transformer fault-recovery inrush currents in mmc-hvdc systems and mitigation strategies

Microsoft Word - Thesis_Draft6.docxTransformer fault-recovery inrush currents in MMC-HVDC systems and mitigation strategies
A thesis submitted to The University of Manchester for the Degree of Doctor of Philosophy in the Faculty of Engineering and Physical Sciences
2016
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1.3.1 Occurrence of transformer inrush currents upon fault clearance ................ 44
1.4 Transformer inrush currents in power-electronic systems- A literature review .... 47
1.4.1 Power electronic systems which handle fault-recovery inrush currents ..... 50
1.5 Research scopes and objectives ............................................................................. 51
1.6 Outline of the thesis ............................................................................................... 55
Chapter 2 Transformer modelling for inrush current transient studies ........................... 59
2.1 Introduction ........................................................................................................... 59
2.2 Topology-based transformer models ..................................................................... 60
2.2.1 Magnetic equivalent circuit of a single-bank core-type transformer [84] ... 60
2.2.2 Duality approach to model a single-bank core-type transformer [84] [87] 61
2.2.3 UMEC approach to model a single-bank core-type transformer [88] ......... 64
2.2.4 UMEC approach vs Duality approach: cross-verification .......................... 67
2.2.5 Limitation of the inbuilt UMEC transformer model in PSCAD/EMTDC .. 73
2.3 Classical transformer model .................................................................................. 75
2.3.1 Steinmetz transformer model and its magnetic duality ............................... 75
2.3.2 Relative merits of the Steinmetz transformer model................................... 78
2.4 Summary and conclusions ..................................................................................... 82
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Chapter 3 Validation of the PSCAD/EMTDC inbuilt classical transformer model ....... 83
3.1 Introduction ........................................................................................................... 83
3.2 An introduction to the PSCAD-inbuilt classical transformer model .................... 84
3.3 A description of the candidate system used for inrush current measurement and
the transformer name plate data ....................................................................................... 85
3.4 Parameterisation of the classical transformer model ............................................ 86
3.4.1 Conversion of short circuit test data ........................................................... 86
3.4.2 Conversion of the open circuit test data ..................................................... 87
3.4.3 Summary of classical transformer model parameters ................................. 91
3.5 Parameterisation of the source model ................................................................... 92
3.5.1 Verification ................................................................................................. 96
3.6 Validation .............................................................................................................. 96
3.6.1 Discussion ................................................................................................. 101
3.7.1 Sensitivity of inrush current magnitude to air-core inductance ................ 102
3.7.2 Sensitivity of inrush current magnitude to knee point .............................. 103
3.7.3 Sensitivity of inrush current magnitude to rated magnetisation current ... 104
3.7.4 Discussion ................................................................................................. 104
Chapter 4 MMC-HVDC system and transformer inrush currents ............................... 107
4.1 Introduction ......................................................................................................... 107
4.3.2 Active and reactive power control ............................................................ 115
4.3.3 Circulating current suppression control .................................................... 117
4.3.4 MMC modulator: Capacitor balancing control and nearest level control 120
4.4 Modelling levels of fidelity of an MMC ............................................................. 121
4.4.1 Traditional Detailed Model (TDM) .......................................................... 121
4.4.2 Detailed Equivalent Model (DEM) .......................................................... 122
4.4.3 Average Value Model (AVM) .................................................................. 123
4.5 Impact of transformer inrush currents in an MMC-HVDC system .................... 124
4.6 Summary and conclusions .................................................................................. 129
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Chapter 5 The impact of current sensor placement on inrush current behaviour ......... 131
5.1 Introduction ......................................................................................................... 131
5.2 Behaviour of fault-recovery inrush currents: An introduction to problems ........ 132
5.2.1 Attenuation of DC magnetisation currents ................................................ 133
5.2.2 Direction of flow of DC magnetisation currents ....................................... 135
5.3 Dynamic model of the plant with average magnetisation inductance ................. 138
5.3.1 Average model of the magnetisation inductance ...................................... 138
5.3.2 Derivation of a dynamic model of a VSC-HVDC system incorporating magnetisation characteristic .................................................................................... 139
5.3.3 Verification ............................................................................................... 144
5.4.1 Attenuation of DC magnetisation currents ................................................ 145
5.4.2 Flow of DC magnetisation currents .......................................................... 146
5.5 Discussion: Impact of the non-linearity of the magnetisation inductance .......... 150
5.6 Summary and conclusions ................................................................................... 152
Chapter 6 Assessment of peak inrush current magnitude ............................................. 153
6.1 Analytical study ................................................................................................... 154
6.1.2 Verification ............................................................................................... 157
6.2 Applicability and limitations of the analytical equations in fault-recovery
transients ........................................................................................................................ 158
6.2.2 The impact of fault-resistance ................................................................... 164
6.3 The variation of peak flux-linkage and the peak inrush current magnitudes ...... 167
6.3.1 When relay trigger duration is long .......................................................... 168
6.3.2 When the relay trigger duration is short .................................................... 178
6.3.3 Discussion ................................................................................................. 187
Chapter 7 Inrush current mitigation using an auxiliary feedforward compensation
scheme: A critique on a prior art ........................................................................................ 195
7.1 Introduction ......................................................................................................... 195
7.2 Inrush current reduction technique proposed in [56] .......................................... 196
7.2.1 Relation between pre-recovery DC flux offsets and post-recovery peak flux- linkage magnitudes ................................................................................................. 196
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7.2.2 A technique for eliminating pre-recovery DC flux-offsets using a converter: A conceptual explanation ....................................................................................... 197
7.2.3 A description of the compensation control scheme proposed in [56] ...... 198
7.3 Implementation and verification in PSCAD/EMTDC ........................................ 201
7.4 Relative merits of the proposed compensation scheme ...................................... 205
7.4.1 Sensitivity of the resistance, tR ................................................................ 205
7.4.2 Challenges for an MMC to inject DC currents: Implementation of the proposed mitigation strategy in a detailed MMC-HVDC model ............................ 209
7.4.3 Other issues ............................................................................................... 213
7.5 Summary and conclusions .................................................................................. 214
Chapter 8 Inrush current mitigation using an auxiliary feedback control loop ............ 215
8.1 Introduction ......................................................................................................... 215
8.2 Selection of an appropriate auxiliary feedback control loop- design and
optimisation ................................................................................................................... 218
8.2.2 Design and Optimisation .......................................................................... 221
8.2.3 Proportional vs Proportional-Integral controller ...................................... 224
8.3 Implementation and verification in PSCAD/EMTDC ........................................ 228
8.4 Relative merits of the proposed inrush current mitigation strategy .................... 233
8.4.1 Robustness against the sensitivity of the resistance in-between the magnetisation branch and the AC source ............................................................... 233
8.4.2 Post-recovery contribution for inrush harmonics suppression ................. 237
8.4.3 The impact of fault resistance ................................................................... 239
8.4.4 Implementation in an MMC-HVDC system ............................................. 249
8.4.5 Implementation in a two-level-converter based HVDC system ............... 254
8.5 Conclusions ......................................................................................................... 257
Chapter 9 The impact of fault-recovery inrush currents in an islanded MMC-HVDC
system and novel mitigation strategies .............................................................................. 259
9.1 Introduction ......................................................................................................... 259
9.2 Control system for an MMC operating in the islanded mode ............................. 260
9.2.1 Control scheme in the synchronous (dq0) reference frame ...................... 261
9.2.2 Control scheme in the natural (abc) reference frame ................................ 263
9.3 Implementation of a detailed (islanded mode) MMC-HVDC system in
PSCAD/EMTDC and investigation of the impact of fault-recovery inrush currents .... 268
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9.4.1 DC flux offset at sag-recovery and inrush currents .................................. 274
9.4.2 Conditions to avoid inrush currents at sag-recovery ................................. 276
9.4.3 Inrush current mitigation strategies: Implementation guidelines .............. 280
9.5 Verification of the proposed inrush current mitigation strategies and analysis of
relative merits ................................................................................................................. 282
9.5.1 Verification of the IPOW strategy: Calculation of inrush-free final POW based on the initial POW of the fault ...................................................................... 282
9.5.2 Verification of the FVFL strategy: Calculation of inrush-free final POW based on the DC flux-linkage and sag magnitude ................................................... 289
9.6 Discussion ........................................................................................................... 295
Chapter 10 Conclusions and Further work ..................................................................... 297
10.1 Summary and concluding remarks .................................................................. 297
10.1.1 Identification of an appropriate transformer model for inrush current transient studies and its validation ......................................................................................... 297
10.1.2 Preliminary investigation of transformer inrush currents in a MMC-HVDC system and a basic remedial action ......................................................................... 298
10.1.3 Assessment of peak inrush current magnitude .......................................... 299
10.1.4 Devising advanced inrush current mitigation strategies for a MMC-HVDC system 300
10.2 Main contributions ........................................................................................... 302
10.3 Further work .................................................................................................... 302
10.3.1 Identification of an appropriate transformer model for inrush current transient studies and its validation ......................................................................................... 302
10.3.2 Preliminary investigation of transformer inrush currents in a MMC-HVDC system and a basic remedial action ......................................................................... 303
10.3.3 Assessment of peak inrush current magnitude .......................................... 304
10.3.4 Devising advanced inrush current mitigation strategies for a MMC-HVDC system 304
References .......................................................................................................................... 307
A.3 UMEC Approach- Derivation of inductance and resistance matrix ....................... 323
A.4 Parameterisation of a linear duality circuit ............................................................. 328
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A.5 Parameterisation of a non-linear duality circuit ...................................................... 330
A.6 Derivation of flux-linkage vs current curve using open-circuit test results ............ 334
A.7 Improved parameterisation of the inbuilt UMEC model in PSCAD/EMTDC ....... 337
Appendix B ........................................................................................................................ 341
B.1 TSAT21 subroutine ................................................................................................. 341
B.2 The input data required by the inbuilt classical transformer component in
PSCAD/EMTDC ........................................................................................................... 342
B.3 Conversion of open circuit test results into peak voltage vs peak resistive-current
and peak flux-linkage vs peak inductive-current values ................................................ 342
B.4 Curve fitting for TSAT21 subroutine ...................................................................... 347
Appendix C ........................................................................................................................ 351
Appendix D ........................................................................................................................ 357
D.3 Disturbance sensitivity transfer functions ............................................................... 358
Appendix E ........................................................................................................................ 363
E.2 Peak flux-linkage magnitude data ........................................................................... 366
E.3 Peak magnetisation current magnitude variation with different active and reactive
power set-points ............................................................................................................. 367
Appendix F ........................................................................................................................ 371
Appendix G ........................................................................................................................ 375
G.1 Disturbance sensitivity and command tracking transfer functions with a proportional
only controller ................................................................................................................ 375
G.2 . Disturbance sensitivity and command tracking transfer functions with a PI
controller ........................................................................................................................ 376
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G.3 Dynamic and transient analysis of different options of the auxiliary feedback based
control strategy ............................................................................................................... 378
G.5 Two-level converter specific parameters ................................................................ 392
Appendix H ........................................................................................................................ 393
H.1 Control scheme in the synchronous reference frame .............................................. 393
H.2 When the MMC is connected to an active load: wind farm .................................... 398
H.3 Synchronous reference frame to stationary reference frame ................................... 406
H.4 The impact of fault-recovery transients on the DC side .......................................... 407
H.5 Conditions to avoid inrush currents at sag-recovery ............................................... 420
Word count: 79,871
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List of Figures
Figure 1.1. VSC topologies a) Two-level b) Three-level c) Modular Multi-level (left to
right) [12] ............................................................................................................................. 41
Figure 1.2. Qualitative illustration of inrush phenomena and the effect of residual flux [18]
.............................................................................................................................................. 43
Figure 1.3. Inrush current field measurement (carried out in [18]) ..................................... 43
Figure 1.4. A system model in PSCAD consists of transformer, resistive load and source 44
Figure 1.5. Three-phase breaker-currents, secondary-side (load-side) voltages, flux
linkages and magnetisation currents (from top to bottom) .................................................. 45
Figure 1.6. Voltage waveform with a phase-hop condition [52] ......................................... 49
Figure 2.1. Single-bank core-type transformer with mean flux-paths ................................. 60
Figure 2.2. Magnetic equivalent circuit ............................................................................... 61
Figure 2.3. Topological development .................................................................................. 62
Figure 2.4. Electrical duality ................................................................................................ 62
Figure 2.5. With ideal transformers and loss elements ........................................................ 63
Figure 2.6. Internal elements referred to primary-side: An intermediate stage ................... 63
Figure 2.7. Internal elements referred to primary-side: Final stage ..................................... 64
Figure 2.8. a) Single-phase core-type transformer b) Magnetic equivalent circuit ............. 65
Figure 2.9. Magnetic equivalent circuit used for UMEC approach ..................................... 65
Figure 2.10. Open-circuit test condition in a simulation set-up ........................................... 69
Figure 2.11. Primary side voltage, primary side current, secondary side voltage and
secondary side current (from top to bottom) from different transformer models; inbuilt-
UMEC model, custom-made UMEC model and duality-circuit model ............................... 69
Figure 2.12. Winding-1 leg flux, winding-2 leg flux, winding-1 leakage flux, winding-2
leakage flux, yoke flux (from top to bottom); here primary is winding-1 and secondary is
winding-2 ............................................................................................................................. 70
Figure 2.13. Primary side voltage, primary side current, secondary side voltage and
secondary side current (from top to bottom) from different transformer models; inbuilt-
UMEC model and duality-circuit model .............................................................................. 72
Figure 2.14. Winding-1 leg flux, winding-2 leg flux, winding-1 leakage flux, winding-2
leakage flux, yoke flux (from top to bottom); here primary is winding-1 and secondary is
winding-2 ............................................................................................................................. 73
Figure 2.15. Open circuit test results; factory-test results and simulation-test results using
UMEC and duality models (plots of UMEC and Duality models coincide)........................ 74
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Figure 2.16. Steinmetz standard equivalent model of a transformer [86] ........................... 75
Figure 2.17. Topological development a) Steinmetz electrical equivalent circuit of a single-
phase transformer: the secondary-side elements are referred to the primary-side and
winding and core-resistances are neglected b) equivalent magnetic circuit: relutance of the
magnetisation inductance is lumped at the lower branch c) equivalent magnetic circuit:
relutance of the magnetisation inductance is lumped at the upper branch .......................... 77
Figure 2.18. Magnetic equivalent circuits from the perspective of a single-phase a) core-
type b) shell-type transformer .............................................................................................. 78
Figure 2.19. a) Modified equivalent Steinmetz model b) Realisation in PSCAD/EMTDC 79
Figure 2.20. Comparison of open circuit test results ........................................................... 81
Figure 3.1. Equivalent circuit of the PSCAD inbuilt classical transformer model when core
saturation is modelled .......................................................................................................... 84
Figure 3.2. Core-saturation characteristic as defined by TSAT21 subroutine [88] ............. 84
Figure 3.3. Schematic diagram of the system used in [18] for detailed inrush current studies
............................................................................................................................................. 85
Figure 3.4. Delta connected piece-wise linear resistor and inductor representing the open
circuit condition of the transformer ..................................................................................... 88
Figure 3.5. Derived saturation curve for transformer, T2 .................................................... 90
Figure 3.6. Reduced model of the system ............................................................................ 93
Figure 3.7. Resultant short circuit current [101] .................................................................. 94
Figure 3.8. AC component of short circuit current [101] .................................................... 94
Figure 3.9. DC component of short circuit current [101] .................................................... 94
Figure 3.10. Measurement and simulation of three-phase voltages at PCC ........................ 97
Figure 3.11. Measurement and simulation results of phase-A inrush current (without a
model for the current sensor) ............................................................................................... 98
Figure 3.12. Measurement and simulation results of phase-B inrush current (without a
Figure 3.13. Measurement and simulation results of phase-C inrush current (without a
Figure 3.14. Measurement and simulation of phase-A inrush current (with a model for the
current sensor) ................................................................................................................... 100
Figure 3.15. Measurement and simulation of phase-B inrush current (with a model for the
current sensor) ................................................................................................................... 100
Figure 3.16. Measurement and simulation of phase-C inrush current (with a model for the
current sensor) ................................................................................................................... 101
Figure 3.17. Variation of maximum inrush current magnitude with air-core inductance .. 103
Figure 3.18. Variation of maximum inrush current magnitude with knee point................ 103
Figure 3.19. Variation of maximum inrush current magnitude with the rated magnetisation
current ................................................................................................................................ 104
Figure 4.1. MMC construction showing sub modules [9] ................................................. 107
Figure 4.2. Conceptual circuit of MMC and output waveform [108] ................................ 108
Figure 4.3. MMC-HVDC system ....................................................................................... 108
Figure 4.4. Cascaded control structure ............................................................................... 110
Figure 4.5. Equivalent circuit of an MMC ......................................................................... 112
Figure 4.6. Equivalent circuit representation of the AC side of an MMC system ............. 113
Figure 4.7. SFSB of the plant a) d-axis b) q-axis ............................................................... 114
Figure 4.8. Current control loops ....................................................................................... 114
Figure 4.9. Active power control loop ............................................................................... 116
Figure 4.10. SFSB of the circulating current component of the plant ............................... 119
Figure 4.11. Circulating current suppression control loops ............................................... 119
Figure 4.12. MMC modulator circuit (based on [125] and [5]) ......................................... 120
Figure 4.13. a) Equivalent circuit of a sub module b) Chain of submodules [111] ........... 122
Figure 4.14. Thevenin equivalent of a combined-submodule component (fundamental
DEM component) [111] ..................................................................................................... 122
Figure 4.15. Reduced component in System 2 (fundamental DEM component) and its
subsystem in System 1 [111] ............................................................................................. 123
Figure 4.16. AC-side and DC side equivalent circuits used in the AVM .......................... 124
Figure 4.17. Detailed MMC-HVDC system model with its control unit as implemented in
PSCAD ............................................................................................................................... 124
transformer grid-side currents, transformer converter-side currents, arm currents- in upper
(up) and lower (low) arms (from top to bottom); overcurrent protection is disabled ........ 127
Figure 4.19. Breaker currents, PCC voltages, flux-linkages, magnetisation currents,
transformer grid-side currents, transformer converter-side currents, arm currents- in upper
(up) and lower (low) arms (from top to bottom); overcurrent protection is enabled ......... 128
Figure 5.1. Placement of current sensor a) Grid side of the transformer (GST) b) Converter
side of the transformer (CST) ............................................................................................ 132
Figure 5.2. AC side plant model of a MMC-HVDC system as implemented in
PSCAD/EMTDC ................................................................................................................ 133
Figure 5.3. RMS grid-voltages, instantaneous magnetisation currents and DC values of the
magnetisation currents during a fault-recovery transient (a) Case GST (b) Case CST ..... 134
Figure 5.4 Magnetisation currents, converter-side currents and grid-side currents in Case
GST (a) Instantaneous values (b) DC values ............................................................ 135
Figure 5.5. Magnetisation currents, converter-side currents and grid-side currents in Case
CST (a) Instantaneous values (b) DC values ............................................................. 136
Figure 5.6. Magnetisation current flow in a) Case GST b) Case CST ............................. 137
Figure 5.7. Piece-wise linearised magnetisation inductance ............................................. 138
Figure 5.8. Simplified circuit diagram of the VSC-HVDC system ................................... 139
Figure 5.9. SFSB diagram that relates d-axis converter voltage and converter current .... 142
Figure 5.10. SFSB diagram that relates d-axis converter voltage and grid current ........... 142
Figure 5.11. Closed loop dynamic models of the d-axis inner current control loop a) Case
GST b) Case CST .............................................................................................................. 143
Figure 5.12. Simulation results for Case GST ................................................................... 144
Figure 5.13. Dominant poles of Case GST and CST ......................................................... 145
Figure 5.14. Dynamic stiffness plots (a) Case GST (b) Case CST .................................... 148
Figure 5.15. Variation of dominant poles with saturation level for Case CST ................. 150
Figure 5.16. DC components of magnetisation currents with a) non-linear inductance b)
unsaturated inductance ( 0) c) saturated inductance ( 1) .......................................... 151
Figure 6.1. AC side plant model of a VSC-HVDC system ............................................... 155
Figure 6.2. PCC (primary-side) voltages and ‘virtual’ flux-linkages phases A, B and C
(from top to bottom) .......................................................................................................... 156
Figure 6.3. PCC voltages, and primary and secondary ‘virtual’ flux-linkages along with
calculations for peak flux-linkage magnitudes from Format 1 and Format 2 for phases A, B
and C (from top to bottom) ................................................................................................ 158
Figure 6.4. AC side plant model of a VSC-HVDC system with non-ideal source ............ 159
and C (from top to bottom) ................................................................................................ 160
Figure 6.6. Simulation results of breaker currents, primary-side voltages, secondary-side
currents, secondary-side voltages and secondary-side flux-linkages (from top to bottom)
........................................................................................................................................... 161
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zero-sequence current controller is deployed ..................................................................... 163
and C (from top to bottom); zero-sequence current controller is deployed ....................... 164
Figure 6.10. Minimal (bottom most curves) and maximal (top most curves) arc resistances
in a line-to-ground fault at 400 kV system; calculated for instantaneous protection in [134]
............................................................................................................................................ 165
Figure 6.11. Fault currents, PCC voltages, and primary and secondary ‘virtual’ flux-
linkages along with calculations for peak flux-linkage magnitudes from Format 1 and
Format 2 for phases A, B and C (from top to bottom); zero-sequence current controller is
deployed and fault resistance is 4 ohms. ............................................................................ 166
Figure 6.12. AC side plant model of a VSC-HVDC system .............................................. 167
Figure 6.13. Simulation results for breaker currents, PCC voltages and flux-linkages
showing relay trigger duration and fault-durations ............................................................ 168
Figure 6.14. Variation of the peak flux-linkage magnitude in each phase with different
fault-durations (Initial POW= 0 degrees) ........................................................................... 169
relay trigger-durations (Initial POW= 0 degrees) .............................................................. 170
Figure 6.16. Fault current of phase A: Zero crossing instants are marked ........................ 170
Figure 6.17. Variation of the highest peak flux-linkage magnitude within three-phases with
different relay trigger-durations; initial POW is kept as 0 degrees .................................... 171
Figure 6.18. Variation of the peak flux-linkage magnitude within three-phases with
different relay trigger-durations; initial POW is kept as 30 degrees .................................. 171
fault-durations (Initial POW= 30 degrees) ......................................................................... 172
relay trigger-durations (Initial POW= 30 degrees) ............................................................ 172
different relay trigger-durations and different initial POWs .............................................. 173
different relay trigger-durations and different initial POWs; bird’s eye view ................... 173
Figure 6.23. Converter-side voltages, flux-linkages and magnetisation currents (from top to
bottom); when the saturation is disabled ............................................................................ 174
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bottom); when the saturation is enabled ............................................................................ 174
different relay trigger-durations and different initial POWs; saturation is enabled .......... 176
Figure 6.26 Variation of the highest peak flux-linkage magnitude within three-phases with
different relay trigger-durations and different initial POWs; saturation is enabled- bird’s
eye view ............................................................................................................................. 176
Figure 6.27. Variation of the highest peak magnetisation current magnitude within three-
phases with different relay trigger-durations and different initial POWs; saturation is
enabled ............................................................................................................................... 177
phases with different relay trigger-durations and different initial POWs; saturation is
enabled- bird’s eye view .................................................................................................... 177
Figure 6.29. Fault current of phase A ................................................................................ 178
fault-durations (Initial POW= 0 deg) ................................................................................. 179
Figure 6.31 Variation of peak flux-linkage magnitude with (a shorter) relay trigger-
duration .............................................................................................................................. 179
Figure 6.32. Fault current of phase A (with a short duration snap) ................................... 180
Figure 6.33. Variation of the highest peak flux-linkage magnitude (within the three-phases)
with different relay trigger-durations; initial POW is kept as 0 degree ............................. 180
Figure 6.34. Breaker currents, converter-side voltages and flux-linkages (from top to
bottom) when the relay trigger duration is 15.5 cycles; here the time scale covers the fault
initiation instant and the fault clearance instant ................................................................ 181
clearing instant only ........................................................................................................... 182
clearing instant only ........................................................................................................... 182
different relay trigger-durations and different initial POWs; saturation disabled ............. 184
different relay trigger-durations and different initial POWs; saturation disabled- bird’s eye
view .................................................................................................................................... 184
different relay trigger-durations and different initial POWs; saturation enabled .............. 185
different relay trigger-durations and different initial POWs; saturation enabled- bird’s eye
view .................................................................................................................................... 185
phases with different relay trigger-durations and different initial POWs; saturation enabled
............................................................................................................................................ 186
phases with different relay trigger-durations and different initial POWs; saturation enabled-
bird’s eye view ................................................................................................................... 187
phases with different relay trigger-durations (between 1.5 cycles and 30.5 cycles in 1 cycle
interval); saturation enabled ............................................................................................... 188
phases with fault resistance (between 1.5 cycles and 30.5 cycles in 1 cycle interval);
saturation enabled, initial POW is 52 degrees, relay trigger duration is 15.275 cycles ..... 189
phases with different tap settings; saturation enabled, initial POW is 52 degrees, relay
trigger duration is 15.275 cycles ........................................................................................ 190
phases with different reactive power set points; saturation enabled, initial POW is 52
degrees. relay trigger duration is 15.275 cycles ................................................................. 191
Figure 7.1. Variation of peak flux-linkage magnitude with final point on wave ............... 197
Figure 7.2. Single-line circuit diagram of an MMC-HVDC system .................................. 197
Figure 7.3. Control architecture with DC flux-offset compensation scheme (modified from
[56]) .................................................................................................................................... 199
Figure 7.4. DC flux-offset compensation scheme in the a,b,c domain .............................. 199
Figure 7.5. Simplified circuit diagram of the MMC-HVDC system with its control unit as
implemented in PSCAD/EMTDC (with nonlinear magnetisation inductors).................... 201
Figure 7.6. Voltages at the magnetisation branches (top), flux-linkages (middle) and
magnetisation currents (bottom) when compensation is disabled...................................... 203
magnetisation currents (bottom) when compensation is enabled ...................................... 203
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Figure 7.8. Simulation results of i) compensation start/finish signal, (ii) compensation
command currents (iii) DC components of the converter currents, (iv) DC components of
the voltages at the magnetisation branches and (v) DC components of the flux-linkages
(from top to bottom) .......................................................................................................... 204
Figure 7.9. Circuit diagram of the MMC-HVDC system with its control unit as
implemented in PSCAD/EMTDC (the standard Steinmetz model with nonlinear
magnetisation inductors is used) ........................................................................................ 206
Figure 7.10. Simulation results: voltages at the magnetisation branches (top), flux-linkages
(middle) and magnetisation currents (bottom) when compensation is enabled; here the
magnetisation branches are placed according to the standard Steinmetz transformer model
........................................................................................................................................... 207
model is used ..................................................................................................................... 208
model is used ..................................................................................................................... 208
PSCAD/EMTDC ............................................................................................................... 209
magnetisation currents (bottom) when compensation is disabled; DEM model is used in the
simulation set-up. ............................................................................................................... 210
magnetisation currents (bottom) when compensation is enabled; DEM model is used in the
simulation set-up. ............................................................................................................... 210
Figure 7.16. Simulation results: Compensation command currents, converter-side currents,
voltages in the top most capacitor of upper arms and voltages in the top most capacitor of
lower arms (top to bottom) from the simulation set-up with the DEM model, Figure 9.8 212
Figure 7.17. Compensation command currents (top) and converter currents (bottom) from
the simulation set-up with the AVM model, Figure 7.5 .................................................... 212
Figure 8.1. Flux-linkage sensed feedback control loops a) Current set-point modification b)
Voltage set-point modification .......................................................................................... 215
modification b) Voltage set-point modification ................................................................ 216
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Figure 8.3. Simplified (linear) circuit diagram of the MMC-HVDC system under the
consideration ...................................................................................................................... 218
modifying the current set-point .......................................................................................... 219
Figure 8.5. Step responses of the disturbance sensitivity transfer function, ( )fD s with
different values of pmK ....................................................................................................... 221
Figure 8.6. Step responses of the disturbance sensitivity transfer function, ( )cD s with
different values of pmK ....................................................................................................... 223
Figure 8.7. Frequency responses of the command tracking transfer function, ( )cG s with
different values of pmK ........................................................................................................ 224
Figure 8.8 Flux-linkage sensed feedback control loop with PI controller modifying the
current set-point ................................................................................................................. 224
Figure 8.9. Frequency responses of the command tracking transfer function, ( )cG s with
different values of imK ......................................................................................................... 225
Figure 8.10. Variation of the step response of the disturbance sensitivity transfer function
in (8.17) with imK ............................................................................................................... 226
implemented in PSCAD/EMTDC (with nonlinear magnetisation inductors).................... 228
Figure 8.12. Voltages at the magnetisation branches, flux-linkages, magnetisation and
converter currents (from top to bottom); without the auxiliary feedback control loop ..... 230
Figure 8.13. Voltages at the magnetisation branches, flux-linkages, magnetisation and
converter currents (from top to bottom); with the auxiliary feedback control loop as shown
in Figure 8.4 ....................................................................................................................... 230
Figure 8.14. (D-axis) voltages, flux-linkages, magnetisation currents and converter currents
(from top to bottom); without the auxiliary feedback control loop ................................... 231
Figure 8.15. (D-axis) voltages, flux-linkages, magnetisation currents and converter currents
(from top to bottom); with the auxiliary feedback control loop as shown in Figure 8.4 ... 231
Figure 8.16. Grid voltages (top) and grid-side currents (bottom); without the auxiliary
feedback control loop ......................................................................................................... 232
Figure 8.17. Grid voltages (top) and grid-side currents (bottom); with the auxiliary
feedback control loop as shown in Figure 8.4.................................................................... 232
implemented in PSCAD/EMTDC (with nonlinear magnetisation inductors in the standard
Steinmetz model) ............................................................................................................... 233
Figure 8.19. Voltages (top), flux-linkages (middle) and currents (bottom); with the
auxiliary feedback control loop as shown in Figure 8.4 .................................................... 234
feedforward compensation, reproduced from Figure 7.10 in Chapter 7 ............................ 234
auxiliary feedback control loop as shown in Figure 8.4 .................................................... 236
feedforward compensation, reproduced from Figure 7.12 in Chapter 7 ............................ 236
magnetisation currents (bottom) with the auxiliary feedback control loop as shown in
Figure 8.4 ........................................................................................................................... 238
Figure 8.24. Voltages (top), flux-linkages (middle) and currents (bottom) with the
feedforward compensation in the system shown in Figure 7.5 in Chapter 7 ..................... 238
implemented in PSCAD/EMTDC (with nonlinear magnetisation inductors); fault at the
PCC .................................................................................................................................... 239
Figure 8.26. Breaker currents, voltages at the magnetisation branches (top), flux-linkages
(middle) and magnetisation currents (bottom) with the auxiliary feedback control loop as
shown in Figure 8.4; here a three-phase fault is applied at the PCC and cleared by a circuit-
breaker ............................................................................................................................... 240
(middle) and magnetisation currents (bottom) with the auxiliary feedback control loop as in
Figure 8.4 (magnified from Figure 8.26); here a three-phase fault is applied at the PCC and
cleared by a circuit-breaker ............................................................................................... 241
(middle) and magnetisation currents (bottom) with the auxiliary feedback control loop as in
Figure 8.4 (magnified from Figure 8.13); here a three-phase symmetrical full-voltage sag is
applied at the source and recovered ................................................................................... 241
magnetisation currents (bottom); with the auxiliary feedback control loop in Figure 8.4 and
fault resistance of 2 ........................................................................................................ 243
magnetisation currents (bottom); with the feedforward compensation and fault resistance of
2 (reproduced from Figure F.5 in Appendix F) ............................................................. 243
21
Figure 8.31. Voltages at the magnetisation branches, flux-linkages, magnetisation currents
and converter currents (from top to bottom) without the auxiliary feedback control loop 245
and converter currents (from top to bottom); the auxiliary feedback control loop in Figure
8.4 with 2pmK ................................................................................................................... 245
and converter currents (from top to bottom); the auxiliary feedback control loop in Figure
8.4 with 4pmK ................................................................................................................... 246
Figure 8.34. AVM model based simulation set-up for an MMC-HVDC system as
implemented in PSCAD/EMTDC ...................................................................................... 246
Figure 8.35. Variation of the highest peak magnetisation current magnitude within the
three-phases with different relay trigger-durations and different initial POWs. Here the
auxiliary feedback control loop in Figure 8.4 is disabled and relay trigger duration is varied
between 5 to 6 cycles ......................................................................................................... 247
auxiliary feedback control loop in Figure 8.4 is enabled and relay trigger duration is varied
between 10 to 11 cycles ..................................................................................................... 248
between 10 to 11 cycles ..................................................................................................... 248
PSCAD/EMTDC ................................................................................................................ 249
magnetisation currents (bottom) without the auxiliary feedback control loop .................. 251
Figure 8.41. Voltages (top), flux-linkages (middle) and magnetisation currents (bottom)
with the auxiliary feedback control loop as shown in Figure 8.4 ...................................... 251
Figure 8.42. Compensation command currents, converter-side currents, voltages in the top
most capacitor of upper arms and voltages in the top most capacitor of lower arms (top to
bottom) when the feedback topology in Figure 8.4 is used ............................................... 252
22
Figure 8.45. Detailed Two-Level-Converter based HVDC system model with its control
unit as implemented in PSCAD/EMTDC .......................................................................... 254
and converter currents (from top to bottom) obtained from the two-level converter HVDC
system shown in Figure 8.45; without the auxiliary feedback control loop ...................... 255
and converter currents (from top to bottom) obtained from the two-level converter HVDC
system shown in Figure 8.45; with the auxiliary feedback control loop shown in Figure 8.4
........................................................................................................................................... 255
Figure 9.1. MMC-HVDC system in the islanded control mode ........................................ 260
Figure 9.2. Direct control scheme for MMC operates in the islanded mode [143] ........... 261
Figure 9.3. Cascaded control scheme in the synchronous reference frame (where subscript
k refers phase a,b,c and superscript ' is used when a signal is referred to the converter-side
of the transformer) ............................................................................................................. 262
Figure 9.4. Simulation results when the synchronous reference frame based control scheme
is used; d,q voltage set-points, PCC voltages, active and reactive power (from top to
bottom) ............................................................................................................................... 263
23
Figure 9.5. Cascaded control scheme in the natural reference frame for an islanded MMC
(where subscript k refers phase a,b,c and superscript ' is used when a signal is referred to
the converter-side of the transformer) ................................................................................ 266
Figure 9.6. Circulating current control loop of a phase in the natural reference frame
(where subscript k refers phases a,b,c; diffi refers differential current) .............................. 266
Figure 9.7. Simulation results when the natural reference frame based (PR) control scheme
is used; PCC measured voltage along with the set-voltage (from top, Phase A, B and C),
active and reactive power (bottom) .................................................................................... 267
PSCAD/EMTDC ................................................................................................................ 268
Figure 9.9. Simulation results of breaker currents, set-voltages, PCC voltages, flux-
linkages, magnetisation currents, converter-side currents and load currents (from top to
bottom) when the magnetisation saturation is enabled at the transformer model .............. 270
bottom) when the magnetisation saturation is disabled at the transformer model ............. 271
Figure 9.11. Simulation results of converter currents, arm-currents, DC current and line-
line DC voltage at the converter terminal (from top to bottom) when the magnetisation
saturation is enabled ........................................................................................................... 273
Figure 9.12. Simulation results of converter currents, arm-currents, DC current and line-
line DC voltage at the converter terminal (from top to bottom) when the magnetisation
saturation is disabled .......................................................................................................... 273
Figure 9.13. Passive load connected to a voltage source ................................................... 274
Figure 9.14. Voltages at the source-side of the transformer, instantaneous and DC flux-
linkages of phase A, B and C and magnetisation currents (from top to bottom) ............... 275
linkages of phase A, B and C and magnetisation currents (from top to bottom). Here the
sag is recovered when the condition in equation (9.8) ( , , f k i k ) is met. ...................... 277
sag in each phase is recovered when the condition in equation (9.8) ( , , f k i k ) is met.
............................................................................................................................................ 278
24
sag in each phase is recovered when the condition in equation (9.9) (
1 , ,cos 2 (1 )DC
f k k sag h V ) is met. .......................................................................... 279
Figure 9.18. Strategies to suppress inrush currents at fault-recovery ................................ 280
bottom) without any inrush current mitigation strategies .................................................. 283
bottom) with the IPOW strategy. Here PCC voltages are kept for 0.06 s forcefully after the
fault clearance. ................................................................................................................... 284
bottom) with the IPOW strategy. Here PCC voltages are kept for 0.005 s forcefully after
the fault clearance .............................................................................................................. 285
Figure 9.22. Simulation results of arm-currents, DC current and line-line DC voltage at the
converter terminal (from top to bottom) without any inrush current mitigation strategies286
converter terminal (from top to bottom) with the IPOW strategy ..................................... 286
Figure 9.24. Simulation results of PCC voltages, flux-linkages and magnetisation currents
(from top to bottom) when -10% error is added to the actual initial POW measurement . 288
(from top to bottom) when the relay trigger duration is set to 15.5 cycles and Strategy-
initial is used ...................................................................................................................... 288
bottom) with the FVFL strategy when a three-phase to ground fault was applied ............ 290
converter terminal (from top to bottom) with the FVFL strategy ..................................... 291
bottom) with the FVFL strategy when a single-phase (A) to ground fault was applied ... 292
bottom) with the FVFL strategy when a double-line (A and B) to ground fault was applied
........................................................................................................................................... 293
25
(from top to bottom) when the relay trigger duration is set to 15.5 cycles and the FVFL
strategy is used ................................................................................................................... 294
(from top to bottom) when the magnetisation branches are placed at the converter-side of
the transformer and flux-linkages are calculated using the voltages at the PCC; Strategy-
final is used ........................................................................................................................ 295
27
List of Tables
Table 1.1. Grid code requirements for (HV)DC converter under fault/voltage sag recovery
.............................................................................................................................................. 52
Table 2.2. Parameterisation of primary and secondary winding-leg non-linear inductances '' ''
a bL L ................................................................................................................................. 71
Table 2.4. Open-circuit test results ...................................................................................... 74
Table 2.5. Parameterisation of magnetisation inductor of Steinmetz transformer model .... 80
Table 2.6. Open-circuit test results ...................................................................................... 80
Table 3.1. Transformer T2 (345 MVA) test report [18] ...................................................... 86
Table 3.2. Transformer T3 (415 MVA) test report [18] ...................................................... 86
Table 3.3. Peak voltage vs peak resistive-current values ..................................................... 87
Table 3.4. Peak flux-linkage vs peak inductive-current values ........................................... 87
Table 3.5. Comparison of open circuit test results and simulation results ........................... 88
Table 3.6. Peak flux-linkage vs peak inductive-current values in pu .................................. 90
Table 3.7. A comparison of open circuit test results and simulation results ........................ 91
Table 3.8. Parameterisation of the classical transformer model for transformer, T2 ........... 91
Table 3.9. Parameterisation of the classical transformer model for transformer, T3 ........... 92
Table 3.10. Fault level information for Langage substation in winter 2011/12 [101] ......... 93
Table 3.11. A comparison of simulation results against short circuit data .......................... 96
Table 3.12. DC currents corresponding to residual fluxes ................................................... 97
Table 5.1. Dominant poles of Case GST and Case CST .................................................... 145
Table 5.2. Impedance at 50 Hz........................................................................................... 149
Table 6.1. Active and reactive power set-points: Case scenarios ...................................... 192
Table 8.1. Different options for constructing the auxiliary flux offset feedback control loop
............................................................................................................................................ 217
Table 8.2. Comparison of different options for constructing the auxiliary feedback control
loop ..................................................................................................................................... 227
29
Abbreviations
C-EPRI China Electric Power Research Institute
COP21 21st Conference of the Parties
CST Converter Side of the Transformer
DC Direct Current
GHG Green House Gas
HVDC High Voltage Direct Current
IGBT Insulated-Gate Bipolar Transistor
MMC Modular Multilevel Converter
NPC Neutral Point Clamped
POW Point On Wave
including DC
UNFCC United Nations Framework Convention on Climate Change
UPS Uninterruptible Power Supply
VSC Voltage Source Converter
31
Abstract Transformer fault-recovery inrush currents in MMC-HVDC systems and mitigation strategies, Doctor of Philosophy, The University of Manchester, March 2016 The UK Government has set an ambitious target to achieve 15% of final energy consumption from renewable sources by 2020. High Voltage Direct Current (HVDC) technology is an attractive solution for integrating offshore wind power farms farther from the coast. In the near future, more windfarms are likely to be connected to the UK grid using HVDC links. With the onset of this fairly new technology, new challenges are inevitable. This research is undertaken to help assist with these challenges by looking at possibilities of problems with respect to faster AC/DC interaction modes, especially, on the impact of inrush currents which occur during fault-recovery transients. In addition to that, possible mitigation strategies are also investigated.
Initially, the relative merits of different transformer models are analysed with respect to inrush current transient studies. The most appropriate transformer model is selected and further validated using field measurement data. A detailed electro-magnetic-transient (EMT) model of a grid-connected MMC-HVDC system is prepared in PSCAD/EMTDC to capture the key dynamics of fault-recovery transformer inrush currents. It is shown that the transformer in an MMC system can evoke inrush currents during fault recovery, and cause transient interactions with the converter and the rest of the system, which should not be neglected. It is shown for the first time through a detailed dynamic analysis that if the current sensors of the inner-current control loops are placed at the converter-side of the transformer instead of the grid-side, the inrush currents will mainly flow from the grid and decay faster. This is suggested as a basic remedial action to protect the converter from inrush currents.
Afterwards, analytical calculations of peak flux-linkage magnitude in each phase, following a voltage-sag recovery transient, are derived and verified. The effects of zero- sequence currents and fault resistance on the peak flux linkage magnitude are systematically explained. A zero-sequence-current suppression controller is also proposed. A detailed study is carried out to assess the key factors that affect the maximum peak flux- linkage and magnetisation-current magnitudes, especially with regard to fault specific factors such as fault inception angle, duration and fault-current attenuation.
Subsequently, the relative merits of a prior-art inrush current mitigation strategy and its implementation challenges in a grid-connected MMC converter are analysed. It is shown that the feedforward based auxiliary flux-offset compensation scheme, as incorporated in the particular strategy, need to be modified with a feedback control technique, to alleviate the major drawbacks identified. Following that, eight different feedback based control schemes are devised, and a detailed dynamic and transient analysis is carried out to find the best control scheme. The relative merits of the identified control scheme and its implementation challenges in a MMC converter are also analysed.
Finally, a detailed EMT model of an islanded MMC-HVDC system is implemented in PSCAD/EMTDC and the impacts of fault-recovery inrush currents are analysed. For that, initially, a MMC control scheme is devised in the synchronous reference frame and its controllers are systematically tuned. To obtain an improved performance, an equivalent control scheme is derived in the stationary reference frame with Proportional-Resonant controllers, and incorporated in the EMT model. Following that, two novel inrush current mitigation strategies are proposed, with the support of analytical equations, and verified.
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33
Declaration
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
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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
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which may be described in this thesis, may not be owned by the author and may be
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http://www.manchester.ac.uk/library/aboutus/regulations) and in The University’s
policy on Presentation of Theses
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35
Acknowledgements
Creating a PhD thesis is a challenging effort but it is not merely an individual experience; there are many people who have walked along with me. First of all, I would like to thank Dr. A. Atputharajah and Mr. M. Anparasan from University of Peradeniya, Sri Lanka who have inspired and mentored me to undertake this PhD journey.
I would like to express my sincere gratitude to my PhD supervisor Prof. Mike Barnes for the opportunity he has provided to undertake a PhD Degree at The University of Manchester. This PhD would not have been possible without his unparalleled support, expert guidance and encouragement. I am thankful for his trust, understanding and patience throughout my PhD research for past four years. In addition, I would like to thank Dr. Roger Shuttleworth for his indispensable advice, information and support on different aspects of my PhD research as a co-supervisor.
It would not have been possible for me to undertake my PhD degree without a research scope and financial support to cover all my tuition fees and living expenses. Therefore, I would like to sincerely acknowledge National Grid Electricity Transmission plc, UK for providing me a full scholarship and Dr. Paul Coventry, HVDC technical leader at National Grid for his technical support in this project of “AC/DC VSC HVDC Interaction- Detailed Model (TAO/22119)”. Also I would like to acknowledge Prof. Zhongdong Wang and Dr. Jinsheng Peng for providing an inrush current measurement data and Dr. Antony Beddard for providing technical support on modelling MMC-HVDC system.
I would also like to thank my colleagues in the Power Conversion Group. This includes co- members of ‘BAFT’ meeting group- Bin Chang and Oliver Cwikowski, the other fellow students and research associates of my supervisor, especially Jesus Carmona-Sanchez and Wenyuan Wang, and my fellow Sri Lankan companion Ruchira Yapa for their suggestions and interesting discussions on my research which resulted into fruitful ideas.
I would also like to express my gratitude to my external examiner Dr. Donald (Ewen) Macpherson from The University of Edinburgh and my internal examiner Dr. Ognjen Marjanovic. Your in-depth understanding and passion on my PhD thesis have made my PhD defence an enjoyable session. Thank you for your brilliant comments and suggestions.
My life at Manchester would not have been enjoyable and interesting without various other friends. Big thanks goes to all my Sri Lankan friends in Manchester – you were very supportive and welcoming, Rusholme friends and flatmates at student halls – you made me laugh together even at harder times, and all my friends and members of Manchester University Shotokan Karate Club and Shotokan Karate Academy – for keeping me physically and mentally active through training, grading, competitions and socials – Oss for Sensei Garry Harford.
Finally, but most importantly, I would like to express my heartiest gratitude to my father for his unconditional love and support, my mother for her silent support and love, and my loving sister and her family for their deepest understanding and for sharing my duties; all of which have made me to travel freely in my PhD world.
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37
Dedication
Mrs. Rathivathani Jeganathan
As teachers of science who raised me with the love of science
and technology.
39
1.1 Background
At the Conference of the Parties (COP21) held in Paris in 2015, the United Nations
Framework Convention on Climate Change (UNFCC) emphasized to its member nations
the need for “pursuing efforts to limit the (global average) temperature increase to 1.5 °C
above preindustrial levels” and also invited nations “to deposit their respective instruments
of ratification, acceptance, approval or accession, where appropriate, as soon as
possible”[1]. To combat this long-lasting challenge against climate change, there is an
alarming need to reduce Green House Gas (GHG) emissions [2]. This in turn requires less
exploitation of fossil fuels and an increase of renewable energy share in the energy-mix.
The UK Government has set an ambitious target to achieve 15% of final energy
consumption from renewable sources by 2020 [3]. This requires 34.5 % of electricity
generation from renewable sources [3] and wind power generation plays a vital role in
meeting these energy targets. According to the ‘Gone Green’ scenario of National Grid
(UK), 26.5 GW of electrical power should be generated from onshore and offshore wind
resources by 2020 [3]. When compared to onshore wind power generation, up to 70 %
more energy yield can be achieved from offshore wind parks due to the frequency of very
strong winds [4]. Moreover, onshore wind power projects often need to overcome protests
against public with the mind-set of ‘Not-In-My-Back-Yard’. These factors drive wind
power developers towards offshore solutions.
Offshore wind power plants are connected through submerged cables beneath the sea-bed.
The main drawback of using AC transmission through cables is the requirement of surplus
reactive power to charge and discharge the cable capacitance. As a result, AC transmission
links using cables have a maximum practical length of about 50 to 100 km [4]. Thus, the
High Voltage Direct Current (HVDC) technology is an attractive solution for integrating
offshore wind power farms farther from the coast. For example, the majority of Round 3
windfarms are more likely to be connected to the UK grid using HVDC links due to their
location [5, 6]. With the onset of this fairly new technology, new challenges are inevitable.
This research is undertaken to help assist with these challenges by looking at possibilities
and problems with respect to faster AC/DC interaction modes.
40
1.2 VSCHVDC technology
Until 1997, HVDC links were developed only by using classical line-commutated
converters (LCCs) which are mainly based on thyristors. Nowadays, this classical HVDC
technology is mainly used for bulk power transmission. Typically these links have power
ratings between 100 and 8000 MW; usually they are used to transmit power for distances
over 600 km with overhead lines or for distances of 50 to 100 km with subsea cables [4].
This classical HVDC technology is mature now and had its commercial inception in 1954.
Considering its maturity and applications, hereafter, this thesis will not substantially
discuss this technology further.
In 1997, ABB introduced Voltage-Source-Converter (VSC) based HVDC technology to
the market. VSCs are realised using Insulated Gate Bipolar Transistors (IGBTs) which
have both turn-on and turn-off capability. VSC-HVDC technology offers more benefits
when compared to the classical HVDC technology such as superior independent control of
active and reactive power, secure power control and quick power restoration during a
blackout, capability to support weak AC grids, ability to use extruded cables and reduced
foot print [4]. VSC-HVDC technology has found various applications such as for grid
interconnection, offshore windfarm integration, strengthening power networks and to
power offshore oil/gas platforms [4].
VSC-HVDC converter topologies have varied somewhat between major HVDC
manufacturers. The first generations of VSCs were realised using two or three-

transformer fault-recovery inrush currents in mmc-hvdc systems and mitigation strategies

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