waveform in the side yoke is due to the reducing the ratio of cross-section

between side yoke and main yoke; but the main yoke is in an opposite way.

Figure 1 Side yoke magnetic flux density at 70% supplied AC voltage and 0.1Wb DC

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Flu

x D

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

235

Figure 2 Main yoke magnetic flux density at 70% supplied AC voltage and 0.1Wb DC

From Figure 3 and Figure 4, both of them are shown that the magnitude of fundamental

frequency, second harmonic and third harmonic in both side yoke and main yoke is

decreased with the percentage ratio of the cross-section area between side yoke and

main yoke. However, the magnitude of DC component frequency is increased with the

percentage decreasing of the ratio of the cross-section area between side yoke and main

yoke in the side yoke.

Due to the side yoke function is for the unbalanced flux passing through, and then the

magnitude of DC flux density is increased in the side yoke when decreasing of the ratio

of the cross-section area between side yoke and main yoke. In addition, the magnitude

of DC flux is increased from 0.9T to 1.54T in the side yoke, and is decreased from 0.3T

to 0.21T in the main yoke.

Figure 3 Maximum value of each harmonic in the side yoke

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04Fl

ux

De

nsi

ty (

T)Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

itu

de

of

Ma

gn

eti

c d

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

236

Figure 4 Maximum value of each harmonic in the main yoke

Table 1 shows the maximum magnitude of fundamental flux density at side yoke and

main yoke in different cross-section area ratio. From this table, we can also see that the

amplitudes of the magnetic flux density are decreased with the ratio of the cross-section

area between side yoke and main yoke.

Table 1 Maximum magnitude in 50Hz of flux density


0.5:0.5 1.0071 1.5818

0.45:0.55 0.9727 1.5198

0.4:0.6 0.9379 1.4691

0.35:0.65 0.8950 1.4279

0.3:0.7 0.8313 1.3971

Table 1 shows the maximum magnitude of DC flux density at side yoke and main yoke

in different cross-section area ratio. It can be seen that the amplitudes of the DC

magnetic flux density are decreased in the main yoke with the ratio of the cross-section

area between side yoke and main yoke; but is increased in the side yoke. IN addition,

the speed of the increasing in the side yoke is much more serious than the decreasing in

the main yoke.

Table 2 Maximum magnitude in DC flux density


0.5:0.5 0.9318 0.3105

0.45:0.55 1.0353 0.2823

0.4:0.6 1.1636 0.2580

0.35:0.65 1.3298 0.2381

0.3:0.7 1.5516 0.2217

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

itu

de

of

Ma

gn

eti

c d

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

237

2.2 Sensitivity study on knee area with GIC situation

When increasing the supplied voltage to rated AC voltage which means the transformer

core working at knee area, the magnetic flux density waveform of side yoke and main

yoke are shown in Figure 5 and Figure 6. The waveforms are all distorted.

It can be seen from Figure 5, which the peak value of the magnetic flux density does not

change at side yoke area with the ratio of the cross-section area between side yoke and

main yoke, but it is shift up by the ratio, which means the amplitude is decreased.

Figure 5 Side yoke magnetic flux density at rated supplied AC voltage and 0.1Wb DC

From Figure 6, it can be seen that the amplitude and the peak value of the flux density is

not changed, only the waveform become less distorted with ratio of the cross-section

area between side yoke and main yoke deceased.

Figure 6 Main yoke magnetic flux density at rated supplied AC voltage and 0.1Wb DC

From Figure 7 and Figure 8, both of them are shown that the magnitude of fundamental

frequency, second harmonic and third harmonic in both side yoke and main yoke is

decreased with the percentage ratio of the cross-section area between side yoke and

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Flu

x D

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Flu

x D

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sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

238

main yoke. However, the magnitude of DC component frequency is increased at the

side yoke with the percentage decreasing of the ratio of the cross-section area between

side yoke and main yoke.

There is the same trend as the linear region which is that the magnitude of DC flux

density is increased in the side yoke when decreasing of the ratio of the cross-section

area between side yoke and main yoke.




main yoke in different cross-section area ratio. It can be seen that the magnitude of the

magnetic flux density in 50Hz are decreased with the ratio of the cross-section area

between side yoke and main yoke.



0.5:0.5 1.677 2.110

0.45:0.55 1.614 2.046

0.4:0.6 1.532 2.005

0.35:0.65 1.427 1.978

0.3:0.7 1.291 1.960

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

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de

of

Ma

gn

eti

c d

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

itu

de

of

Ma

gn

eti

c d

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

239




area between side yoke and main yoke; but is increased in the side yoke. In addition, the

speed of the increasing in the side yoke is much more serious than the decreasing in the

main yoke.



0.5:0.5 0.932 0.311

0.45:0.55 1.036 0.282

0.4:0.6 1.165 0.259

0.35:0.65 1.331 0.239

0.3:0.7 1.553 0.222

2.3 Sensitivity study on non-linear region with GIC situation

Continuing to increase the supplied voltage to 110% rated AC voltage which is the

transformer working at the on no-linear region, the magnetic flux density waveform of

side yoke and main yoke are shown in Figure 9 and Figure 10. The waveforms of the

magnetic flux density are all distorted. The waveforms shapes do not change much

compare with the supplied rated voltage; the only difference is the magnitude is

increased. This is due to the supplied rated voltage and 0.1 Wb DC flux to the

transformer, the transformer is already saturated.


-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Flu

x D

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sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

240


From Figure 11 and Figure 12, both of them are shown that the magnitude of

fundamental frequency, second harmonic and third harmonic in both side yoke and

main yoke is decreased with the percentage ratio of the cross-section area between side

yoke and main yoke. There is the same trend as the linear region and the knee area

which is that the magnitude of DC flux density is increased in the side yoke when

decreasing of the ratio of the cross-section area between side yoke and main yoke.



-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Flu

x D

en

sity

(T)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

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de

of

Ma

gn

eti

c

de

nsi

ty(T

)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000

Ma

gn

itu

de

of

Ma

gn

eti

c

de

nsi

ty(T

)

Time(s)

0.5:0.5 0.45:0.55 0.4:0.6 0.35:0.65 0.3:0.7

Appendix

241


main yoke in different cross-section area ratio. It can be seen that the magnitude of the

magnetic flux density in 50Hz are decreased with the ratio of the cross-section area

between side yoke and main yoke. And the magnitude of the fundamental flux density

at main yoke is always higher than the side yoke area in all three cases.



0.5:0.5 1.880 2.299

0.45:0.55 1.821 2.226

0.4:0.6 1.741 2.179

0.35:0.65 1.636 2.149

0.3:0.7 1.496 2.131




area between side yoke and main yoke; but is increased in the side yoke. In addition, the

speed of the increasing in the side yoke is much more serious than the decreasing in the

main yoke. The magnitude of the DC flux density at main yoke is always lower than the

side yoke area in all three cases.



0.5:0.5 0.932 0.311

0.45:0.55 1.036 0.282

0.4:0.6 1.165 0.259

0.35:0.65 1.331 0.239

0.3:0.7 1.553 0.222

Through the investigation above, it can be seen that higher main yoke area would obtain

lower flux density in the main yoke and in the side yoke; however it will cost more

material to build up the transformer. So the balance between the reliability of the

transformer and the costly of the material to build up the transformer become quite

important for the manufacturers.

Appendix

242

3 Cable information

Table 7 Dimension of single core cable

Parameter Value

(mm) Calculation of cable diameter (mm)

Diameter of conductor 21.5 21.5+0=21.5

Thickness of Conductor screen 0.8 21.5+0.8*2=23.1

Thickness of insulation 19.0 23.1+19*2=61.1

Thickness of core screen 1.0 61.1+1.0*2=63.1

Thickness of Semicon WST 1.0 63.1+1.0*2=65.1

Thickness of lead sheath 3.5 65.1+3.5*2=72.1

Thickness of Bitumen 0.5 72.1+0.5*2=73.1

Thickness of MDPE sheath 3.65 73.1+3.65*2=80.4

4 Publication

1. Rui Zhang; T. Byrne; D. Jones; Zhongdong Wang; "A Technical Experience

During Network Asset Replacement: Investigating Cable and Transformer Switching

Interactions," CIRED 2010 Workshop Lyon, France, 7-8 June 2010

2. Rui Zhang; Swee Peng Ang; Haiyu Li; Zhongdong Wang; "Complexity of

ferroresonance phenomena: sensitivity studies from a single-phase system to three-

phase reality," High Voltage Engineering and Application (ICHVE), 2010 International

Conference on vol., no., pp.172-175, 11-14 Oct. 2010

3. Rui Zhang; Haiyu Li; Zhongdong Wang; "Switching Ferroresonant Transient

Study using Finite Element Transformer Model, " 4th Universities High Voltage

Network Conference, 18-19 Jan. 2011

4. Rui Zhang; Jinsheng Peng; Swee.Peng Ang; Haiyu. Li; Zhongdong Wang; Paul

Jarman, “Statistical Analysis of Ferroresonance in a 400 kV Double-Circuit

Transmission System”, IPST 2011, Delft, Netherlands, June 14-17, 2011.

5. C.A. Charalambous; Rui Zhang; Zhongdong. Wang, “Simulating Thermal

Conditions around Core Bolts when Transformer Experiencing Ferroresonance”, IPST

2011, Delft, Netherlands, June 14-17, 2011.

Documents

TRANSFORMER MODELLING AND INFLUENTIAL PARAMETERS