WIDE AREA MONITORING, PROTECTION
AND CONTROL IN THE FUTURE GREAT
BRITAIN POWER SYSTEM
A thesis submitted to the
University of Manchester
For the degree of
Doctor of Philosophy
In the Faculty of Engineering and Physical Sciences
2012
By
Deyu Cai
School of Electrical and Electronic Engineering
Preface
List of Contents
List of Contents ............................................................................................................... 1
List of Figures .................................................................................................................. 4
List of Tables ................................................................................................................. 10
Abstract .......................................................................................................................... 13
List of Abbreviations .................................................................................................... 14
Declaration ..................................................................................................................... 15
Copyright Statement ..................................................................................................... 16
Acknowledgements........................................................................................................ 18
Chapter 1 Introduction ................................................................................................. 19
1.1 Research Background ........................................................................................... 19
1.1.1 Power system blackouts ................................................................................. 19
1.1.2 Wide area monitoring, protection and control ............................................... 22
1.2 Objectives of the Research .................................................................................... 24
1.3 Thesis Structure..................................................................................................... 26
1.4 Main Contributions of This Research ................................................................... 28
Chapter 2 Synchronized Measurement Technology .................................................. 29
2.1 Introduction ........................................................................................................... 29
2.2 Phasor Measurement Unit ..................................................................................... 31
2.3 Data Concentrator ................................................................................................. 34
2.4 Synchrophasor Standard ....................................................................................... 35
2.5 Summary ............................................................................................................... 35
Chapter 3 Applications and Benefits of Synchronized Measurement Technology . 36
3.1 Introduction ........................................................................................................... 36
3.2 Off-line Applications of SMT ............................................................................... 36
3.2.1 Post-disturbance analysis ............................................................................... 36
3.2.2 Benchmarking, validation and fine-tuning of system models........................ 38
3.3 On-line Applications of SMT ............................................................................... 39
3.3.1 Wide area phase angular and power flow monitoring ................................... 39
3.3.2 Wide area frequency monitoring.................................................................... 41
2.3.3 Wide area voltage monitoring ........................................................................ 42
3.3.4 Inter-area oscillation monitoring .................................................................... 44
3.3.5 Power system restoration ............................................................................... 45
3.3.6 Improved state estimation .............................................................................. 47
3.3.7 Dynamic rating of overhead transmission lines ............................................. 48
2.3.8Intelligent controlled islanding ....................................................................... 49
2.3.9 Adaptive under-frequency load shedding ...................................................... 50
3.4 Conclusions ........................................................................................................... 51
Chapter 4 Architecture of a WAMPAC System ........................................................ 52
4.1 Introduction ........................................................................................................... 52
4.2 Architecture of a WAMPAC System .................................................................... 52
4.3 Communication Networks of WAMPAC System ................................................ 55
4.3.1 Available communication media for WAMPAC ........................................... 55
4.3.2 Communication protocols and format for phasor data transmission ............. 57
4.3.3 Communication latency ................................................................................. 59
4.4 Architecture of future GB WAMPAC system ...................................................... 59
4.5 Conclusions ........................................................................................................... 61
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Preface
Chapter 5 The Roadmap to the Future GB WAMPAC System ............................... 62
5.1 Introduction ........................................................................................................... 62
5.2 The Roadmap to a WAMPAC System ................................................................. 63
5.3 The Future GB Power System .............................................................................. 65
5.4 GB’s strategy for WAMPAC ................................................................................ 68
5.4.1 Short term strategy ......................................................................................... 68
5.4.2 Long term strategy ......................................................................................... 71
5.5 Conclusions ........................................................................................................... 81
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power
Systems ........................................................................................................................... 82
6.1 Introduction ........................................................................................................... 82
6.2 Nonlinear Simulations........................................................................................... 82
6.2.1 Local oscillatory mode in Area 1 ................................................................... 83
6.2.2 Local oscillatory mode in Area 2 ................................................................... 84
6.2.3 Inter-area oscillatory mode ............................................................................ 85
6.2.4 Large disturbance ........................................................................................... 87
6.3 Modal Analysis ..................................................................................................... 88
6.3.1 Dynamic system representation ..................................................................... 89
6.3.2 System linearization for modal analysis ........................................................ 90
6.3.3 Eigenvalues and eigenvectors ........................................................................ 92
6.3.4 Eigenvalues and small signal stability ........................................................... 93
6.3.5 Participation factors ....................................................................................... 94
6.3.6 Modal analysis for inter-area oscillation study .............................................. 95
6.4 The origin of lightly damped/unstable inter-area oscillations ............................ 100
6.5 Conclusions ......................................................................................................... 102
Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm ..... 104
7. 1 Introduction ........................................................................................................ 104
7.2 Signal Model Representation .............................................................................. 105
7.3 Newton Type Algorithm Derivation ................................................................... 108
7.4 Computer Simulated Tests .................................................................................. 110
7.4.1 Static tests .................................................................................................... 111
7.4.2 Noise tests .................................................................................................... 113
7.4.3 Dynamic tests ............................................................................................... 116
7.5 Dynamic Simulation of a Multi-machine System ............................................... 118
7.6 Real-life Conditions Tests................................................................................... 122
7.7 Conclusions ......................................................................................................... 124
Chapter 8 The Application of Power Electronic Devices for Damping Inter-area
oscillations .................................................................................................................... 126
8.1 Introduction ......................................................................................................... 126
8.2 Modal Analysis for Control ................................................................................ 127
8.2.1 Transfer functions ........................................................................................ 127
8.2.2 Residue based damping controller design .................................................... 128
8.3 Inter-area Oscillation Damping Control with HVDC ......................................... 131
8.3.1 HVDC transmission system modelling ........................................................ 132
8.3.2 System performance without HVDC damping controller............................ 139
8.3.3 Residue based HVDC damping controller design ....................................... 140
8.3.4 System performance with a HVDC damping controller .............................. 143
8.4 Inter-area Oscillation Control with TCSC .......................................................... 146
8.4.1 TCSC modelling .......................................................................................... 146
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8.4.2 System performance without TCSC damping controller ............................. 148
8.4.3 Residue based TCSC damping controller design ......................................... 149
8.4.4 System performance with TCSC damping controller .................................. 151
8.5 Inter-area Oscillation Control with SVC............................................................. 154
8.5.1 SVC modelling ............................................................................................. 154
8.5.2 System performance without SVC damping controller ............................... 155
8.5.3 Residue based SVC damping controller design ........................................... 157
8.5.4 System performance with SVC damping controller .................................... 158
8.6 Conclusions ......................................................................................................... 162
Chapter 9 Wide Area Monitoring and Control System (WAMCS) in a Future GB
Power System............................................................................................................... 163
9.1 Introduction ......................................................................................................... 163
9.2 Assessment of the Inter-area Oscillations in GB Power System ........................ 163
9.2.1 GB power system modelling ........................................................................ 163
9.2.2 Inter-area oscillations study in GB power system........................................ 165
9.3 Wide Area Monitoring and Control System (WAMCS) in a Future GB Power
System ....................................................................................................................... 170
9.3.1 Architecture of WAMCS in GB power system ........................................... 170
9.3.2 Inter-area oscillation monitoring using NTA ............................................... 172
9.3.3 Wide area inter-area oscillation damping control with HVDC in GB ......... 174
9.3.4 The impact of time delays on wide-area control .......................................... 177
9.3.5 Interaction between PSSs and HVDC damping control system .................. 180
9.4 Conclusions ......................................................................................................... 182
Chapter 10 Conclusions and Future Work............................................................... 184
10.1 Conclusions ....................................................................................................... 184
10.2 Future Work ...................................................................................................... 187
References .................................................................................................................... 190
Appendices ................................................................................................................... 196
10.1 Appendix A ....................................................................................................... 196
10.2 Appendix B ....................................................................................................... 199
10.3 Appendix C ....................................................................................................... 205
10.4 Appendix D ....................................................................................................... 210
10.5 Appendix E ....................................................................................................... 213
10.6 Appendix F ........................................................................................................ 217
10.7 Appendix G ....................................................................................................... 221
10.7.1 Published journal papers ............................................................................ 221
10.7.2 Submitted journal papers ........................................................................... 221
10.7.3 Published conference papers ...................................................................... 221
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Preface
List of Figures
Figure 1.1: Statistics of blackouts: customers affected ................................................... 19
Figure 1.2: Line of separation from the European grid................................................... 20
Figure 1.3: A Generalized WAMPAC system ................................................................ 23
Figure 2.1: Phasor representation of a sinusoidal signal ................................................. 30
Figure 2.2: Synchronized phasor measurement in remote substations ........................... 30
Figure 2.3: A functional block diagram of a typical PMU ............................................. 31
Figure 2.4: State estimation v.s. PMU measurements .................................................... 32
Figure 2.5: Two standalone PMUs ................................................................................. 32
Figure 2.6: Two integrated PMUs................................................................................... 33
Figure 2.7: Data concentrator in a WAMPAC system.................................................... 34
Figure 2.8: SEL Data Concentrator................................................................................. 34
Figure 3.1: The reconstruction of system frequencies after a large disturbance in WECC,
14th June, 2004 ............................................................................................................... 37
Figure 3.2: Comparison of the recorded system response to the 10th August, 1996
disturbance in USA with the simulation results .............................................................. 38
Figure 3.3: RTDMS – a wide area visualization platform for the North American power
system.............................................................................................................................. 40
Figure 3.4: Disturbance localization using PMUs and the triangulation method ........... 42
Figure 3.5: Estimation of the Thevenin equivalent with local measurements ................ 43
Figure 3.6: T and Thevenin representation of transmission corridor .............................. 44
Figure 3.7: Oscillations observed by two PMUs in the European grid........................... 45
Figure 3.8: PMU measurements from three areas during reclosing attempts: UCTE, 4
November 2006 ............................................................................................................... 46
Figure 3.9: PMUs installed at both ends of a transmission line ...................................... 48
Figure 3.10: Visualization of the real time mentoring of the thermal condition of an
overhead transmission corridor in APG .......................................................................... 49
Figure 4.1: The general architecture of a typical WAMPAC system ............................. 53
Figure 4.2: The combination of different communication media for a WAMPAC system
......................................................................................................................................... 57
Figure 4.3: Generic schematic of the dataflow in WAMPAC system ............................ 58
Figure 4.4: A simple demonstration of communication latency in WAMPAC system .. 59
Figure 4.5: A general architecture of future GB WAMPAC system .............................. 60
Figure 5.1: WAMPAC application tree with full “smart fruits” ..................................... 63
Figure 5.2: Roadmap for deploying PMU applications .................................................. 64
Figure 5.3: UK energy target 2020 and 2030.................................................................. 66
Figure 5.4: Power transfers across the boundary between Scotland and England at peak
load condition.................................................................................................................. 66
Figure 5.5: New TCSC and HVDC in GB transmission networks ................................. 67
Figure 5.6: Locations of off-shore wind farms in GB power system (2020-2030) ........ 67
Figure 5.7: ‘Logical filter one’ – The number of PMUs required .................................. 69
Figure 5.8: ‘Logical filter two’ – Commercial availability of PMU applications .......... 69
Figure 5.9: ‘Logical filter three’ – Necessity of PMU application for investors ............ 69
Figure 5.10: Global power angle and frequency monitoring system .............................. 70
Figure 5.11: Real time monitoring system over inter-tie corridors................................. 71
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Preface
Figure 5.12: PMU placements in SHPTN ....................................................................... 72
Figure 5.13: PMU placements at the boundary between Scotland and England ............ 73
Figure 5.14: PMU placements in central England .......................................................... 74
Figure 5.15: PMU placements in the South of England ................................................. 74
Figure 5.16: A PMU installed in the Torness substation ................................................ 75
Figure 5.17: Three PMUs installed in the Crekey Beck, Keadby and Grimsby West
substations ....................................................................................................................... 75
Figure 5.18: One PMU installed in the Sizewell substation ........................................... 76
Figure 5.19: Two PMUs installed in the North Wales substations of Wylfa and Stanah76
Figure 5.20: A PMU installed in the Alverdiscott substation ......................................... 76
Figure 5.21: PMU placements for the future GB wide area monitoring system............. 77
Figure 5.22: A SMT-based adaptive UFLS scheme in the future GB power system ..... 78
Figure 5.23: Inter-area oscillation damping control with power electronic devices in GB
power system................................................................................................................... 79
Figure 5.24: Closed loop inter-area oscillation control using HVDC............................. 80
Figure 5.25: Closed loop inter-area oscillation control using TCSC .............................. 81
Figure 6.1: A typical two-area system ............................................................................ 83
Figure 6.2: Generator rotor speed responses to the disturbances occurred in area 1 ...... 84
Figure 6.3: Generator rotor speed responses to the disturbances occurred in area 2 ...... 85
Figure 6.4: Generator rotor speed oscillations dominated by inter-area mode ............... 85
Figure 6.5: System frequency responses in inter-area mode........................................... 86
Figure 6.6: Oscillatory active power flow on transmission line 3 .................................. 87
Figure 6.7: Oscillatory active power flow on transmission line 1 .................................. 87
Figure 6.8: Responses of the Generator rotor speeds to the large disturbance ............... 88
Figure 6.9: Active power transfer over the tie line after the disturbance ........................ 88
Figure 6.10: Oscillatory modes in the two-area system .................................................. 97
Figure 6.11: Right eigenvector (mode shape) of inter-area mode .................................. 99
Figure 6.12: The effect of inter-area power flow on system oscillatory mode ............. 101
Figure 7.1: A global block diagram of the test procedure............................................. 111
Figure 7.2: Computer generated test signal .................................................................. 112
Figure 7.3: Estimation results of the magnitude of DC component, A0 ....................... 112
Figure 7.4: Estimation results of the magnitude of oscillatory component A1 ............. 112
Figure 7.5: Estimation results of the damping factor of oscillatory component, σ ..... 112
Figure 7.6: Estimation results of the frequency of oscillatory component, f. ............... 113
Figure 7.7: Estimation results of the phase angle of oscillatory component, φ ........... 113
Figure 7.8: Computer generated test signal and estimated signal ................................. 113
Figure 7.9: Algorithm tracking capabilities in presence of noise ................................. 115
Figure 7.10: Computer generated signal with step change of σ .................................. 116
Figure 7.11: Estimation results of the magnitude of DC component, A0, for different
Tdw ................................................................................................................................. 116
Figure 7.12: Estimation results of the magnitude of oscillatory component, A1, for
different Tdw .................................................................................................................. 117
Figure 7.13: Estimation results of damping factor, σ , for different Tdw ....................... 117
Figure 7.14: Estimation results of the frequency of oscillatory component, f, for
different Tdw .................................................................................................................. 117
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Figure 7.15: Estimation results of the phase angle of oscillatory component, φ , for
different Tdw .................................................................................................................. 117
Figure 7.16: Dynamic testing: comparison between the actual and estimated signal... 118
Figure 7.17: A block diagram of the testing procedure based on dynamic simulation of a
multi-machine test system ............................................................................................. 118
Figure 7.18: Two-area test system with HVDC link .................................................... 119
Figure 7.19: Generator rotor speed changes after the disturbance ................................ 119
Figure 7.20: Inter-area oscillatory mode shape estimated by NTA .............................. 120
Figure 7.21: Oscillatory active power (on line 2) after the disturbance ....................... 121
Figure 7.22: Estimated frequency of the inter-area oscillatory mode by NTA and Prony
method ........................................................................................................................... 121
Figure 7.23: Estimated damping factor of the inter-area oscillatory mode by NTA and
Prony method ................................................................................................................ 121
Figure 7.24: Estimated frequency of the inter-area oscillatory mode by reduced-order
Prony method and NTA ................................................................................................ 122
Figure 7.25: Estimated damping factor of the inter-area oscillatory mode by reducedorder Prony method and NTA ....................................................................................... 122
Figure 7.26: Estimated oscillatory active power from estimated parameters ............... 122
Figure 7.27: Oscillatory voltage phase angle difference between Glasgow and London
....................................................................................................................................... 123
Figure 7.28: Estimated frequency of inter-area oscillatory mode in the GB network .. 123
Figure 7.29: Estimated damping ratio of inter-area oscillatory mode in the GB network
....................................................................................................................................... 124
Figure 7.30: Oscillatory signal based on estimated oscillatory parameters .................. 124
Figure 8.1: Closed loop system with feedback control ................................................. 129
Figure 8.2: The structure of a feedback damping control ............................................. 129
Figure 8.3: The shift of an eigenvalue caused a feedback damping control ................. 130
Figure 8.4: A two-area system with HVDC .................................................................. 131
Figure 8.5: Two types of power converters .................................................................. 132
Figure 8.6: Rectifier equivalent circuit ......................................................................... 133
Figure 8.7: Inverter equivalent circuit........................................................................... 134
Figure 8.8: Monopolar HVDC link ............................................................................... 135
Figure 8.9: Bipolar HVDC link..................................................................................... 135
Figure 8.10: Homopolar HVDC link ............................................................................ 136
Figure 8.11: Equivalent circuit of HVDC link .............................................................. 136
Figure 8.12: Voltage profile of the equivalent circuit of HVDC link ........................... 136
Figure 8.13: Basic control scheme of HVDC system ................................................... 138
Figure 8.14: Inverter’s β control for constant voltage .................................................. 138
Figure 8.15: Rectifier’s α control for constant current ................................................. 138
Figure 8.16: Oscillatory modes in the two-area system with HVDC ........................... 139
Figure 8.17: Generator rotor speed responses to the small disturbances without HVDC
damping control ............................................................................................................ 140
Figure 8.18: System frequency responses to the small disturbances without HVDC
damping control ............................................................................................................ 140
Figure 8.19: Rectifier control with supplementary damping control ............................ 141
Figure 8.20: Feedback control with multiple input signals ........................................... 141
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Figure 8.21: An illustration of the estimation of the phase angle of the residue .......... 142
Figure 8.22: An estimation of the residue’s phase angle for HVDC damping control
design ............................................................................................................................ 143
Figure 8.23: Oscillatory modes versus the gain of HVDC damping controller ............ 144
Figure 8.24: Generator rotor speed responses to the small disturbances with and without
HVDC damping control ................................................................................................ 144
Figure 8.25: Active power flow (line 3) responses to the small disturbances with and
without HVDC damping control ................................................................................... 145
Figure 8.26: Generator rotor speed responses to a three-phase fault with and without
HVDC damping control ................................................................................................ 145
Figure 8.27: Active power flow (line 3) responses to a three-phase fault with and
without HVDC damping control ................................................................................... 146
Figure 8.28: Typical two-area system with TCSC ........................................................ 146
Figure 8.29: A structure of a typical TCSC .................................................................. 147
Figure 8.30: An ideal model of TCSC for power system stability study ...................... 147
Figure 8.31: An equivalent circuit of the transmission corridor with TCSC ................ 147
Figure 8.32: A block diagram of TCSC control............................................................ 148
Figure 8.33: Oscillatory modes in the two-area system with TCSC ............................. 148
Figure 8.34: Generator rotor speed responses to the small disturbances without TCSC
damping control ............................................................................................................ 149
Figure 8.35: System frequency responses to the small disturbances without TCSC
damping control ............................................................................................................ 149
Figure 8.36: A block diagram TCSC supplementary damping control ........................ 150
Figure 8.37: An estimation of the residue’s phase angle for TCSC damping control
design ............................................................................................................................ 150
Figure 8.38: Oscillatory modes versus the gain of TCSC damping controller ............. 151
Figure 8.39: Generator rotor speed responses to the small disturbances with and without
TCSC damping control ................................................................................................. 152
Figure 8.40: Active power flow (line 3) responses to small disturbance with and without
TCSC damping control ................................................................................................. 152
Figure 8.41: Generator rotor speed responses to a three-phase fault with and without
TCSC damping control ................................................................................................. 153
Figure 8.42: Active power flow (line 3) responses to a three-phase fault with and
without TCSC control ................................................................................................... 153
Figure 8.43: Modified two-area system with SVC ....................................................... 154
Figure 8.44: A structure of a typical SVC .................................................................... 154
Figure 8.45: An ideal model of SVC ............................................................................ 155
Figure 8.46: Block diagram of SVC control ................................................................. 155
Figure 8.47: Oscillatory modes in the two-area system with SVC ............................... 156
Figure 8.48: Generator rotor speed responses to the small disturbances without SVC
damping control ............................................................................................................ 156
Figure 8.49: Oscillatory voltage angle difference between bus3 and bus5 caused by the
disturbances ................................................................................................................... 157
Figure 8.50: A block diagram of a SVC damping controller ........................................ 157
Figure 8.51: An estimation of the residue’s phase angle for SVC damping control design
....................................................................................................................................... 158
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Preface
Figure 8.52: Oscillatory modes versus the gain of SVC damping controller ............... 159
Figure 8.53: Generator rotor speed responses to the small disturbances with and without
SVC damping control.................................................................................................... 160
Figure 8.54: Active power flow (line 3) responses to small disturbance with and without
SVC damping control.................................................................................................... 160
Figure 8.55: Generator rotor speed responses to a three-phase fault with and without
SVC damping control.................................................................................................... 161
Figure 8.56: Active power flow (line 3) responses to a three-phase fault with and
without SVC damping control ...................................................................................... 161
Figure 9.1: 500 kV HVDC links and 400 kV Series Compensators that are installed in
the GB power system (vision 2015).............................................................................. 164
Figure 9.2: Inter-area oscillation monitoring SPTN and NGETN ................................ 165
Figure 9.3: Three large generators selected in Scotland for monitoring inter-area
oscillations .................................................................................................................... 166
Figure 9.4: Three large generators selected in central England for monitoring inter-area
oscillations .................................................................................................................... 166
Figure 9.5: Two large generators selected in the South of England for monitoring interarea oscillations ............................................................................................................. 167
Figure 9.6: The oscillatory inter-area power flow on the Harker-Hutton line after a large
disturbance .................................................................................................................... 167
Figure 9.7: The system frequency variations caused by a large disturbance ................ 168
Figure 9.8: The oscillatory inter-area power flow caused by a large disturbance in the
original and PSSs-reduced GB system.......................................................................... 168
Figure 9.9: System frequency variations caused by the large disturbance in the PSSsreduced system .............................................................................................................. 169
Figure 9.10: System frequency variations measured in substations HUER and DEES in
the PSSs-reduced system .............................................................................................. 169
Figure 9.11: Architecture of the wide-area inter-area oscillation monitoring and control
system in GB ................................................................................................................. 172
Figure 9.12: Inter-area oscillation mode identified by NTA in GB system .................. 173
Figure 9.13: Estimated inter-area oscillation mode shape of GB system ..................... 173
Figure 9.14: Schematic diagram of HVDC damping system........................................ 174
Figure 9.15: Responses of the generator rotor speeds (PEHE, LOAN, HUER and EGGB)
to the large disturbance with and without the wide area HVDC damping control ....... 175
Figure 9.16: Responses of the generator rotor speeds (WBUR, RUGE, SIZE and DUNG)
to the large disturbance with and without the wide area HVDC damping control ....... 176
Figure 9.17: The response of the inter-area power flow on the Harker-Hutton line to the
large disturbance, with and without HVDC damping control ...................................... 176
Figure 9.18: Inter-area oscillation mode identified by NTA in the GB system, with and
without HVDC damping control ................................................................................... 177
Figure 9.19: An illustration of the time delay involved in the data transmission in GB
WAMCS........................................................................................................................ 178
Figure 9.20: A block diagram of HVDC damping controllers (with time delay) ......... 178
Figure 9.21: The effect of time delay in the wide area damping controllers
(50 milliseconds to 200 milliseconds) .......................................................................... 179
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Figure 9.22: The effect of time delay in the wide area damping controllers
(300 milliseconds to 700 milliseconds)......................................................................... 179
Figure 9.23: Responses of the generator rotor speeds (PEHE, LOAN, HUER and EGGB)
to the large disturbance (all PSSs in service) ................................................................ 180
Figure 9.24: Responses of the generator rotor speeds (WBUR, RUGE, SIZE and DUNG)
to the large disturbance (all PSSs in service) ................................................................ 181
Figure 9.25: The influence of HVDC damping control on the inter-area power flow in
complete GB system ..................................................................................................... 182
Figure A-1: A single line diagram of two-area system ................................................. 196
Figure A-2: Block diagram of static exciter of G1, G2 and G3 and G4 ....................... 197
Figure A-3: Block diagram of speed governor of G1, G2, G3 and G4 ......................... 197
Figure B-1: A single line diagram of the two-area system with HVDC ....................... 199
Figure B-2: Block diagram of DC exciter of G1, G3 and G4 ....................................... 200
Figure B-3: Block diagram of static exciter of G2........................................................ 200
Figure B-4: Block diagram of speed governor of G1, G2, G3 and G4 ......................... 201
Figure B-5: Rectifier operation condition (DIgSILENT interface) .............................. 202
Figure B-6: Rectifier’s α control for constant current................................................... 202
Figure B-7: Inverter operation condition (DIgSILENT interface) ................................ 203
Figure B-8: inverter’s β control for constant voltage .................................................... 203
Figure C-1: A single line diagram of the two-area system with HVDC ....................... 205
Figure C-2: Block diagram of static exciter of G1, G2 G3 and G4 .............................. 205
Figure C-3: Block diagram of speed governor of G1, G2, G3 and G4 ......................... 206
Figure C-4: Rectifier operation condition (DIgSILENT interface) .............................. 207
Figure C-5: Rectifier’s α control for constant current................................................... 207
Figure C-6: Inverter operation condition (DIgSILENT interface) ................................ 208
Figure C-7: inverter’s β control for constant voltage .................................................... 208
Figure C-8: Rectifier control with supplementary damping control ............................. 209
Figure D-1: A single line diagram of the two-area system with TCSC ........................ 210
Figure D-2: Block diagram of static exciter of G1, G2 and G3 and G4 ....................... 210
Figure D-3: Block diagram of speed governor for G1, G2, G3 and G4 ....................... 211
Figure D-4: TCSC with supplementary damping control. ............................................ 211
Figure E-1: A single line diagram of the two-area system with SVC ........................... 213
Figure E-2: Block diagram of static exciter of G1, G2 and G3 and G4 ........................ 213
Figure E-3: Block diagram of speed governor of G1, G2, G3 and G4 ......................... 214
Figure E-4: SVC composite (DIgSILENT interface).................................................... 215
Figure E-5: Primary voltage control of SVC ................................................................ 215
Figure E-6: SVC supplementary damping controller.................................................... 216
Figure F-1: Rectifier operation condition (DIgSILENT interface) ............................... 217
Figure F-2: Rectifier’s α control for constant current ................................................... 217
Figure F-3: Inverter operation condition (DIgSILENT interface) ................................ 218
Figure F-4: inverter’s β control for constant voltage .................................................... 218
Figure F-5: HVDC supplementary damping controller in GB full model .................... 219
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Preface
List of Tables
Table 2.1: Summary of available standalone and integraed PMUs ................................ 33
Table 5.1: Three scenarios for meeting the 2020 UK renewable targets ........................ 66
Table 6.1: Eigenvalues of the two-area system............................................................... 96
Table 6.2: Oscillation modes in the two-area system ..................................................... 97
Table 6.3: Right eigenvector for eigenvalue 28 (associated with inter-area mode) ....... 98
Table 6.4: Participation vector for Eigenvalue 28 (associated with inter-area mode) .. 100
Table 6.5: The effect of inter-area power flow on inter-area mode .............................. 101
Table 6.6: Effect of inter-tie line impedance on inter-area mode ................................. 102
Table 7.1: Sensitivity analysis for random noise .......................................................... 114
Table 7.2: Sensitivity analysis for sampling for frequency .......................................... 115
Table 7.3: Sensitivity analysis for data window size .................................................... 115
Table A-1: Synchronous machine parameters of G1, G2 and G3 and G4 .................... 196
Table A-2: Power generation conditions of G1, G2 and G3 and G4 ............................ 196
Table A-3: Parameters of static exciter ......................................................................... 197
Table A-4: Parameters of speed governor..................................................................... 197
Table A-5: Transformer parameters .............................................................................. 197
Table A-6: AC transmission line parameters ................................................................ 198
Table A-7: Load data .................................................................................................... 198
Table A-8: Shunt capacitors.......................................................................................... 198
Table B-1: Synchronous machine parameters of G1, G2 and G3 and G4 .................... 199
Table B-2: Power generation conditions of G1, G2 and G3 and G4 ............................ 199
Table B-3: Parameters of DC exciter ............................................................................ 200
Table B-4: Parameters of static exciter ......................................................................... 201
Table B-5: Parameters of speed governor ..................................................................... 201
Table B-6: Transformer parameters .............................................................................. 201
Table B-7: AC transmission line parameters ................................................................ 201
Table B-8: DC transmission line parameters ................................................................ 202
Table B-9: Parameters of rectifier control .................................................................... 202
Table B-10: Parameters of inverter control................................................................... 203
Table B-11: Load data................................................................................................... 203
Table B-12: Shunt capacitors ........................................................................................ 204
Table C-1: Synchronous machine parameters of G1, G2 and G3 and G4 .................... 205
Table C-2: Power generation conditions of G1, G2 and G3 and G4 ............................ 205
Table C-3: Parameters of static exciter ......................................................................... 206
Table C-4: Parameters of speed governor ..................................................................... 206
Table C-5: Transformer parameters .............................................................................. 206
Table C-6: AC transmission line parameters ................................................................ 206
Table C-7: DC transmission line parameters ................................................................ 207
Table C-8: Parameters of rectifier control .................................................................... 207
Table C-9: Parameters of inverter control..................................................................... 208
Table C-10: Parameters of HVDC supplementary control ........................................... 209
Table C-11: Load data................................................................................................... 209
Table C-12: Shunt capacitors ........................................................................................ 209
Table D-1: Synchronous machine parameters of G1, G2 and G3 and G4 .................... 210
-10-
Preface
Table D-2: Power generation conditions of G1, G2 and G3 and G4 ............................ 210
Table D-3: Parameters of Static Exciter........................................................................ 211
Table D-4: Parameters of Governor .............................................................................. 211
Table D-5: The capacitor and reactor of TCSC under steady state............................... 211
Table D-6: Parameters of TCSC supplementary damping control ............................... 212
Table D-7: Transformer parameters .............................................................................. 212
Table D-8: Transmission line parameters ..................................................................... 212
Table D-9: Load data .................................................................................................... 212
Table D-10: Shunt capacitors ........................................................................................ 212
Table E-1: Synchronous machine parameters of G1, G2 and G3 and G4 .................... 213
Table E-2: Power generation conditions of G1, G2 and G3 and G4............................. 213
Table E-3: Parameters of static exciter ......................................................................... 214
Table E-4: Parameters of speed governor ..................................................................... 214
Table E-5: Transformer parameters .............................................................................. 214
Table E-6: Transmission line parameters...................................................................... 214
Table E-7: Load data ..................................................................................................... 215
Table E-8: Shunt capacitors .......................................................................................... 215
Table E-9: Parameters of the primary voltage control of SVC ..................................... 215
Table E-10: Parameters of the primary voltage control of SVC ................................... 216
Table F-1: DC transmission line parameters................................................................. 217
Table F-2: Parameters of rectifier control ..................................................................... 217
Table F-3: Parameters of rectifier control ..................................................................... 218
Table F-4: Parameters of the HVDC damping controller ............................................. 219
Table F-5: A list of the PSS in service .......................................................................... 220
-11-
Preface
-12-
Preface
Abstract
The growing issue of power-grid congestion and a global increase in disturbances have
emphasized the need to enhance electrical power networks using Wide Area Monitoring,
Protection, and Control (WAMPAC). This is a cost-effective solution for improving
power system planning and operation. In addition to these existing issues, the Great
Britain (GB) power system is facing significant changes, in terms of both power
transmission technology and the nature of the generation mix, that will cause the
operation of the future GB power system to become more unpredictable and complex.
Therefore, developing a WAMPAC system will be essential to enhance the stability and
optimise the operation of the future GB power system.
The main objectives of the research presented in this thesis are to design a GB
WAMPAC system and develop solutions to overcome the challenges that will be
involved in the initial stage of the GB WAMPAC project.
As Synchronized Measurement Technology (SMT) is the most essential element and
enabler of WAMPAC, this thesis first provides a study of SMT and its applications.
This study also reviews the state of the art of these SMT applications, and worldwide
experience with the operation of WAMPAC in terms of system architecture,
communication technologies and data management.
After the basic study of WAMPAC, this thesis presents a new methodology for
designing a roadmap that will ensure the future GB WAMPAC system will be
developed in a logical and economic manner. This methodology takes into account the
international experience with WAMPAC project management and the practical
challenges faced in the future GB power system. With this new methodology, the GB
strategies for the development of WAMPAC are devised.
Two major SMT applications are then developed that can form main parts of the
proposed future GB WAMPAC system. These applications are developed to enhance
the small signal stability of the future GB power system.
1. Wide Area Inter-area Oscillation Monitoring using Newton Type Algorithm.
2. Wide Area Inter-area Oscillation Control using Power Electronic Devices.
Finally, the operation of a proposed GB WAMPAC system is demonstrated using the
DIgSILENT software package. The proposed real time applications are tested and
evaluated using dynamic simulations of a full GB power system model. In addition,
some key factors that will influence the operation of the future GB WAMPAC system
will be analyzed and discussed.
-13-
Preface
List of Abbreviations
WAMS
WAMCS
WAMPAC
GPS
IED
SMT
PMU
DC
ISO
EMS
SCADA
SIPS
SPS
WECC
EIPP
ADSL
VPN
TCP
UDP
IP
SE
PE
RTDMS
FNET
VIP
UVLS
UFLS
KF
FFT
LS
NTA
HVDC
CSC
VSC
TCSC
SVC
AVR
TG
PSS
SPTN
SHETN
NGETN
Wide Area Monitoring System
Wide Area Monitoring, Control System
Wide Area Monitoring, Protection and Control
Global Positioning System
Intelligent |Electronic Device
Synchronized Measurement Technology
Phasor Measurement Unit
Data Concentrator
Independent System Operator
Energy Management System
Supervisory Control and Data Acquisition
System Integrity Protection Scheme
System Protection Scheme
Western Electricity Coordinating Council
Eastern Interconnection Phasor Project
Advanced Digital Signal Link
Virtual Private Networks
Transport Control Protocol
User Datagram Protocol
Internet protocol
State Estimation
Parameter Estimation
Real Time Dynamic Monitoring System
Frequency Monitoring Network
Voltage Instability Predictor
Under-Voltage Load Shedding
Under-Frequency Load Shedding
Kalman Filter
Fast Fourier Transform
Least Square
Newton Type Algorithm
High Voltage Direct Current
Current Source Converter
Voltage Source Converter
Thyristor Controlled Series Compensator
Static Var Compensator
Automatic Voltage Regulator
Turbine Governor
Power System Stabilizer
Scottish Power Transmission Network
Scottish Hydro-Electric Transmission Network
National Grid Electricity Transmission Network
-14-
Preface
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.
-15-
Preface
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 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://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant
Thesis restriction declarations deposited in the University Library, The
University
Library’s
regulations
http://www.manchester.ac.uk/library/aboutus/regulations)
University’s policy on Presentation of Theses.
-16-
(see
and
in
The
Preface
To my mother Yumei, my father Baotian, my girl friend Laura and Professor Terzija
-17-
Preface
Acknowledgements
The Research and Development (R&D) project, “Wide Area Monitoring, Protection and
Control (WAMPAC) in the Future GB Power System”, presented in this thesis is funded
by the National Grid Ltd (UK), Scottish Power Ltd and Scottish Southern Electricity
Ltd.. This R&D project started in April 2008 under the direct supervision of Professor
Vladimir Terzija at the School of Electrical and Electronic Engineering, the University
of Manchester.
First of all, I would like to express my great appreciation to my Ph.D. supervisor,
Professor Terzija, for giving me this great opportunity to be his Ph.D. student. I have no
doubt to claim that this Ph.D. has hugely changed my life, and will benefit me and my
family in the rest of my life. Professor Terzija has been constantly involved in my
research, and provided me with strong guidance and support all through the project. I
wish to express my gratitude for his constant help.
I also would like to thank my Ph.D. advisor, Professor Peter Crossley and external
project supervisor, John Fitch and Mark Osborn, for their sound advice and kind help.
Thanks to all my friends, in particular, Gustavo Valverde, Jairo Quiros, Pawel Regulski,
Peter Wall and Gary Preston for their help and deep friendship.
Lastly, my parents and my girlfriend, Laura Guo, have unwaveringly believed in my
efforts. Their constant support provides me with confidence and courage to ultimately
complete my thesis.
-18-
Chapter 1 Introduction
Chapter 1 Introduction
1.1 Research Background
1.1.1 Power system blackouts
Despite large-scale power system blackouts being very low probability events, their
study is of great interest, due to the immense costs and consequences of such events for
customers, societies and industries [1]. In previous decades, due to economic pressure
from electricity markets and environmental constraints, power system operators have
been forced to operate power transmission systems in highly stressed conditions closer
to the system limits than ever before [1]. In this same period, the number, and size, of
large-scale power system blackouts has increased. For example, the US-Canada
blackout on August 14, 2003 [2] and the Italy blackout on September 28, 2003 [3]
involved more than 100 million customers. Figure 1.1 presents the consequences, in
terms of customers affected, of significant blackouts.
Customers Affected
19
65
,N
E
US
19
67
,N
E
19
US
77
,
N
De
ew
c.
Yo
19
rk
94
,W
Ju
e
ly
st
19
US
96
Au
,W
g.
19
es
96
tU
,W
S
es
t
er
20
n
03
US
,U
SCa
na
da
20
03
,I
ta
20
ly
03
,S
we
de
n
20
03
,C
hi
le
20
04
G
re
ec
e
60,000,000
50,000,000
40,000,000
30,000,000
20,000,000
10,000,000
0
Figure 1.1: Statistics of blackouts: customers affected [1].
It is rare for large-scale power system blackouts to be directly caused by a single large
disturbance. However, a single large disturbance in a stressed system may cause a
series, or cascade, of unplanned and unexpected sequential events. These events will
incrementally increase the stress on the system and force it into a more vulnerable state
of operation. If proper protection and control actions are not taken quickly and properly
(e.g. load shedding, reactive power support and controlled islanding), then the system
-19-
Chapter 1 Introduction
may experience further cascading events and separate into unplanned islands, or even
completely collapse [4][5][6].
Figure 1.2: Line of separation from the European grid [3].
For example, on September 28th 2003 a sequence of events, which would lead to the
separation of Italy from the interconnected European Power System, was triggered by
the tripping of a Swiss 380 kV transmission line. The line between Mettlen and Lavorgo
(marked as 1 in Figure 1.2), was tripped off at 03:01 due to a permanent fault. This
tripping meant that other transmission lines began to carry the power that was
previously transferred over the tripped line. This caused a second Swiss 380 kV
transmission line, between Sils and Soazza (marked as 2 in Figure 1.2), to trip at 03:25
due to overload. Combined with insufficient reserve in Italy, the loss of these lines
meant that the levels of overload on the remaining interconnections into Italy quickly
became intolerable. This led to the automatic and, almost, simultaneous tripping of
remaining transmission lines, with the effect that the Italian system was isolated from
the European network. The Italian power system lost a large amount of the active power
imported from its European neighbours (about 25% of the country’s total load). Such a
large loss of active power caused a sudden frequency drop of approximately 1 Hz to
occur in Italy. Furthermore, this significant loss of power caused multiple Italian
generators to trip for various reasons, e.g. under-frequency relay operation, high
temperature of exhaust gases. Despite additional load shedding, the frequency continued
to decrease and the system collapsed in three minutes [3].
-20-
Chapter 1 Introduction
Whilst it is impossible to develop a solution that completely eliminates the possibility of
a blackout, several measures can be implemented to minimize the probability of a
blackout occurring. For many years, Energy Management System (EMS) has been used
for the on-line monitoring of system conditions and assessment of system security.
Traditional EMS uses measurements with a low-refresh rate (several seconds to one
minute), from a Supervisory Control and Data Acquisition (SCADA) system, to
estimate the system operating condition and to perform off-line system stability studies
[7]. The EMS can provide sufficient information and support for normal steady-state
system operation and to plan the system response to slow changes in the operating
conditions. However, EMS is not capable of capturing system dynamics, particularly
when the system is subjected to large disturbances. In addition, off-line studies cannot
be used to fully anticipate all of the conditions faced by operators. These unplanned
contingencies have the potential to initiate a cascade of events that will lead to a system
blackout.
System Integrity Protection Schemes (SIPSs) are designed to preserve system integrity
after a large disturbance, and restore the system to the normal state when the system is
in an emergency condition [4] [5]. Traditionally, these schemes use the results of offline
studies to determine their actions [7]. These studies are based on the pre-calculated
system behaviour for the assumed operational state of the system. In addition, as
traditional SIPSs only use local or regional (within a power utility) measurements they
lack awareness of the operating conditions in the neighbouring power systems [4] [5].
Consequently, the traditional SIPS may not be sufficient to ensure proper control of any
system instabilities that may occur.
The US-Canadian and Italian blackouts provided very strong evidence that the lack of a
real time dynamic wide area monitoring system and the lack of real-time optimal and
centralized protection and control schemes across a large interconnected network, was
the root cause of these large scale blackouts [2] [3].
Furthermore, attempts to avert climate change through the introduction of renewable
energy policies will force radical changes in future power systems. The most significant
of these is that a large percentage of electrical energy will be generated using renewable
resources (wind, solar and tidal). For example, in the GB power system, the target is for
approximately 45% of electricity to be generated using renewable resources by 2030 [8].
This will prove problematic as electricity generation using renewable resources is
-21-
Chapter 1 Introduction
highly influenced by climatic conditions and the resulting intermittent nature of the
renewable resources. This will make the operation of future power systems more
variable and unpredictable. In addition, renewable energy generation and transmission
requires the support of power electronic technologies such as HVDC and SVC. The use
of these technologies will introduce further complexity and uncertainty into power
systems [9] [10]. The introduction of further variation, complexity and unpredictability
to power systems will dramatically increase the likelihood of large scale power system
blackouts. This will prove a serious problem, as current systems already find themselves
increasingly vulnerable to such blackouts in the absence of a real time wide area
monitoring system.
The development of a real time wide area monitoring system is essential if the future
changes in our power systems do not change the current trend toward an increase in the
number and size of large-scale blackouts. A real time wide area monitoring system will
allow the introduction of optimal, real time protection and control schemes that can be
used to counter the growing threat of large scale blackouts. With the breakthrough made
in the field of Synchronized Measurement Technology (SMT) and the availability of
high-speed communication channels it is now possible to implement a practical real
time wide area monitoring system. These technological developments, combined with
financial support from governments, will allow the emergence of real time, wide area
monitoring, protection and control systems that will be able to ensure the security of
future power systems in the face of an increasingly unstable operational environment.
1.1.2 Wide area monitoring, protection and control
Wide Area Monitoring, Protection, and Control (WAMPAC) involves the use of wide
area synchronized measurements, reliable and high bandwidth communication networks
and advanced centralized protection and control schemes [6]. SMT and related
applications are the essential element, and enabler, of WAMPAC. Presently, Phasor
Measurement Units (PMUs) are the most accurate and advanced synchronized
measurement technology available. They provide voltage and current phasors and
frequency information synchronized with high precision to a common time reference,
the Global Positioning System (GPS). The measurement functions of a PMU are based
on numerical algorithms. These algorithms must be both computationally efficient and
suitable for real-time applications, particularly when the measurements are used to
support dynamic-response applications [6].
-22-
Chapter 1 Introduction
Figure 1.3 shows the main components and structure of a generalized WAMPAC
system. In this system, the necessary synchronized voltage and current phasors are
produced by PMUs. The measurement data from these PMUs is transmitted through a
Wide-Area Network (WAN) and aggregated at one, or more Data Concentrators (DCs).
The aggregate data is then stored locally in the DC before being transmitted to the
various Application Software or Servers (ASS) of the different utilities. The main task
performed by the DCs is alignment of the received PMU data; however, the opportunity
also exists to perform additional pre-processing tasks before forwarding the data to ASS
[6].
Utility’s
WAN
PMU_1
Utility’s
WAN
PMU_n
PMU_1
PMU_n
Figure 1.3: A Generalized WAMPAC system [6].
The necessity for WAMPAC has gained worldwide acceptance [6], and a number of
WAMPAC systems have been established, or initialized, in different power utilities
throughout the world. For example, a Real Time Dynamic Monitoring System (RTDMS)
has been implemented in the Eastern North American bulk power system. A wide area
inter-area oscillation monitoring and control system was established by China South
Power Grid [11]. Other countries, such as Switzerland, Sweden, Denmark, Austria, and
Japan, have developed SMT based applications to improve power system stability [12].
-23-
Chapter 1 Introduction
1.2 Objectives of the Research
Over the coming decades, the biggest change of the GB power system is that a large
percentage of electrical energy will be generated from off-shore wind farms. Majority of
the off-shore wind farms will connect to the power grid with back-to-back HVDC link;
hence, they will not provide inertia to the system. Coupled with replacement of the
conventional coal generators with the new wind farms, the inertia of the future UK
power system will be reduced. In addition, a number of Power System Stabilizers (PSSs)
installed on the synchronous generators will be out of service when conventional coal
generators will be replaced by wind farms.
The reduction of system inertia and PSSs will reduce the small signal stability of power
systems, e.g. lightly or unstable damped inter-area oscillations. Therefore, the main
objectives of this research are to propose a WAMPAC system to improve the inter-area
oscillatory stability in the future GB power system and develop solutions to overcome
the challenges that are involved in the initial stage of the GB WAMPAC project.
However, the thesis will not be focused on the assessment of future GB systems with
wind farms, e.g. the system inertia reduction caused by the high penetration of wind
farms connected to the grid over power electronic devices.
The capital investment and logistical effort necessary for the implementation of a
WAMPAC system, particularly for a network with the size and complexity of the GB
power system, mean that it is infeasible to implement it in a single step. Therefore a
well planned roadmap is necessary to ensure the proposed WAMPAC system is
developed in a logical and economic manner. The design of the roadmap should seek to
ensure that the various elements of WAMPAC functionality become available as soon
as is reasonably possible, to maximize the benefit offered to the system operator. This
requirement will lead to the roadmap being separated into multiple stages. Each stage
will focus upon making certain elements of functionality (e.g. system monitoring
applications) available to the operators, whilst ensuring that the actions taken during this
stage are not short term and will lead to needless future redundancy and waste. This
means that each stage will serve as a base for the implementation of more complex
functionality at a future stage.
-24-
Chapter 1 Introduction
The development of such a roadmap is a significant challenge, and as such it constitutes
the primary task for this research project. As different power utilities have different
requirements of WAMPAC, a generic methodology for determining the roadmap is
required. This methodology is based upon an assessment of worldwide experience with
building WAMPAC systems and the analysis of operational challenge of power systems.
Using the roadmap developed from this research, a proposed future GB WAMPAC
system will be created. To support the implement of the proposed WAMPAC system in
the future GB power system, essential WAMPAC applications and algorithms for
improving the inter-area oscillatory stability in the future GB power system are needed
to be developed in this research. In addition, these WAMPAC applications, algorithms
and the WAMPAC system’s architecture designed for serving these applications should
be tested in a software package before being implemented in a real system. Therefore,
another main aim of this research is to develop a platform in the DIgSILENT
PowerFactory software package for the evaluation of the proposed future GB
WAMPAC system. Using system models constructed in this software package, the key
factors that will influence the operation of the future GB WAMPAC can be analyzed.
The results obtained through these simulations will serve as a base for future work, e.g.
demonstration of the operation of the GB WAMPAC system in a Real Time Digital
Simulator (RTDS).
The main objectives of this research can be summarized as follows:
1) Review of existing WAMPAC solutions, from applications, system
architecture and technology point of view.
2) Developing a generic methodology for determining the roadmap for the
development of the future GB WAMPAC system.
3) Developing new WAMPAC applications and essential algorithms for
improving the inter-area oscillatory stability in the future GB power system.
4) Establishing
a
testing
platform
in
DIgSILENT
PowerFactory
for
demonstrating and evaluating the operation of the GB Wide Area Monitoring
and Control System (WAMCS).
-25-
Chapter 1 Introduction
1.3 Thesis Structure
Chapter 1 – Introduction
This chapter briefly introduces the history of power system blackouts and summarises
the root causes of these blackouts. Based on the evaluation of existing solutions for
power system monitoring, protection and control (EMS and SIPSs), and the anticipation
of developments in future power systems, it is determined that a SMT-based WAMPAC
system is the only technology that could be used to reliably manage the next generation
of power systems. The aims of this research are detailed in this chapter along with a list
of the main contributions.
Chapter 2 –Synchronized Measurement Technology
This chapter briefly introduces the concept and technology behind synchronized phasor
measurements. This includes the hardware and functionality of SMT devices such as
Phasor measurement Unit (PMU) and Data Concentrator (DC). It will conclude with the
details of major commercial PMUs and DCs.
Chapter 3 – Applications and Benefits of Synchronized Measurement Technology
A study of the major applications of SMT will be provided in this chapter as well as an
evaluation of the state of the art and worldwide experience with these applications.
Chapter 4 – Architecture of a WAMPAC System
This chapter introduces the architecture of a typical WAMPAC system. This covers the
core components of a WAMPAC system, i.e. the measurement devices, communication
technologies, and their connectivity. The architecture for a future GB WAMPAC
system is then constructed based on international experience with the operation of
WAMPAC.
Chapter 5 – The Roadmap to the Future UK WAMPAC System
In this chapter, a methodology for designing a roadmap for the GB WAMPAC project is
introduced. This methodology takes into account the international experience with
WAMPAC project management and the practical challenges faced in a future GB
network. With this methodology, the GB’s strategies (both short term and long term) for
the development of a GB WAMPAC system are devised.
-26-
Chapter 1 Introduction
Chapter 6 – The Physical Nature of Inter-area Oscillations
The strategy for a GB WAMPAC project has highlighted that a real time inter-area
oscillation monitoring and control system is an important SMT application for the future
GB system. As such, a fundamental study of inter-area oscillations is provided in this
chapter. Two classical methods are introduced to investigate the nature of inter-area
oscillations i.e., nonlinear simulations and modal analysis.
Chapter 7 – Inter-area Oscillation Monitoring Using Newton Type Algorithm
In this Chapter, a new inter-area oscillation monitoring method developed for the short
term strategy of the GB WAMPAC project is presented. The core of this novel Wide
Area Monitoring System (WAMS) application is a nonlinear numerical algorithm,
Newton Type Algorithm (NTA) that processes real time oscillatory signals to estimate
the dominant inter-area oscillatory mode. Two data sets are tested using the new
algorithm, one based on simulated models and the other based on real-life data records.
Chapter 8 – The Application of Power Electronic Devices for Damping Inter-area
oscillations
In this Chapter, several closed loop control schemes that use power electronics devices
i.e. HVDC, TCSC and SVC to stabilize inter-area oscillations are presented. A modal
analysis based linear control theory is used for tuning the parameters of the damping
controllers; and then these damping controllers are tested through dynamic simulation in
a typical two-area system model.
Chapter 9 – Wide Area Monitoring and Control System in a future GB Power
System
In this Chapter, a proposed Wide Area Monitoring and Control System (WAMCS) for
the future GB power system is presented. This WAMCS is designed to enhance the
small signal stability of the future GB power system, i.e., improve the damping of the
inter-area oscillatory mode between Scotland and England. The operation of the
WAMCS will be demonstrated in the DIgSILENT software package. Some key factors
that will influence the operation of the future GB WAMCS will be discussed, including
the time delay involved in the wide area data transmission, and the reactions between
the new wide area control system and conventional Power System Stabilizers (PSSs).
-27-
Chapter 1 Introduction
Chapter 10 – Conclusions and Future Work
The last chapter presents the major conclusions of this research and suggests further
directions for future research.
1.4 Main Contributions of This Research
1) Review of the state of the art of SMT applications and the worldwide experience
of the operation of WAMPAC systems.
2) Construction of an architecture prototype for the future GB WAMPAC system,
based on the international experience with WAMPAC and the likely
characteristics of the future GB power system.
3) Introduction of a methodology for designing a roadmap to implement
WAMPAC in the future GB power system.
4) Proposal of the UK’s strategies (short term and long term) to guide the
development of the future GB WAMPAC system.
5) Development of a novel nonlinear numerical algorithm, Newton Type Algorithm
(NTA), for identifying dominant inter-area oscillation mode.
6) Modelling of Power electronic devices, HVDC, TCSC and SVC.
7) Proposal of a detailed procedure for the design of a wide area inter-area
oscillation damping control system using power electronic devices, i.e. HVDC,
TCSC and SVC.
8) Establishment of a testing platform in the DIgSILENT software package for
demonstrating and evaluating the operation of the GB Wide Area Monitoring
and Control System (WAMCS).
-28-
Chapter 2 Synchronized Measurement Technology
Chapter 2 Synchronized Measurement
Technology
2.1 Introduction
The voltage phase angles at the buses in an electrical power transmission network have
always been of special interest to power system operators. It is well-known that active
power flow over a transmission line is nearly proportional to the sine of the angle
difference between the voltages at the two terminals of the transmission line. As many
of the planning and operational considerations in electrical power systems are directly
concerned with the active power flow, measuring voltage angle differences across the
transmission line has been of concern for many years [14].
Consider a pure sinusoidal signal as shown in Figure 2.1. If the observation of the signal
begins at the time t = 0 s, the signal can be represented by a complex number with a
magnitude equal to the Root Mean Square (RMS) value of the signal and with a phase
angle. In a digital measuring system, the samples of the waveform in one period are
collected, and then the fundamental frequency component of the signal can be
calculated by using the following equation [14]:
2 N
X =
xk e − j 2 kπ / N
∑
N k =1
(2.1)
where N is the total number of samples in one period, X is the phasor representing the
sinusoidal signal, and x k is kth sample of the signal. In a real measurement system, the
signal is continuously sampled and each time a new sample is acquired a new phasor is
produced as the data window is moved to include the new sample. The most efficient
method for dealing with continuous monitoring of the input waveforms is to use a
recursive form of the phasor equation [15].
-29-
Chapter 2 Synchronized Measurement Technology
φ
Xm
φ
Figure 2.1: Phasor representation of a sinusoidal signal [16].
For the evaluation of the performance of a real power system, the positive sequence
voltages and currents are far more useful than the single phase quantities. Positivesequence voltages of a network constitute the state vector of a power system, and it is of
fundamental importance in all forms of power system analysis. The positive sequence
phasor can be computed according to its definition:
X1 =
1
( X a + αX b + α 2 X c )
3
(2.2)
As illustrated in Figure 2.2, when the voltages and currents in different substations are
measured and converted to positive sequence phasors in this way, their phasors can be
put in the same phasor diagram.
Substation B
Substation A
At different locations
Phasor A
Phasor B
Figure 2.2: Synchronized phasor measurement in remote substations [16].
In a large power system, if all the substations are equipped with synchronized phasor
measurement devices, the real time system operating condition can be directly measured
rather than estimated; including the system frequency, the voltage phasor of each bus
and the power flow between substations. The first paper to identify the importance of
synchronized phasor measurement technology was published in 1983 [17]. At this time
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Chapter 2 Synchronized Measurement Technology
the Global Positioning System (GPS) [18] was beginning to be fully deployed and
offered a source for the necessary synchronising clock signal. The timing pulse offered
by GPS is accurate to within 1 microsecond at any location on earth. It became clear
that GPS offered the most effective way of synchronizing power system measurements
over long distances.
2.2 Phasor Measurement Unit
At present, phasor measurement units (PMUs) are the most accurate and advanced
synchronized phasor measurement equipment. Figure 2.3 gives a functional block
diagram of a typical PMU. The GPS receiver provides the 1 pulse-per-second (pps)
signal, and a time tag consisting of the year, day, hour, minute, and second. The l-pps
signal is usually divided by a phase-locked oscillator into the number of pulses per
second required for the sampling of the analogue signals. The analogue signals are
derived from three-phase voltage and current transformers with appropriate anti-aliasing
filtering. The microprocessor calculates the positive sequence voltage and current
phasors, and determines the timing message from the GPS, along with the sample
number at the beginning of a window [16].
Figure 2.3: A functional block diagram of a typical PMU [16].
If enough PMUs can be installed across a large power transmission network, the real
time system operating condition can be directly measured by PMUs. In addition, as the
PMUs have a high data reporting rate, the system dynamics can be captured when the
system is subjected to disturbances [19]. Figure 2.4 compares the voltage angle
difference between two substations obtained using PMU measurements and traditional
state estimation. This comparison demonstrates clearly that a real time monitoring
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Chapter 2 Synchronized Measurement Technology
system made up of PMUs will provide much more precise and dynamic system
operation information than the traditional state estimation.
Figure 2.4: State estimation v.s. PMU measurements [16].
In a real implementation of synchronized measurement technology, there are two sorts
of PMUs, standalone PMUs and integrated PMUs. A standalone PMU is a device that
performs dedicated, high accuracy, time stamped, precision synchronized measurement
tasks in a standalone device. Figure 2.5 shows two commercial standalone PMUs.
Macrodyne 1690
ABB RE8521
Figure 2.5: Two standalone PMUs [16].
An integrated PMU is an Intelligent Electronic Device (IED), in which synchronized
precision measurement tasks are integrated, such as a digital relay, a digital meter, a
digital fault recorder. Figure 2.6 shows two integrated PMUs. As the cost of realising
synchronized measurement functionality in an IED has become much affordable, and
will continue to fall, IEDs with synchronized measurement capability will become more
prevalent in the years to come. These integrated PMUs will be installed in large
quantities in power systems, mainly for their primary functionalities (protective relaying,
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Chapter 2 Synchronized Measurement Technology
electricity usage metering, fault event recordings, etc.) rather than to offer pure
monitoring. However, whatever the primary task of these integrated PMUs the result of
their deployment will be that a substantial number of IEDs in a power system will be
capable of offering synchronized measurements [7].
GE N60
SEL 421
Figure 2.6: Two integrated PMUs [16].
Table 2.1 gives a summary of available standalone and integrated PMUs, including
manufacturers, model, and the number of inputs and outputs [16].
Table 2.1: Summary of available standalone and integraed PMUs
Manufacturer
ABB
Model
RES521
Arbiter
1133A
Arbiter
GE
Macrodyne
SEL
SEL
SEL
933A
N60
1690
SEL-311
SEL-421
SEL-451
SEL
AMETEK_RIS
QualiTrol
REASON
REASON
SEL-734
TR2000
Q9
RPV304
RPV310
Other
functions
No
Revenue
Meter, Power
Quality
Portable
Power
Quality Meter
Relay
No
Relay
Relay
Relay
Revenue
Meter
DTR
No
DFR
DFR
Internal GPS
receiver
Yes
Number of input channels
(positive sequence phasor
outputs)
18(6)
Yes
9(3)
No
Yes
Yes
No
No
No
9(3)
16 (5)
30 (10)
12 (4)
12 (4)
12 (4)
No
Yes
Optional
No
No
12 (4)
32 (10)
16 (5)
16 (5)
64 (21)
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Chapter 2 Synchronized Measurement Technology
2.3 Data Concentrator
……
ASS Z
ASS A
DC
WAN
……
SMU_1
SMU_n
Figure 2.7: Data concentrator in a WAMPAC system [16].
As shown in Figure 2.7, Data Concentrator (DC) is another critical ‘building block’ of a
SMT-based WAMPAC system. The DC collects the synchronized phasor data and
aligns that data into a single data packet for each unique time stamp; it then forwards
this data to different SMT applications. The data concentrator may also include other
functions, such as system event detection and archiving, data reprocessing for various
applications and data calibrations.
Figure 2.8: SEL Data Concentrator [16].
Figure 2.8 gives a representative view of a commercially available DC from Schweitzer
Engineering Laboratories (SEL). In addition, other power system device manufacturers
and power utilities have also developed their own DCs, such as PSGuard 830 of ABB,
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Chapter 2 Synchronized Measurement Technology
the DC developed by Bonneville Power Administration (BPA) and the “Super-DC”
developed by the Tennessee Valley Authority (VTA) in the USA.
2.4 Synchrophasor Standard
Actually, as shown in Figure 2.8, in a large-scale SMT-based WAMPAC system there
will be PMUs from different vendors, as the deployment of the system typically
involves multiple entities. Therefore, a WAMPAC system requires a consistent
performance from all of the PMUs installed, to meet its application requirements.
To ensure a uniform performance among the PMUs from different manufacturers,
establishing a standard is an essential step for initializing a WAMPAC system. The
IEEE PES Power System Relaying Committee has published the IEEE C37.118-2005
standard to replace the original IEEE 1344 standard for synchrophasor measurements. It
addresses the definition of a synchronized phasor, time synchronization, application of
time tags, a method for verifying measurement compliance with the standard, and
message formats for communication. However, the Standard has not addressed the
dynamic performance requirement of a PMU. Also, the Standard does not specify the
method with which conformance tests should be conducted [6].
2.5 Summary
In this chapter, the concept and technology of synchronized phasor measurement has
been breifly introducted. In [14] the algorithms behind synchrnized phasor measurement,
including the phasor estimation with nominal frequency inputs and the phasor
estimation with off-nominal frequency inputs are detailed. The hardware and functions
of PMUs and DCs have also been introduced, as well as the major commercial PMUs
and DCs. To ensure a consistent performance among the PMUs from different
manufacturers in a WAMPAC system, synchrophasor measurement standards were
developed. So far, the IEEE standard C37.118-2005 has replaced the original IEEE
standard 1344. However, more detailed standard conformity testing must be developed,
based on a clearly defined test requirement, setup, and procedure. It is also important
that qualified test entities are established, to ensure that the tests themselves are
executed consistently.
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
Chapter 3 Applications and Benefits of
Synchronized Measurement Technology
3.1 Introduction
Synchronized Measurement Technology (SMT) is the most essential element and
enabler of WAMPAC. All of the advanced functions in a WAMPAC system are
developed based on synchronized measurements. Therefore, in this chapter, a study of
the major applications of SMT will be provided as well as an evaluation of the state of
the art and worldwide experience of these applications. From this study, power utilities
that expect to develop WAMPAC systems will be able to have a clear understanding of
how SMT can be used to help improving the stability of modern electrical power system
operation, and how SMT will be essential to the future power systems. Access to this
information will allow power utilities to be more confident when developing their own
WAMPAC systems.
Generally, SMT applications are divided into two groups, off-line applications and online applications. Off-line applications are usually used to improve and validate the
system model, to make system planning and off-line stability studies more reliable. Online applications are used to assist system operators in real time, by offering on-line
monitoring, protection and control. This study attempts to provide a comprehensive
analysis of all major applications that are being developed. However, the lack of
maturity of some applications and continuing development of others means that some
applications are not fully covered by this study.
3.2 Off-line Applications of SMT
3.2.1 Post-disturbance analysis
The main objective of post-disturbance analysis is investigating the system dynamics
during large disturbances and analyzing the system sequential events caused by those
disturbances. To achieve this, power system analysts collect and assemble the data
recordings from various data recorders that are at different and remote positions
throughout the entire network. However, the considerable amount of the data that has
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
been used for many years is not synchronized. Therefore, it has been extremely difficult
and time-consuming to reconstruct this data on the same time axis. This reconstruction
is a prerequisite for understanding the sequential events that have occurred during and
after the disturbance [20] [6].
Application of SMT allows all of the data gathered during the system disturbance to be
time tagged based on the same synchronizing GPS signal. Therefore, it is much easier to
reconstruct the sequence of events after the disturbance has occurred. Simplifying the
reconstruction process will allow the time spent analyzing the vast amount of data to be
reduced from months, to days, or even hours [1].
Figure 3.1 presents one example from the Western Electricity Coordinating Council
(WECC) of using PMU data for the reconstruction of the sequence of events that
occurred after a large disturbance, this reconstruction was performed using the post
disturbance analysis software, Power System Outlook (PSO). PSO was developed by
Southern California Edison (SCE) Corporation [21]; it has been used by 11 states on the
west coast of the USA as well as two Provinces in both Canada and Mexico. It helps
power system analysts and operators to understand the dynamic characteristics of the
system by producing visualizations of the real data recorded during disturbances.
06/14/04 Event at 07:40 Pacific Time (06/14/04 at 14:40 GMT )
60.025
59.820
59.615
59.410
59.205
59.000
14:40:34.00
14:40:44.00
14:40:54.00
14:41:04.00
14:41:14.00
14:41:24.00
VINC
JDAY
DEVR
MALN
BGCR
COLS
ALAM
BE23
SONG
BE50
KRMR
SYLM
DEV2
MPLV
ANTP
KEEL
VLLY
CPJK
MAGN
SUML
LUGO
SLAT
GC50
SCE1
14:41:34.00
Pacific Time
Figure 3.1: The reconstruction of system frequencies after a large disturbance in WECC, 14th
June, 2004 [16].
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
3.2.2 Benchmarking, validation and fine-tuning of system models
When benchmarking and validating system models the main tasks are the identification
of the potential errors in the power system model, and the calculation of accurate values
for any erroneous parameters. Accurate and reliable system models are essential for
reliable and secure system operation, planning, and delivery of efficient and robust
power system control. Inaccurate system models may cause power system operators to
make conservative or incorrect decisions of system planning and operation; this could
result in inefficient utilization of assets, and even system blackouts.
Figure 3.2 shows a typical example of the mismatch between the actual system response
and the simulated response to the same disturbance [22] in WECC. It was the mismatch
that caused system planners to make an incorrect decision and led the system to
blackout after the occurrence of a large disturbance.
Figure 3.2: Comparison of the recorded system response to the 10th August, 1996 disturbance
in USA with the simulation results [22].
Here, power system model validation is not limited to the steady-state models; it also
includes the dynamic models. In the aspect of the validation of static model parameters,
which includes synchronous machine inner resistance and reactance, transformer tap
position and transmission line impedance etc, the algorithms are well developed and
commercially available which is commonly referred to as Parameter Estimation (PE)
[20]. The emergence of precise SMT has significantly improved the performance of PE
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
algorithms, as the estimated phasor values in the PE algorithms can be directly replaced
by measured phasor values. For example, with a PMU installed at both ends of a long
transmission line, the transmission line impedance can be directly calculated using the
voltage and current phasors [20].
In comparison to dealing with a static model, the benchmarking and fine-tuning of
dynamic system models is much harder and more complex. This is because it requires
careful evaluation of the actual system response to the events. Dynamic model
validation is usually achieved by comparing the data recorded during system events
with the response of system models to the same disturbances. When differences are
encountered, the dynamic model parameters are tuned until a corresponding response is
obtained [20]. The high data reporting rate offered by PMUs is capable of capturing the
system dynamics, with a sufficient number of PMUs installed across a large power
network the dynamic characteristics of the system can be precisely profiled by using the
synchronized recordings. The procedures and principles that should be observed when
validating power system models are described in [22] [23] [24] and [25], alongside
algorithms that allow wide area synchronized measurements to be used for the finetuning of dynamic system models.
3.3 On-line Applications of SMT
3.3.1 Wide area phase angular and power flow monitoring
Since PMUs can directly measure the phase angle differences across power
transmission lines, they have an inherent advantage when system operators want to
monitor the real time power transfer stress on the power transmission network. This real
time monitoring allows the system operators a greater degree of confidence when
managing critical transmission corridors; allowing operation closer to the real stability
limit of the corridor, whilst still maintaining a safe security level. As a consequence, the
marginal cost between two power generation areas will be reduced, as the constraints on
the transmission of the electrical power that is produced by the generators with low
generation costs will be relaxed. Furthermore, confident operation of transmission lines
closer to their stability margins will also reduce the need for investment in transmission
line reinforcement.
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
In addition, in large interconnected power networks, a real time phase angle monitoring
system, consisting of PMUs, can provide clear understanding of the entire operational
situation to the system operators. The August 14, 2003 blackout that occurred in the
United States and Canada demonstrated the necessity to implement such a monitoring
system throughout bulk interconnected power networks, because it was the lack of
awareness of the neighbouring grids’ operational status that allowed the cascading
blackouts to occur. After this blackout, the provision of a real time wide area
monitoring system for all transmission owners and regional transmission operators was
recommended [2].
Figure 3.3: RTDMS – a wide area visualization platform for the North American power system
[26].
Figure 3.3 presents one application of wide area phase angular monitoring in USA, i.e,
Real Time Dynamic Monitoring System (RTDMS) that was developed for the North
American bulk power system. Assisted by this visualization tool, the system operators
will make optimum and confident decisions when operating the system, since both the
local and global operational situations are clearly observed. The RTDMS visualization
tool also offers: 1) Voltage Magnitude monitoring, 2) System Frequencies monitoring, 4)
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
Real and Reactive Power Flow across Monitored Lines, 5) a Summarized Information
Display [26].
3.3.2 Wide area frequency monitoring
Power system frequency is one of the most valuable information for on-line assessment
of system stability, since the system frequency is the direct measure of the balance
between generation and demand. During large disturbances, in particular, the system
frequency is rapidly varying and very different in different parts of a bulk system. In the
next generation of power systems, one of the biggest changes will be the high
integration of renewable generation resources. This will reduce the system’s ability to
provide frequency control services, because generation from renewable sources tends to
be less controllable than conventional synchronous generators. Therefore, power system
operators require an accurate wide-area frequency measurement system, and adaptive
emergency frequency control scheme for remaining system frequency stability after
power system being subjected to a large disturbance e.g. a sudden outage of large
generator.
The high data reporting rate offered by PMUs has afforded an opportunity for power
system operators to obtain accurate measurements of the dynamic system frequency. If
the entire power network is monitored by a synchronized frequency measurement
system, then the dynamic frequency behaviour of the system can be precisely captured.
The most important application of such wide area frequency information is the analysis
of system disturbances (e.g. outage of a large generator), which includes the
identification of disturbance locations and the estimation of the magnitude of
disturbances. The results of such an analysis serve as the preliminaries for the power
system emergency load shedding scheme [27].
The Triangulation method, which was traditionally used to detect the epicentre of
earthquakes, has proven a simple and effective way of determining the location of a
disturbance, such as the outage of a large generator [27] [28] [29]. This method has
been utilized in the Frequency Monitoring Network (FNET) that is in use in the United
States, and the disturbance locations estimated by the method were very close to the
actual positions of the disturbances. The estimation results for a disturbance that
occurred on August 4th, 2004 are presented in Figure 3.4. The red dot represents the
estimated disturbance location, while the green square is the actual location. The same
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
algorithm for disturbance location was also tested in a small power network in South
Korea, and the results were also acceptable [30].
Figure 3.4: Disturbance localization using PMUs and the triangulation method [27].
Load shedding is a key action when trying to help a system recover from extreme
under-frequency conditions. The ability to immediately produce an accurate estimate of
the power imbalance between the generation and demand after a disturbance will be a
quite useful input for an adaptive load shedding scheme. The active power imbalance
(ΔP) is proportional to the rate of frequency change (df/dt), the system inertia serves as
the constant of proportionality in this relationship. The wide area frequency
measurement system provides real time frequency and the rate of the change of
frequency, based on which the magnitude of the disturbance can be estimated. In the
case presented in Figure 3.4, the estimated tripped generation was 786 MW, while the
actual tripped generation was around 870 MW [27].
2.3.3 Wide area voltage monitoring
Voltage instability is a well known problem for power networks that have long
transmission lines with heavy power transfer, such as WECC [1]. Conventional
approaches for preventing voltage instability, such as Voltage Instability Predictor (VIP)
and Under-Voltage Load Shedding (UVLS) only use local voltage and current
measurements. With these local measurements, an approximate two-bus equivalent of a
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
complex network and the generator at the remote end can be estimated, as shown in
Figure 3.5.
i
v
i
Z th
E th
v
ZL
Figure 3.5: Estimation of the Thevenin equivalent with local measurements [31].
The Thevenin equivalent circuit and the maximum power transfer principle can be used
to estimate the voltage collapse point of the equivalent network [32]. When the voltage
of the local bus is close to the estimated collapse point a certain amount of load is
disconnected, with a certain time-delay, until the voltage rises above the threshold [31].
However, the drawback of these conventional approaches is that a single set of local
measurements do not contain enough information to directly compute the parameters of
the Thevenin equivalent accurately, this inaccuracy may lead to a large error in the
estimation of the voltage collapse point.
Real time voltage monitoring software, supported by a network of PMUs that are
installed at both end substations of a complex transmission corridor, can overcome the
shortcomings of conventional VIP. In the first stage of the application, the T-equivalent
of the transmission corridor can be directly computed using the voltage and current
phasors that are measured by the installed PMUs, as presented in Figure 3.6. In addition,
the source impedance is calculated by using dynamic data collected from the PMUs at
the sending end of the corridor. Furthermore, the dynamic parameters of the load, such
as the coefficient of voltage-dependence, are estimated by using the PMU data collected
at the receiving end of the corridor. In the next stage, the T-equivalent of the
transmission corridor is combined with the source impedance and the dynamic load
model, calculated in the first stage. Once the real time combined model of the critical
transmission corridor is available, the voltage stability analysis can be directly carried
out [31]. ABB has developed a PMU-based voltage stability application for real time
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
voltage-stability monitoring and assessment, based on the methodology described above
[33]. This application has been implemented in the Croatia power network [12].
v1
i2
i1
i1
ZT / 2
Zg
E th
ZT / 2
Z sh
v1
v2
i2
v2
ZL
Figure 3.6: T and Thevenin representation of transmission corridor [31].
3.3.4 Inter-area oscillation monitoring
To reduce the CO2 emissions produced from conventional generators (coal, oil and gas),
electrical power engineers have been integrating as much renewable based generation
(Hydro, wind and photovoltaic) as possible. The geographical location of renewable
resources is fixed, and as such they are distributed throughout different power utilities.
Previously isolated power networks have to be connected to form a larger power grid to
share the renewable energy resources. Consequently, this has resulted in long distance
power transfers between adjacent power grids; which carries the potential risk of lightly
damped inter-area oscillations in a large interconnected power system.
The inter area oscillation mode is used to define the perturbations associated with a
group of generators in one area are swinging against a group of generators in another
area. A large system usually involves several inter area oscillation modes. Most
analyses of inter-area oscillations are performed off line. They use system models that
are limited to individual power utilities, and do not consider the complete
interconnected power system [1]. The typical frequency range of inter-area oscillations
is from 0.1 Hz to 0.8 Hz [34]. Hence, it is extremely difficult to capture inter area
oscillations by using conventional EMS, due to its low refresh rate. A wide area
monitoring system (WAMS) that consists of PMUs can offer a great opportunity to
monitor the dynamic behaviour of power systems, and identify the inter-area oscillatory
modes, as presented in Figure 3.7 [1]. The high data reporting rate of PMUs and the
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
availability of fast communication links are the primary enablers of this opportunity to
monitor the inter-area oscillations.
So far, a considerable amount of work has been done by different power utilities in
developing techniques to identify the dominant inter-area oscillation modes. For
example, the Prony Method has been used in the southern power grid of China and the
West coast power grid of the USA [35][36]. The Nordic power system has used an
adaptive Kalman Filter (KF) to track the inter-area oscillations [37] [38], and the Fast
Fourier Transform (FFT) has been used in the Japanese system for estimating the
oscillatory parameters [39].
Figure 3.7: Oscillations observed by two PMUs in the European grid [1].
3.3.5 Power system restoration
It has to be accepted that some of power system blackouts are unavoidable because of
its nature [14]. It then becomes essential that strategies for restoring power after a
blackout with minimum delays and minimum cost should be made. Quick restoration of
power is extremely important as it can significantly minimize user inconvenience due to
electrical power outage and the cost of blackouts.
The existing procedures for power restorations are made in the form of written manuals
that prescribe steps to be followed during restoration, along with appropriate
checkpoints along the way in order to verify that everything goes according to the plan
[40] [41]. However, these guidelines are based on assumed system conditions, which
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
may not be the same as those encountered at the present status [1]. During power
system restoration, power system operators often encounter excessive standing phase
angle difference across the breakers that connect adjacent power grids. Incorrectly
closing such a circuit breaker could shock the power system, causing high currents,
voltage drops and severe equipment damage [1]. In addition, unsuccessful attempts to
reclose the tripped power lines, rather than taking other actions, could cost valuable
time when the power system is operating in the emergency state [3].
The main value of using PMUs in power system restoration schemes is the ability to
provide the operator with real-time information about the phase angles in relevant parts
of the interconnecting grids. This ability helps the operator to know if reclosing a circuit
breaker can be done without affecting the stability of the system. When the angle
differences across the breakers are within acceptable bounds, the system operator can
safely reconnect the adjacent areas immediately. As a consequence, the time spent on
power system restoration will be significantly reduced.
Figure 3.8: PMU measurements from three areas during reclosing attempts: UCTE, 4 November
2006 [42].
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
Figure 3.8 shows the PMU measurements recorded during the reclosing attempts for the
power lines between two areas, including the successful reclosing between those two
areas and a third area. Seven attempts to connect these zones failed, as the operators did
not use the PMU data to assist the restoration. If the PMU data had been used during the
restoration these unsuccessful reclosing attempts could have been avoided [42].
3.3.6 Improved state estimation
Power system State Estimation (SE) is one of the most important online applications
needed for the Energy Management System (EMS) and operational security
assessments. The state estimator produces the optimal solution of the system state
(voltage magnitudes and angles) using network models and estimation methods, e.g. the
weighted least square method and Kalman filter, the performance of which is based on
the system models and redundant measurements (voltage and current magnitudes) in the
system. A brief account of the benefits of using PMUs to support SE is provided below.
ƒ
Phasor-Based Linear State Estimation
Synchronized and accurate phasor measurements can significantly improve the
overall quality of state estimation. This improvement would be seen both at the bus
where phasors are introduced, and at adjacent buses in which the states can be
directly calculated using the transmission line parameters, and voltage and current
phasors. As the number of PMUs is increased the observability will also increase,
until complete observability is achieved and the estimation method will become
linear. A linear estimation method would have a lower computational burden and
greater accuracy than a non-linear method.
ƒ
Unifying Neighbouring State Estimations
When state estimations of neighbouring systems perform independently they do not
have a common reference bus. Therefore, the results cannot be used to form a single
estimator for the entire network. However, if a PMU is installed at the reference bus
in each of the neighbouring systems the voltage angle difference between the
reference-buses can be directly measured. These angle differences can be used to
create a common reference point for the state estimators across the entire
interconnected system.
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
ƒ
Real-Time Network Model Parameter Estimation
In the traditional Parameter Estimation (PE), the system line parameters are
estimated from available telemetries; a high level of redundancy and accuracy in the
measurements used is essential for PE. Synchronized phasor measurements can be
used to calculate the actual line impedances and charging admittances, as the
voltage and current phasors are directly measured at both ends of the transmission
line, as presented in Figure 3.9.
i
I ik
g
ik
+ jb
ik
I ki
g
g + jb
si
si
sk
k
+ jb
sk
Figure 3.9: PMUs installed at both ends of a transmission line [6].
3.3.7 Dynamic rating of overhead transmission lines
In electrical power systems, overhead transmission line capacity is limited by the
performance of the conductor at high temperatures, and by safety standards that specify
the minimum allowable ground clearance. A number of the overhead transmission lines
in power systems are designed using conservative criteria. These conservatively
designed lines will have excess capacity that may not be fully exploited. There is lack of
practical technology that enables real time monitoring and dynamic rating of overhead
transmission lines. Such technology will allow system operators to fully utilize the
available transmission infrastructure with confidence [1]. This will be of particular
benefit as the conservative use of overhead transmission lines may lead to unnecessary
investment in new transmission lines.
With PMUs installed at both terminals of an overhead line, the synchronized phasor
measurements allow the actual impedance and shunt admittance to be calculated, from
which the line resistance can be calculated. Based on the known characteristics of the
conductor material, the conductor temperature can be estimated in real time from the
line resistance. The advantage of using a PMU-based method for monitoring a line is
the low cost and relative ease of installation, as only a pair of PMUs is needed for each
line.
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
Figure 3.10: Visualization of the real time mentoring of the thermal condition of an overhead
transmission corridor in APG [12].
A commercial product that offers this application, “Line Thermal Monitoring” from
ABB, has been installed at two locations in Europe, one in the Austrian Power Grid
(APG) and another in Switzerland [12]. Figure 3.10 shows the overhead line monitoring
system in APG. It provides power system operators with real time information about the
network stress caused by heavy power transfer. Upon the detection of an extraordinary
status, the monitoring system alerts the operator by giving an early warning or
emergency alarm [12].
2.3.8Intelligent controlled islanding
Power system islanding is a measure of last resort that is employed when the system
operation is in an extremely stressed state (thermal limits, phase angles across system
beyond limits, voltage or frequency excursions beyond planned thresholds) and further
disturbance propagation that will result in uncontrolled system separation is
unavoidable. System islanding is conventionally accomplished by using a System
Integrity Protection Scheme (SIPS), also known as remedial System Protection
Schemes (SPS) [4] [5]. These schemes are designed based on extensive planning studies
for a range of scenarios that cover various loading levels, topologies, contingencies, etc.
However, in many practical situations the prevailing system conditions are quite
different from those upon which the SIPS settings are based. Consequently, the
performance of the system will not be optimal for the prevailing system state.
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
Wide area real time synchronized measurements provide important information about
the prevailing system conditions that can be used to improve the action of SIPS. These
synchronized measurements may be used to improve conventional system islanding
schemes in the following areas [14].
1. Using real time data provided by PMUs to detect whether a power system is
approaching an unstable state, e.g. the phase angles across the system beyond
limits, and if network islanding is needed to prevent a blackout.
2. Determine optimal islanding boundaries according to the prevailing system
conditions. For example, establish which groups of generators will separate due
to the loss of synchronism and how to optimally balance generation and demand
in each island.
2.3.9 Adaptive under-frequency load shedding
Under-frequency load shedding (UFLS) is a common practice that is used by most
power systems to help prevent extreme frequency drops when a large disturbance
occurs, such as a sudden outage of a large generator [43]. Nowadays, the existing UFLS
protection scheme adopted by power utilities are predominantly deterministic, not
taking into account the actual system state and topology, operating point, and the nature
or magnitude of the disturbance. The frequency measurements are performed locally in
distribution substations, when the frequency drops below the preset point the designated
load feeder will trip [44]. As a consequence, the existing UFLS protection scheme very
often disconnect more or less load, than is required.
The availability of synchronized wide area measurements provides a great opportunity
for developing an adaptive and efficient UFLS protection scheme. The adaptive UFLS
protection scheme is based on real time wide area measurements of system frequency
and the rate of change of system frequency. With known system inertia constant (H) the
magnitude of the imbalance between generation and demands can be immediately
estimated after the disturbance [45]. In addition, the wide area monitoring system can
also provide other auxiliary information to support the adaptive UFLS protection
scheme, for example, real time active power outputs from renewable resources, power
generation reserve from synchronous generators and the power flow conditions over the
tie-lines that connect adjacent power grids. This real time wide area information will
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Chapter 3 Applications and Benefits of Synchronized Measurement Technology
allow system operators to be more confident when optimizing the UFLS protection
scheme.
3.4 Conclusions
In this chapter, the major applications and benefits of Synchronized Measurement
Technology (SMT) have been introduced in terms of off-line and on-line applications.
From worldwide experience, off-line applications are usually considered to be the first
step when developing a WAMPAC system; these applications include 1) accurate post
disturbance analysis and 2) system model validation and benchmarking. Concerning online applications, most power systems have utilized synchronized phasor data to
develop wide area real time monitoring systems; these monitoring systems include real
time power flow (power angle), voltage magnitude monitoring, system frequency
monitoring and inter-area oscillation monitoring. In addition, SMT offers opportunities
for improving the quality of conventional power system state estimation and protection.
However, other applications, such as real time power system restoration, smart
controlled system islanding and adaptive load shedding, are still in the research stage,
significant long term effort will be necessary before these research applications are
ready for practical implementation.
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Chapter 4 Architecture of a WAMPAC System
Chapter 4 Architecture of a WAMPAC System
4.1 Introduction
In Chapter 2 and 3, the Synchronized Measurement Technology (SMT) and its major
applications and benefits were introduced. With this information, power system
operators become confident that SMT will significantly improve the stability of future
power systems, and that a SMT-based WAMPAC system will be the only way for
monitoring and managing the future power systems. In this Chapter, the architecture of
a WAMPAC system will be introduced. This introduction covers the core components
of a WAMPAC system, e.g. measurement devices, data concentrators and
communication technologies, and their connectivity. A prototype of architecture for the
future UK WAMPAC system will be constructed based on the current international
experience and practice with the operation of WAMPAC.
4.2 Architecture of a WAMPAC System
Designing a large-scale WAMPAC system is extremely difficult; meticulous work need
to be done to overcome the unique challenges that will exist for each individual
WAMPAC system. First of all, a large-scale WAMPAC system involves a large number
of entities (e.g. power utilities, Independent System Operators (ISOs), regional
organizations). Each entity has its own specific needs that they wish to have satisfied by
the PMU applications. Secondly, the WAMPAC system needs to support a large range
of applications to satisfy the participants, thus it must accommodate a diverse range of
technical requirements, such as data reporting rate, reliability of communication
network. Thirdly, as more power utilities become aware that SMT is essential for the
next generation of power systems, a number of new clients will join the WAMPAC
system and the number of PMUs will increase. Therefore, the system must be scalable
and flexible, so that it is capable of accommodating increasing quantities of PMU data
and the requirements of the new WAMPAC participants and clients [1].
As many PMU applications are still in the research and development stage, the
communication standards that will serve the WAMPAC system are not fully developed;
and the data requirements for supporting each application are still not clearly defined [1].
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Chapter 4 Architecture of a WAMPAC System
Therefore, there still hasn’t been a developed and generic architecture of WAMPAC
system. However, based on the current experience of the operation of existing
WAMPAC systems, a general architecture for a typical WAMPAC system has been
defined; this is shown in Figure 4.1. Although this general architecture doesn’t provide
many details about how a real WAMPAC system works, it presents the essential
components involved in a real WAMPAC system. The results of this work will help
new WAMPAC systems be built logically and economically.
Communication
WAN/LAN
networks
Utility’s
applications
Communication
networks
WAN/LAN
Utility’s DC
Utility’s
applications
Utility’s DC
`
`
SCADA/
EMS
Communication
networks
WAN/LAN
SCADA/
EMS
ISO’s Super DC
`
Data server
SCADA/
EMS
Event archive
Short term archive
Wide area real time
protection and
control
Wide area real time
monitoring
Data Archiving
Long term archive
Figure 4.1: The general architecture of a typical WAMPAC system.
This general WAMPAC system architecture presented in Figure 4.1 was mainly based
on the experience of the real WAMPAC system operating within the Eastern
Interconnection Phasor Project (EIPP) community in the USA [46] [47]. Figure 4.1
shows a four–layer architecture that is typical in the operation of WAMPAC system, 1)
Synchronized Phasor data acquisition 2) Synchronized data collection 3) Data services 4)
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Chapter 4 Architecture of a WAMPAC System
Synchronized measurement applications. The main equipment and functionality within
each layer are briefly described as follows.
Layer 1, Synchronized Phasor Data Acquisition – The primary function of Layer 1 is
to acquire synchronized phasor data. In this layer, PMUs measure three-phase
instantaneous voltage and current magnitudes and produce positive-sequence, voltage
and current phasors for the fundamental frequency.
Layer 2, Synchronized Data Collection – In the Layer 2, the time-stamped phasor
measurements produced in Layer 1 are collected by Data Concentrators (DCs) and then
put into a single data packet for each unique time stamp. In a large WAMPAC system,
covering a number of different power utilities, each participant has its own DC. A
centralized “Super DC” is then needed for the Independent System Operators (ISOs) to
receive the data streams from these local DCs and other unattached PMUs, and package
them together for broadcast to the WAMPAC centre and other participants.
Layer 3, Data Services – The data server in Layer 3 is primarily responsible for
ensuring that the data supplied to the applications in Layer 4 is suitable for their
purposes. For example, the inter-area oscillation monitoring toolbox only needs the
synchronized data from the PMUs at the ends of the long transmission corridor, but with
a very high data-reporting rate. A linear state estimator may need data from hundreds of
PMUs but a much slower data-reporting rate. The data server must also provide data
processing services, e.g. error filtering, noise filtering and synchronization checks.
Layer 4, Synchronized Measurement Applications – Layer 4 consists of the
WAMPAC centre in which the major real time wide area SMT applications perform;
these include:
•
Large–scale data archiving (short term archive, long term archive, event archive);
•
Improved EMS (improved state estimation, etc);
•
Real time wide area monitoring (power angle, voltage, frequency);
•
Real time wide area control (inter-area oscillation damping control, etc);
•
Real time wide area protection (under-frequency load shedding, intelligent
controlled system islanding, etc).
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Chapter 4 Architecture of a WAMPAC System
4.3 Communication Networks of WAMPAC System
A future WAMPAC system requires transmission of huge amounts of data between
power utilities, organizations and clients. Therefore, it is essential to establish a secure,
reliable communication network. Some of the important issues involved in developing
such a communication network are discussed in this section.
4.3.1 Available communication media for WAMPAC
1. Telephone Lines – At present, telephone lines are still the backbone of utility
communication. The main advantages of using telephone lines for synchronized
data transmission between substations are that they are easy to set up and
economical to use [48]. A major drawback of this medium is its narrow
bandwidth (<=56bps). However, advancements in digital communication
technologies, such as Advanced Digital Signal Link (ADSL), have allowed the
bandwidth of telephone lines to be increased significantly [49]. Usually, the
telephone
communication
and
internet
infrastructure
are
owned
by
communication corporations not power utilities. Therefore, the reliability of
using a telephone network as the backbone of the communication network for a
WAMPAC system can not be guaranteed.
2. Power Lines – Power Line communication is a fast growing technology serving
a number of current applications in power system protection and control.
However, PL also has some disadvantages, such as bandwidth limit, propagation
delay and induced electromagnetic interference. Furthermore, Power Line is
subject to lightning, switching surges and power network reconfigurations [50].
3. Satellite Communications – The major advantage of satellite communications,
when compared to phone lines and power lines, is that there is no physical
connection between the signal source and the destination. A satellite receives
microwave signals from ground stations on the Earth’s surface, and transmits
them at a different frequency to other ground stations, potentially thousands of
miles away. This would prove quite suitable for data transmission between
remote substations [50].
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Chapter 4 Architecture of a WAMPAC System
4. Microwave links – Point to point microwave link communication is highly
reliable and easy to set up. Furthermore, it is capable of carrying many
communication channels with a variety of information. However, Microwave
communication technology is affected by electromagnetic interference from
power transmission lines, wind turbines and cell phone transmission towers, etc.
Microwave communication is also affected by heavy moisture, snow, rain and
other bad weather conditions [50].
5. Fibre-optic links – Many utilities have been using fibre-optic cables for power
system protection communications, and the demand for this medium is growing
very quickly. The advantages of using fibre-optic links are their immunity to
electromagnetic and atmospheric interference and the massive bandwidth
available. However, the financial cost of building a dedicated fibre-optic
communication network for power system protection and control is extremely
high [48].
To build a cost effective communication network for a WAMPAC system, the selection
of communication media should take a comprehensive set of factors into account. For
example, the financial cost to build a new communication links, the reliability and
bandwidth of the current communication networks and the requirements of
communication technology for different phasor data applications.
The different demands placed upon the communication network by each application
will be the key factors in determining the nature of the optimum communication
network. For example, the acceptable level of PMU data transmission delay for a PMUintegrated State Estimator is several seconds, and the short-term absence of PMU data,
does not influence the performance of the State Estimator. Therefore, power lines,
phone lines and internet-based Virtual Private Networks (VPN) would be adequate to
serve this application. However, a communication network that is supporting wide area
real time power system protection and control applications should be extremely reliable
and have minimum communication latency. In this case only a dedicated fibre-optic
network would be satisfactory. China South Power Gird has developed a real time wide
area monitoring and control system to monitor and damp inter-area oscillations, for
which a pure fibre-optic dedicated communication network is being commissioned [51].
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Chapter 4 Architecture of a WAMPAC System
Figure 4.2: The combination of different communication media for a WAMPAC system.
To accommodate the communication needs of different applications, whilst limiting the
cost of the communication network, the physical communication layer of a real
WAMPAC system should be a combination of different communication media, as
shown in Figure 4.2. Power lines, microwave and internet/VPN are suitable connections
for PMUs that serve only real time system operation monitoring and state estimation.
Phone lines could be used to transfer the event data recorded by PMUs for post
disturbance analysis, and a dedicated fibre-optic communication network would be
required for PMUs that serve wide area real time protection and control schemes.
4.3.2 Communication protocols and format for phasor data transmission
Generally, communication protocol is a rule that defines the format and the order of
messages exchanged between two or more communicating entities, as well as the
actions taken on the transmission of the messages. The most frequently used message
transport protocols for power system protection and control are Transport Control
Protocol (TCP), User Datagram Protocol (UDP) and Internet protocol (IP).
TCP/IP provides a highly reliable connection over unreliable networks, using
checksums, congestion control, and automatic resending of bad or missing data. UDP/IP
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Chapter 4 Architecture of a WAMPAC System
is a protocol that provides low-latency communication across networks. However, it
doesn’t provide any error-control or resending of missing or bad data, which brings
more latency [52].
Concerning the phasor data format, the IEEE 1344 Standard only defined the phasor
data formats for PMU to PMU communications. There were extended data formats
based on the IEEE 1344 Standard, such as “PDC-stream”. This was defined and has
been widely used, for data transmission beyond PMUs, i.e. from PMUs to DCs, by EIPP
[48]. At present, the new phasor data protocol IEEE C37.118 defines the data format for
this sort of data transmission beyond PMUs. PMU and DC vendors are using the IEEE
C37.118 and its associated standard to replace IEEE 1344 for PMU manufacturing.
Figure 4.3 presents a schematic of the synchronized data flow in a typical WAMPAC
system. DCs collect time-stamped phasor measurements from PMUs. They then
integrate all of the valid PMU measurements into a single data packet with a unique
timestamp. These packets are encoded using the IEEE C.37.118 protocol or “PDCstream” and then streamed to the phasor data applications [53].
WAN
WAN
WAN/LAN
WAN/LAN
Figure 4.3: Generic schematic of the dataflow in WAMPAC system.
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Chapter 4 Architecture of a WAMPAC System
4.3.3 Communication latency
In a WAMPAC system, communication latency defines how long a packet of phasor
measurements takes to be transferred from one point to another remote point. As shown
in Figure 4.4, if the time stamp marked by PMU/sender is T1 and the time when the
DC/receiver receives the data with time stamp T1 is T2, then the difference between T1
and T2 is the communication latency between the PMU/sender and DC/receiver.
WAN/LAN
WAN/LAN
Figure 4.4: A simple demonstration of communication latency in WAMPAC system.
The main factors that cause communication latency includes raw data (voltage and
current instantaneous measurements) buffering for phasor calculation in the PMU,
distant data transmission over communication links, and signal processing in the central
station. The approximate communication latency in a WAMPAC system can be
estimated by using expression (4.1):
Tt = T f + T p +
L
+θ
R
(4.1)
Where Tt is the total communication delay, Tf is the fixed delay associated with
transducers used, phasor calculation, data concentration and multiplexing, Tp is the link
propagation delay associated with different communication media, L is the amount of
data transmitted, R is the data rate of the link, and θ is the random time delay
component [48].
4.4 Architecture of future GB WAMPAC system
The future GB WAMPAC system will serve three interconnected power transmission
networks, as shown in Figure 4.5, Scottish Power Transmission Network (SPTN),
Scottish Hydro-Electric Transmission Network (SHETN) and National Grid Electricity
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Chapter 4 Architecture of a WAMPAC System
Transmission Network (NGETN). In this system, each power grid has its own DC. In
Each power grid, the DC collects synchronized measurements from PMUs and
processes the data to support the regional SMT applications; whilst, the DC also sends
the collected data to the “Super-DC” to support the wide area real time applications. A
“Super-DC” will be installed in the National Grid monitoring and control centre in
Wokingham. The “Super-DC” collects the synchronized data from the three regional
DCs and process the data for the wide area real time applications, whilst’, the “SuperDC” broadcasts the collected data back to the three regional DCs. With such SMTbased WAMPAC system, each power utility will not only supervise its own regional
system operation but also monitor the operational status of the entire GB power network.
WAN
WAN
Figure 4.5: A general architecture of future GB WAMPAC system.
As introduced in Sections 4.2-4.3, a future GB WAMPAC system will use a number of
different communication technologies for the real time data. For example, in the
Scotland, microwave and satellite communication technologies offer good solutions for
communication between remote substations. The power line technology and wideband
phone lines are competent to support the hybrid state estimation with phasor
measurements, whilst the wide area real time protection and control schemes will be
served by a dedicated fibre-optic communication network.
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Chapter 4 Architecture of a WAMPAC System
4.5 Conclusions
This Chapter has introduced the architecture of a typical WAMPAC system. A Four–
layer architecture is considered to be the most accepted approach for serving WAMPAC,
based on the current international experience with WAMPAC operation. PMUs, DCs,
various communication links and application software are the essential components in a
typical WAMPAC system. As a large scale WAMPAC system, such as the future GB
WAMPAC system, usually involves a number of power utilities; a Super-DC is the key
component supporting wide area real time applications. The different SMT applications
required by the power utilities have different demands, in terms of data management,
reliability and security on the communication networks. Therefore, a WAMPAC system
must accommodate a diverse range of technical requirements and increasing quantities
of PMU data and the requirements of the new WAMPAC participants and clients.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Chapter 5 The Roadmap to the Future GB
WAMPAC System
5.1 Introduction
The previous Chapters stressed that the implementation of a WAMPAC system is the
only choice to guarantee the reliable and secure operation of the future power systems.
With this necessity in mind, this Chapter seeks to develop a roadmap that details the key
steps that must be taken to implement WAMPAC in the future GB power system.
Currently, the reliability of the electric power system in the GB is generally well, and
very few stability problems have been encountered in recent years. As such there is no
urgent demand for the introduction of WAMPAC to solve specific problems [54]. This
has meant that the priorities for the deployment of WAMPAC applications in the GB
electric power system have not yet to be determined. However, in the coming years the
GB power system is entering a time of great change, e.g. the increasing integration of
intermittent renewable generation and complex electricity transmission technology
(HVDC and TCSC) that will make the system ever more unpredictable and difficult to
manage. This time of change offers a good opportunity for the initialisation of GB
WAMPAC project.
The roadmap of GB WAMPAC project, and therefore this Chapter, is separated into
several sections. The first of these is devoted to summarizing the current international
experience with the development of WAMPAC systems. Based on the current
international experience, a generic methodology for determining a roadmap that details
the key steps that must be taken to implement a WAMPAC system will be introduced. It
is then necessary to know the characteristics and problems that will be present in the
future GB power system. After that a roadmap for the GB WAMPAC project will be
developed by combining the knowledge gathered from the generic methodology for
roadmap development with the prototype of the future GB power system.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
5.2 The Roadmap to a WAMPAC System
At this time, a number of power utilities in the world are developing some forms of
WAMPAC system. However, each power utility has its own specific needs, in terms of
both system operation and planning, that have been addressed with the introduction of
WAMPAC. Therefore, each utility has developed individual roadmaps to guide their
WAMPAC projects, and as such, there is currently no generic roadmap for the
development of a WAMPAC system. In addition, as many WAMPAC applications are
still in the research stage of their development the requirements for their practical
implementation have not been clearly defined [55] so the development of a generic
roadmap is further complicated. However, it is generally accepted that the development
of a WAMPAC system requires long term effort; it is impossible to achieve all the
WAMPAC applications in the short term. As Figure 5.1 shows, WAMPAC applications
can be grouped into three ranks based on the level of challenge involved in their
development, i.e. low, medium and high [55]. The features considered in this ranking
process include the difficulty of researching practical solutions for delivering these
WAMPAC applications, the communication technology and data management
requirements of the solution, and the limits of financial investment, etc. Those
applications with a low challenge level are termed “low hanging fruits”; these can be
implemented at the initial stage of a WAMPAC project [55].
Figure 5.1: WAMPAC application tree with full “smart fruits”.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
This three tiered ranking of WAMPAC applications means that it would be logical to
develop a WAMPAC project for the delivery of full “smart fruits” in three stages, as
shown in Figure 5.2, the initial stage (1-3 years), the developing stage (3-5 years) and
the developed stage (5-10 years).
Figure 5.2: Roadmap for deploying PMU applications.
In the initial stage of a WAMPAC project the main objective is the use of synchronized
phasor measurements to afford system operators greater visibility and understanding of
the status of a power system. The best applications to implement at this stage of the
project would be those with fully developed, commercially available solutions (e.g. such
as real time power angle (power flow) monitoring, voltage stability monitoring and
inter-area oscillation monitoring). An additional benefit of these applications is that they
require only limited support in terms of the number of PMUs that must be installed.
This is beneficial as limitations on the available finance means that the number of
PMUs deployed in the initial stage will be modest (around 5).
In the second stage, with the increase of the number of PMUs being commissioned in
the system, the system operators will have a deeper understanding of the power system
dynamics. For example, wide area synchronized fault recordings will significantly
improve system model validation. Consequently, system planning, emergency
protection and control schemes will be optimized. The conventional state estimator
could be upgraded to the faster and more accurate linear state estimator in this stage if
25-30% substations have a PMU installed.
At the developed stage, having developed significant operational experience with PMUs
operating over the course of several years, the system operators and planners will have
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Chapter 5 The Roadmap to the Future GB WAMPAC System
become more confident in their use of using synchronized phasor data. This confidence
and experience will afford the opportunity to develop sophisticated closed loop control
and protection schemes.
In Summary, a generic roadmap for development of a WAMPAC system should meet
the following requirements:
1) The roadmap must have the evolutionary character, i.e. it must assume a
stepwise development of a WAMPAC system.
2) The evolutionary character must be expressed in development of two main
strategies for development of a WAMPAC system: a) the short-term and b) the
long term strategy.
3) The short term strategy must be based on the currently most critical system
needs, which as such will determine the minimum requirements to the
WAMPAC system (e.g. the minimal number of PMUs, the minimum
performance of the communication infrastructure). The WAMPAC applications
for the short term strategy must be well developed and tested.
4) The long term strategy must be based on the expected future system challenges
(risks), which as such must be clearly explored and further used as an input for
development of the future WAMPAC system.
5.3 The Future GB Power System
The renewable energy policy against global warming is bringing significant change to
the electrical power systems in the GB. The biggest change is the high integration of
wind resources in electricity generation. Legislative targets in the UK require that 30%
of electricity will be generated using wind resources by 2020. This target will be
increased to 38% for 2030. Correspondingly, the proportion of power generation
supplied by conventional coal power plants will be reduced to 20% by 2020, and 10%
by 2030; the impact of these targets on the future generation mix in the UK can be seen
in Figure 5.3 [8]. Table 5.1 shows three scenarios that would provide the targeted UK
wind capacity for 2020 [8].
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Figure 5.3: UK energy target 2020 and 2030 [8].
Table 5.1: Three scenarios for meeting the 2020 UK renewable targets [8].
Wind
Capacity
Scenario 1
20.9GW in England and
Wales
11.4GW Scotland
Scenario 2
24.3GW in England and
Wales
8GW Scotland
Scenario 3
25.7GW in England and
Wales
6.6GW Scotland
In these scenarios, the minimum installed capacity of wind turbines in Scotland is 6.6
GW. The majority of the power generated by these wind turbines will be transferred to
the remote load centres in Southern England. Therefore, this large increase in the
generation capacity in Scotland will cause a large increase in the power flow between
Scotland and England [8], as shown in Figure 5.4.
Figure 5.4: Power transfers across the boundary between Scotland and England at peak load
condition [8].
Obviously, the increasing levels of power transfer between Scotland and England will
require substantial power transmission line reinforcements and the deployment of new
technologies to facilitate the transmission of “wind power” from Scotland to England.
To strengthen the power transfer capability at the interface, the National Grid Electricity
Transmission (NGET) and Scottish Power Electricity Network (SPEN) are planning the
installation of Thyristor Controlled Series Capacitors (TCSC) into the inter-tie lines and
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Chapter 5 The Roadmap to the Future GB WAMPAC System
new submarine High Voltage Direct Current (HVDC) links between Scotland and the
North of Wales. Figure 5.5 outlines the proposed locations of the TCSC and the new
HVDC link, which is the prototype of the GB future electric power transmission
network (vision 2020/2030) [10].
Figure 5.5: New TCSC and HVDC in GB transmission networks [10]
Figure 5.6: Locations of off-shore wind farms in GB power system (2020-2030) [8].
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Chapter 5 The Roadmap to the Future GB WAMPAC System
The locations of the off-shore wind farms in the future GB power system are shown in
Figure 5.6. These off-shore wind farms will connect to the GB power grid via back-toback HVDC links. This transmission technology will not allow the wind turbines to
provide inertia to the system [56] [9]. This shortcoming, coupled with the increasing
replacement of conventional generators with wind turbines, will cause the inertia of the
future UK power system to be approximately 15-20% lower than it is currently [57].
The utilization of complex power transmission technology, such as TCSC and HVDC,
and the increasing levels of intermittent and low inertia renewable generation that will
be in use by 2020 and 2030, will cause the GB power system operate in a more complex
and dynamic way. This shift will render the power system more difficult to monitor and
control. Therefore, there is an essential need for the provision of WAMPAC across the
entire power system. This will enable improved visibility and understanding of the
system operational conditions as well as more effective protection and control schemes.
5.4 GB’s strategy for WAMPAC
5.4.1 Short term strategy
As introduced in the previous sections, the generic roadmap for WAMPAC
development and the characteristics of the future GB power system provides a strong
position from which to determine the initial motivations of the GB WAMPAC project.
The applications employed in the initial stage of the GB WAMPAC project should meet
three essential requirements. 1) The number of PMUs employed at the initial stage
should be modest (around 5). This is to accommodate the limitations in the availability
of financial investment and Data Concentrator (DC) capacity. 2) The PMU applications
employed at this stage should be fully developed and commercially available. 3) The
functionality offered by the PMU applications employed at this stage should offer
solutions to immediate system issues.
This methodology for determining the prioritization of PMU applications at the initial
stage of GB WAMPAC project are illustrated in Figures 5.7-5.9. The three essential
requirements are represented as ‘logical filters’ and only those applications that
successfully pass all three filters will be considered for implementation during the initial
stage of introducing WAMPAC to the GB power transmission networks.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Figure 5.7: ‘Logical filter one’ – The number of PMUs required.
Figure 5.8: ‘Logical filter two’ – Commercial availability of PMU applications.
Figure 5.9: ‘Logical filter three’ – Necessity of PMU application for investors.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
With this methodology, the GB WAMPAC project may be initialized in one of the
following ways:
⑴ Wide area power angle and frequency monitoring system
As Figure 5.10 shows, this initial project consists of 6 PMUs, located in Scotland,
Wales, Northern England, Central England, Southern England and Western England.
This simple system will provide system operators real time global system frequency and
power flow monitoring. This is a very user friendly application that has been widely
used by many power utilities in the initial stage of a WAMPAC project.
Figure 5.10: Global power angle and frequency monitoring system.
⑵ Real time monitoring over inter-tie transmission lines
This system consists of 6 PMUs, one installed at both ends and the mid-points of the
two transmission corridors between Scotland and England. In the future, there will be a
huge increase in the power transmission over these transmission lines. This application
will help system operators overcome the challenges posed by increased power
transmission by allowing improved awareness of the real time operating conditions of
the inter-tie lines, e.g. thermal stability and small signal stability (inter-area oscillations).
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Chapter 5 The Roadmap to the Future GB WAMPAC System
The proposed PMU placements for this application are presented in the Figure 5.11.
They are Stratheven, Eccles, Harker, Stella West, Penwortham and Thornton.
Figure 5.11: Real time monitoring system over inter-tie corridors.
5.4.2 Long term strategy
Long term development of the GB WAMPAC system will be driven by the new
operational risks that emerge as the system continues to develop. The characteristics and
potential risks that are likely to be present in the future GB power can be summarized as
follows:
① Wind turbines are not as stable in producing electricity as conventional synchronous
generators (coal, gas and oil). The increasing replacement of conventional generators
with wind turbines will undermine the GB power system’s capability to balance power
generation and demand. As a consequence, the system frequency will change
dramatically after large disturbances occur. Furthermore, as electricity generation from
renewable resources is highly influenced by climatic conditions, the power flow patterns
and generation dispatch schemes of the future GB power system will change quite
frequently.
② The majority of the new wind farms, particularly offshore wind farms, will connect
to the power grid via back-to-back Voltage Source Converters [56]. Hence, they will not
provide inertia to the system. Coupled with the increasing replacement of conventional
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Chapter 5 The Roadmap to the Future GB WAMPAC System
generators with wind turbines the inertia of the future UK power system will be largely
reduced. Low inertia systems will experience extremely fast frequency deviations and
lightly damped low frequency oscillations after disturbances.
Based on these characteristics and potential risks, the long term strategy for a UK
WAMPAC system should focus upon (1) Providing a real time wide area monitoring
system, (2) Improving system frequency stability, and (3) Enhancing system damping
for system small signal stability. For these purposes, three long term SMT applications
are proposed.
⑴ Real time wide area monitoring system
With the proportion of total electricity generation coming from renewable resources
increasing, the future GB power system’s operation will become more dynamic and
unpredictable; correspondingly the power flow pattern and generation dispatch scheme
will change quite frequently. The conventional State Estimator may no longer be
capable of providing a wide area, fast and accurate monitoring system for the next
generation of GB system operation. In this case, the development of a SMT-based real
time Wide Area Monitoring System (WAMS) is a necessity. Figures 5.12- 5.15 present
the PMU placements across the GB electricity transmission network that would serve as
a prototype for the future GB WAMS.
Figure 5.12: PMU placements in SHPTN.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
As Figure 5.12 presents, four substations in Scotland will have PMUs installed. These
are Beauly, Kintore, Errochy and Tealing. As seen from Figure 5.12, these substations
are the big substations that have the maximum number of branches in the Scottish
Hydro Power Transmission Network (SHPTN).
In the Scottish Power Transmission Network (SPTN) and the North part of National
Grid Transmission Network (NGTN), there are seven substations where PMUs will be
installed. They are Stratheven, Eccles, Harker, Stella West, Penwortham and Thornton
and Auchencrosh. As shown in Figure 5.13, six PMUs will be used to monitor the
transmission corridor between Scotland and England, as this is a key corridor in the GB
power system and a very large increase in the power transmission across it. The PMU
installed in Auchencrosh will be used to monitor the electricity transmission between
Northern Ireland and GB.
Figure 5.13: PMU placements at the boundary between Scotland and England.
In central England, there are eight substations where PMU will be installed. They are
Deeside, Daines, Cottam, Derakelow, Feckenham, Pembroke, East Cladon and Pelham.
As seen from Figure 5.14, all these substations are big substations of the 400 kV
transmission networks (represented by blue lines). The installation of PMUs into the
275kV transmission network (represented by red lines) is not recommended as it is
unlikely that the operation of this highly meshed network will be improved through the
use of PMU data.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Figure 5.14: PMU placements in central England.
Figure 5.15 presents the PMU placements in the South of England. The PMU installed
at the Sellindge substation will be used to monitor the power transmission between the
UK and France, the other five PMUs are installed at the Indian Queens, Exeter,
Melksham, Bramley and Lovedean substations for the monitoring of the southern 400kv
transmission network.
Figure 5.15: PMU placements in the South of England.
So far, the proposed PMU placements for monitoring the GB electricity transmission
networks have been presented. In addition, around 30% of the electricity in the future
GB power system will be produced by wind farms; this constitutes a significant amount
of relatively unstable electricity generation that will bring more dynamics to the system.
Therefore, the future GB WAMS should also monitor the operation of wind farms,
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Chapter 5 The Roadmap to the Future GB WAMPAC System
particularly large off-shore wind farms. This monitoring could be delivered by installing
PMUs at the substations shown in Figures 5.16-5.20 that will allow the real time
operational information of the large wind farms to be transmitted to the WAMPAC
control centre. With this real time information, more economical and efficient power
generation dispatch schemes can be developed.
Figure 5.16: A PMU installed in the Torness substation.
Figure 5.17: Three PMUs installed in the Crekey Beck, Keadby and Grimsby West substations.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Figure 5.18: One PMU installed in the Sizewell substation.
Figure 5.19: Two PMUs installed in the North Wales substations of Wylfa and Stanah.
Figure 5.20: A PMU installed in the Alverdiscott substation.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
The PMUs discussed above will form the prototype WAMS for the future GB power
transmission network shown in Figure 5.21. With access to the real time monitoring, the
power system operators will have a clear view of the operational status of the entire
transmission network. In addition, the conventional State Estimator could be updated
significantly due to the integration of a significant amount of precise synchronized data.
Figure 5.21: PMU placements for the future GB wide area monitoring system.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
⑵ Wide area adaptive under-frequency load shedding
Under-frequency load shedding (UFLS) is a common practice for most power systems.
It is used to help prevent large frequency declines when a large disturbance occurs such
as the sudden outage of a large generator [4] [58]. Nowadays, the plans adopted by
power utilities are predominantly deterministic, not taking into account the actual
system state and topology, operating point, or the nature and magnitude of the
disturbance. The frequency measurements are performed locally in distribution
substations, when the frequency drops below the preset point the assigned load feeder
will trip [44]. As a consequence, the existing UFLS plans very often disconnect more or
less load than is required.
Figure 5.22: A SMT-based adaptive UFLS scheme in the future GB power system.
The availability of synchronized wide area measurements provides a great opportunity
for developing an adaptive and efficient UFLS scheme. A conceptual view of an
adaptive UFLS protection scheme for the future GB power system is presented in
Figure 5.22. The adaptive UFLS protection scheme is based on the real time wide area
system frequency measurements and the rate of change of system frequencies. With
known system inertia constant (H) the magnitude of the imbalance between generation
and demand can be immediately estimated after the disturbance [45]. In addition, The
wide are monitoring system can also provide other auxiliary information to support the
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Chapter 5 The Roadmap to the Future GB WAMPAC System
adaptive UFLS protection scheme, for example, real time active power outputs from
wind farms, the power generation reserves of synchronous generators and power flow
condition over the tie-line that connects the generation area and the demand area. With
access to so many real time wide area measurements, system operators would be more
confident when optimizing UFLS protection schemes allowing these schemes to be
more efficient and effective.
⑶ Wide-area inter-area oscillation damping control with power electronic devices
As mentioned above, the huge increase in the power transmission over the transmission
corridors between Scotland and England, coupled with reduced system inertia, will lead
to the system experiencing lightly damped inter-area oscillations. The Thyristor
Controlled Series Capacitor (TCSC) and new submarine High Voltage Direct Current
(HVDC) link installed in the inter-tie transmission corridors can be used to improve the
damping of the inter-area oscillatory mode between Scotland and England if their
controllers are set properly.
Figure 5.23: Inter-area oscillation damping control with power electronic devices in GB power
system.
Figure 5.23 provides a conceptual view of the wide area inter-area oscillation
monitoring and control system in the future GB power system. In order to monitor the
inter-area oscillations accurately, six PMUs will be installed over the critical AC
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Chapter 5 The Roadmap to the Future GB WAMPAC System
transmission lines between Scotland and England. The real time inter-area oscillation
signals, such as power angle difference and system frequency across these transmission
lines will be captured by these PMUs. With the real time information of the inter-area
oscillations the control centre calculates the parameters of the controllers of the power
electronic devices to modulate power flow.
A general procedure for real time inter-area oscillation closed-loop control with HVDC
is presented in Figure 5.24. Six PMUs will be installed across the inter-tie transmission
lines to allow monitoring of the inter-area oscillations, as shown in Figure 5.23.
Measurements of the oscillatory signals, such as active power flow, power angle and
system frequency difference, across the inter-tie transmission lines can be used in the
centralized control centre to generate dynamic firing angles for the converters of the
HVDC transmission system. In such a way, the DC power flow will be dynamically
changed to stabilize the inter-area oscillations.
Figure 5.24: Closed loop inter-area oscillation control using HVDC.
Figure 5.25 presents an alternative procedure that uses TCSC, for real time inter-area
oscillation closed-loop control. As for the HVDC closed loop control scheme, the widearea centralized damping controller will use the real time inter-area oscillatory signals
captured by the six PMUs that are monitoring the inter-tie transmission lines. This
controller will determine a suitable firing angle that will allow the capacity of the TCSC
to vary dynamically to modulate the power flow for damping inter-area oscillations.
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Chapter 5 The Roadmap to the Future GB WAMPAC System
Figure 5.25: Closed loop inter-area oscillation control using TCSC.
5.5 Conclusions
In this Chapter, the methodology of designing a roadmap to guide the GB WAMPAC
project has been introduced. This methodology takes into account the international
experience with WAMPAC project management and the practical challenges faced in
the future GB electric power network. Based on this methodology, the GB’s strategy for
the development of WAMPAC is devised. The GB WAMPAC strategy is divided into a
short term strategy and a long term strategy. In the short term, only a few (5-6) PMUs
will be deployed in the GB power system. This is due to the uncertainties related to the
project and the limitations of financial investment. These PMUs can be distributed
across the entire UK transmission network to form a wide area power angle and
frequency monitoring system. In addition, these PMUs can also be used to monitor the
power flow and inter-area oscillations between Scotland and England. In the long term,
with the increase in the number of PMUs deployed in the UK power system, the
conventional state estimator will be upgraded into a new generation of real time wide
area monitoring using the methodology for PMU placement introduced. In addition, a
wide area adaptive load shedding scheme is proposed. This scheme will help GB power
system to overcome the challenge of reduced frequency stability that will be introduced
by the high integration of renewable resources. The most ambitious element of the long
term strategy for the UK WAMPAC system is the use of HVDC and TCSC to damp the
inter-area oscillations between Scotland and England. Successful development of such
an application would constitute a great achievement in improving the operation of
power systems. This is because it will allow the conventional EMS based open loop
control that is currently in use to be upgraded to a sophisticated wide-area closed loop
control system.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
Chapter 6 The Physical Nature of Inter-area
Oscillations in Electrical Power Systems
6.1 Introduction
In Chapter 5, the proposed GB WAMPAC strategies addressed that the real time interarea oscillation monitoring and control are probably the most anticipated SMT
applications in the future GB power system. In the short term strategy of the GB’s
WAMPAC project, it is recommended that several PMUs will be installed across the
transmission corridor between Scotland and England, to monitor the inter-area
oscillations. In the long term strategy, the new power transmission technologies
deployed in the future UK power system, such as HVDC and TCSC, will be used to
enhance the system’s small signal stability. To support this effort toward real time wide
area inter-area oscillation monitoring and control, a fundamental study of inter-area
oscillations will be provided in this Chapter.
First of all, nonlinear simulations will be used to present the physical nature of
electrometrical oscillations in the time domain. In the nonlinear simulations, different
disturbances will be simulated to initiate different oscillatory modes. From the system
response to these disturbances, the physical phenomenon of power oscillations can be
clearly observed. Having recognised the underlying physical phenomena, a
mathematical analysis technique, modal analysis, that is necessary to predict system
performance will be introduced. Modal analysis is performed in the frequency domain,
which is based on the linearized model of the system around an operational equilibrium.
From the outputs of the modal analysis, such as eigenvalues, eigenvectors and
participation factors, the system dynamic characteristic can be accurately analyzed.
6.2 Nonlinear Simulations
To investigate the physical nature of low frequency electromechanical power
oscillations in the time domain, a model of a typical two-area power system was created.
This two-area system was created by Ontario Hydro for a research report commissioned
by the Canadian Electrical Association [59] [60]. This system was designed to exhibit
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
the different types of oscillations that occur in an interconnected system [59] [60]. This
two-area system can be considered as a useful tool for the study of the
electromechanical oscillations in the GB power system. For this purpose Area 1
represents the Scottish power system and Area 2 represents the English power system.
A single line diagram of the two-area system is shown in Figure 6.1, and the full set of
the system parameters i.e., the generator, transformer and transmission line parameters,
as well as the controller settings of the Automatic Voltage Regulator (AVR) and
Turbine Governor (TG) are given in Appendix A.
Figure 6.1: A typical two-area system.
This simple model shows the electromechanical oscillations that are inherent in the twoarea system. There are three possible electromechanical modes of oscillations in this
system. There are two local modes, one in which generator 1 swings against generator 2,
and another in which generator 3 swings against generator 4. In addition, there is also
one inter-area mode, in which the generators in area 1 swing against the generators in
area 2. In this Section, nonlinear simulations will be used to give an insight into the
nature of these different types of electromechanical oscillations. In these nonlinear
simulations, the different modes of oscillation are initiated using a range of different
disturbances.
6.2.1 Local oscillatory mode in Area 1
To investigate the nature of the local mode in Area 1, changes in the mechanical torque
of the generators in that area were simulated. To properly investigate the behaviour of
the local mode in Area 1 it is important to minimise the excitation of the inter area mode
during these simulations. To achieve this goal, equal and opposite step changes in the
mechanical torque of the two generators in Area 1 were simulated simultaneously. For
example, a change of -0.01 p.u. in the mechanical torque of generator 1 is simulated
then a corresponding change of 0.01 p.u. is made in the mechanical torque of generator
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
2. The response of the generators, in terms of speed, to this pair of small disturbances in
Area 1 is presented in Figure 6.2.
rotor speed [p.u.]
1.0002
G1
1.0001
inter-area mode
observed
G2
1
0.9999
0.9998
' local mode 1' observed
0
2
4
Area 1
6
8
10
time [s]
rotor speed [p.u.]
1.0001
G3
G4
1
0.9999
Area 2
0
2
4
6
8
10
time [s]
Figure 6.2: Generator rotor speed responses to the disturbances occurred in area 1.
In Area 1, the rotor speed changes of generator 1 and 2 were in anti-phase i.e. generator
1 oscillated against generator 2 in the local mode. This local mode dominated the
oscillation for approximately 7s, at which time the generators began to swing together in
the inter-area mode. The generators in Area 2 experienced oscillations with lower
amplitude than those seen in Area 1. These oscillations were in phase with one another
and are driven by the inter-area mode, the local mode in Area 2 was not observed here.
These simulation results show that the frequency of the local oscillation mode in area 1
is approximately 1 Hz.
6.2.2 Local oscillatory mode in Area 2
In this Section, the same method used in Section 6.2.1, to excite the local mode in Area
1, is used to excite the local mode in area 2. An equal and opposite step change of the
mechanical torque of the generators in Area 2 was simulated. The change in the
mechanical torque of generator 3 was -0.01 p.u. and the change in the mechanical
torque of generator 4 was 0.01 p.u.. The generator rotor speed responses to the small
disturbances that occurred in area 2 are shown in Figure 6.3.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
speed [p.u.]
1
1
1
G1
1
0
2
G2
4
Area 1
6
8
10
time [s]
1.0002
speed [p.u.]
G3
G4
inter-area mode observed
1.0001
1
0.9999
0.9998
'local mode 2' observed
0
2
4
Area 2
6
8
10
time [s]
Figure 6.3: Generator rotor speed responses to the disturbances occurred in area 2.
For a small disturbance in Area 2, generator 3 immediately began to swing against
generator 4; this local mode dominated the response for about 5s, after which time the
inter-area oscillatory mode began to dominate. The generators in Area 1 were driven by
the inter-area mode and moved together with oscillations of much lower amplitude than
those seen in Area 2. The frequency of the local mode in Area 2 was approximately
1 Hz.
6.2.3 Inter-area oscillatory mode
The inter-area mode can be directly provoked by changing the mechanical torque of one
generator in each of the different areas. In this case, the mechanical torque of generator
2 was increased by 0.01 p.u. whilst the mechanical torque of generator 4 was reduced by
0.01 p.u.. The generator speed responses to these small disturbances are shown in
Figure 6.4.
speed [p.u.]
1.0004
G1
G2
G3
G4
1.0002
1
0.9998
0
2
4
6
8
10
time [s]
Figure 6.4: Generator rotor speed oscillations dominated by inter-area mode.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
As Figure 6.4 presents, the inter-area mode dominated the response of the generator
rotor speeds to these disturbances. The generators in Area 1 began to swing against the
generators in Area 2 immediately after the disturbances, and the magnitudes of the
speed change of the generators in Area 2 were larger than the magnitudes of the speed
change of the generators in Area 1. Initially the oscillations in Area 1 were strongly
influenced by the local mode. This is evident as for the first 4 seconds the generators in
Area 1 oscillated against one another whilst also moving together in the inter-area mode.
The frequency of the inter-area mode was approximately 0.5 Hz. The inter-area mode
was not damped by any external control and the amplitude of the inter-area oscillation
was seen to increase.
For obtaining more information about inter-area oscillations, the responses of the
system frequency and the inter-area active power flow to the disturbances were
analyzed. Figure 6.5 presents the system frequency response to the disturbances
measured in Area 1 (bus 3) and Area 2 (bus 5). The oscillations in the frequency
deviation in Area 1 were approximately in anti-phase to the oscillations in the frequency
deviation in Area 2; which is consistent with the changes seen in the generator rotor
Frequency [Hz]
speeds in Figure 6.4.
fre-bus3
50.002
fre-bus5
50
49.998
49.996
0
2
4
6
8
time [s]
Figure 6.5: System frequency responses in inter-area mode.
10
Figure 6.6 shows the active power flow over line 3 after the disturbances. The
oscillatory power flow on line 3, is purely driven by the inter-area mode; with no
influence from the local modes. This occurs because the physical mechanism behind
electromechanical oscillations is the active power exchange between the generators that
are involved in the oscillatory mode. Therefore, as line 3, like all of the inter-tie lines,
only carries power between the two areas, then only the inter area oscillations, and not
the local mode oscillations, will be seen on these lines.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
210
P [MW]
P-line3
205
200
0
2
4
6
8
10
time [s]
Figure 6.6: Oscillatory active power flow on transmission line 3.
The power exchange driving the local modes in Areas 1 and 2 occurs along lines 1 and
8 respectively. Therefore, the power flow associated with these local oscillation modes
will only be seen on these lines. To demonstrate this, the power flow on line 1 during
the disturbances is shown in Figure 6.7. The variation of the power flow on line 1 shows
the difference between the power flow that supports the local mode and the power flow
that supports the inter-area mode. This can be seen by comparing the power flow during
the first four seconds after the disturbances, where the local mode dominates, with the
power flow during the next six seconds, where the inter-area mode dominates.
700
P [MW]
inter-area mode observed
695
'local mode 1' observed
690
0
2
4
P-line1
6
8
10
time [s]
Figure 6.7: Oscillatory active power flow on transmission line 1.
6.2.4 Large disturbance
To further examine the characteristics of the inter-area oscillations, a three-phase shortcircuit fault was simulated on bus 4, the mid point of the inter-area lines that connect the
two areas. A short circuit represents a much larger disturbance to the system than the
small mechanical power changes simulated in the previous Sections and as such will
offer greater insight into the behaviour of the oscillatory modes. The transient fault
occurred at 0.1s and was cleared after at 0.2s. The response of the rotor speed of each
generator to the disturbance is presented in Figure 6.8, and the active power transfer
over one of the inter-tie line (line 3) is shown in Figure 6.9.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
rotor speed [p.u.]
1.005
G1
G2
4
6
G3
G4
1
0.995
0
2
8
10
time [s]
Figure 6.8: Responses of the Generator rotor speeds to the large disturbance.
300
P [MW]
P-line3
200
100
0
0
2
4
6
8
10
time [s]
Figure 6.9: Active power transfer over the tie line after the disturbance.
As seen from the Figures 6.8 and 6.9, after the system recovered from the transient fault,
the generators in Area 1 started to oscillate against the generators in Area 2 in inter-area
mode around the new system equilibrium point. The inter-area mode was clearly visible
in the generator rotor speed responses and the oscillatory active power flow on the intertie line.
6.3 Modal Analysis
In Section 6.2, a number of nonlinear simulations were performed to show the physical
nature behind power system oscillations. In the nonlinear simulations the transients
were induced using small disturbances (e.g. a 1% change of mechanical torque), and the
system responses were essentially linear. Although the initial system response to the
three-phase transient fault was nonlinear, the response quickly settled into post fault
oscillations that are essentially linear around the post fault equilibrium point. This
means that, for a study of electromechanical oscillations, the system model can be
linearized around the steady state point. The linearization of the system model provides
an excellent opportunity for modal analysis [59]. Modal analysis can be used to perform
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
a wide range of tasks, such as determining the oscillatory modes, the sources of the
oscillatory modes, and the parameters needed for designing oscillation controllers.
In this Section, the modal analysis will be introduced. This analysis tool will then be
used to explain the physical phenomenon of inter-area oscillations presented in the
Section 6.2.
6.3.1 Dynamic system representation
In power system modelling, the dynamic behaviour of an electrical power system can be
described by a group of first order nonlinear differential equations with the following
form [34]:
•
x = f (x, u)
(6.1)
where
⎡ x1 ⎤
⎢x ⎥
x= ⎢ 2⎥
⎢... ⎥
⎢ ⎥
⎣xn ⎦
⎡ f1 ⎤
⎢f ⎥
f = ⎢ 2⎥
⎢... ⎥
⎢ ⎥
⎣ fn ⎦
⎡u1 ⎤
⎢u ⎥
u = ⎢ 2⎥
⎢... ⎥
⎢ ⎥
⎣u r ⎦
The column vector x is the state vector, its elements xi are the state variables, and n is
the number of system states. The column vector u is the vector of inputs to the system,
and r is the number of inputs. f is the vector of the differential equations.
The outputs of the system can be expressed in terms of the state variables and the input
variables with the following form:
y = g(x, u)
where
⎡ y1 ⎤
⎡g1 ⎤
⎢y ⎥
⎢g ⎥
2 ⎥
⎢
and
y=
g=⎢ 2⎥
⎢... ⎥
⎢... ⎥
⎢ ⎥
⎢ ⎥
⎣ ym ⎦
⎣g m ⎦
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(6.2)
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
The column vector y is the vector of outputs, g is the vector of nonlinear functions for
calculating the system outputs, m is the number of system outputs.
6.3.2 System linearization for modal analysis
If there are a set of state variables x0 and a set of inputs u 0 with which all the derivatives
•
•
•
x1 , x 2 ,…, x n are simultaneously zero, as represented by the equation (6.3), we can say
that the system is at a steady state [34].
•
x 0 = f( x 0 , u 0 ) = 0
(6.3)
If a stable system is disturbed from steady state by a small disturbance, i.e. Δ x and Δ u ,
it will eventually come to rest at a new steady state. This transition will still satisfy
equation (6.1), hence we have
•
x = f[( x 0 + Δx), (u 0 + Δu )]
(6.4)
As the disturbance is assumed to be very small, the nonlinear equation f ( x , u ) can be
approximated using a Taylor series expansion in terms of Δx and Δ u . If we only
consider the first order terms of this expansion we will have:
•
•
•
xi = x i 0 + Δ x i = f i [(x 0 + Δx), (u 0 + Δu)]
= f i (x 0 , u 0 ) +
∂f i
∂f
∂f
∂f
Δx1 + ... + i Δxn + i Δu1 + ... + i Δu r
∂x1
∂xn
∂u1
∂u r
(6.5)
•
Since x i 0 = f i ( x 0 , u 0 ) we have
•
Δ xi =
∂f
∂f i
∂f
∂f
Δx1 + ... + i Δxn + i Δu1 + ... + i Δu r i = 1, 2 ,..., n
∂x1
∂xn
∂u1
∂u r
in the same way based on Equation 6.2, we have
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(6.6)
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
Δy j =
∂g j
∂x1
Δx1 + ... +
∂g j
∂xn
Δxn +
∂g j
∂u1
Δu1 + ... +
∂g j
∂ur
Δur j = 1, 2,..., m
(6.7)
Therefore, the linearized system state equations around the equilibrium point are given
as [34]:
•
Δ x = AΔx + BΔu
(6.8)
Δy = CΔx + DΔu
(6.9)
where
∂f ⎤
⎡ ∂f 1
... 1 ⎥
⎢
⎢ ∂x1 ∂x n ⎥
⎥
A = ⎢...
⎢
⎥
⎢ ∂f n ... ∂f n ⎥
⎢ ∂x
⎥
⎣ 1 ∂x n ⎦
⎡ ∂f 1 ∂f 1 ⎤
...
⎢
⎥
u
∂
∂u r ⎥
1
⎢
⎥
B = ⎢...
⎢
⎥
⎢ ∂f n ... ∂f n ⎥
⎢ ∂u ∂u ⎥
r ⎦
⎣ 1
⎡ ∂g1 ∂g1 ⎤
⎢ ∂x ... ∂x ⎥
n ⎥
⎢ 1
⎥
C = ⎢...
⎥
⎢
⎢ ∂g m ... ∂g m ⎥
⎢⎣ ∂x1 ∂x n ⎥⎦
⎡ ∂g1 ∂g1 ⎤
⎢ ∂u ... ∂u ⎥
r
⎥
⎢ 1
D = ⎢...
⎥
⎥
⎢
⎢ ∂g m ... ∂g m ⎥
⎢⎣ ∂u1 ∂ur ⎥⎦
∆x is the state vector of length n
∆u is input disturbance vector of length r
∆y is the output vector of length m
A is the state matrix of size n × n
B is the input matrix of size n × r
C is the output matrix of size m × n
D is a matrix of size m × r , which defines the proportion of the input which directly
influences the output, ∆y.
The small signal stability of the system can be analyzed by using (6.8) and (6.9). In
other words, the system’s small signal stability can be determined by solving the state
equations.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
6.3.3 Eigenvalues and eigenvectors
The following equation is defined as the characteristic equation of matrix A [34].
det(λI − A) = 0
(6.10)
The n solutions of the characteristic equation λ = [λ1 , λ2 ,..., λn ] are the eigenvalues of A.
The eigenvalues may be real or complex. If matrix A is real, then the complex
eigenvalues occur in conjugate pairs.
For any eigenvalue, λ i , a n-column vector, φi , that satisfies
Aφ i = λi φ i i = 1,..., n
(6.11)
is the right eigenvector of the A matrix associated with the eigenvalue λi . The right
eigenvector φi has the form:
⎡φ1i ⎤
⎢φ ⎥
φ i = ⎢ 2i ⎥
⎢... ⎥
⎢ ⎥
⎣φ ni ⎦
(6.12)
The right eigenvector describes how each mode of oscillation is distributed among the
system states. In other words, it indicates on which system variables the mode is more
observable [61]. The magnitudes of the elements of φ i give the extent of the behaviours
of the n state variables in the ith mode, the angles of elements give the phase
displacements of the state variables with regard to the mode. Thus, the right eigenvector
is called mode shape.
Similarly, if a n-row vector ψ i that satisfies:
ψ i A = λi ψ i i = 1,..., n
-92-
(6.13)
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
It is called the left eigenvector of the A matrix associated with the eigenvalue λi . The
left eigenvector has the form:
ψ i = [ψ i1 ψ i 2 ...ψ in ]
(6.14)
The left eigenvector ψ i can be used to identify which combination of state variables
displays only the ith mode. Thus, the kth element of the right eigenvector φ i measures
the activity of the variable x k in the ith mode, and the kth element of the left
eigenvector ψ i weights the contribution of this activity to the ith mode.
6.3.4 Eigenvalues and small signal stability
The free motion (with inputs remaining constant) of a power system around an
operating point, after a small disturbance, can be described by equation (6.15):
Δx& = A Δx
(6.15)
In the time domain the response of the ith state variable can be described by
Δ x (t ) =
n
∑ φ ψ Δx (0) e λ
i =1
i
i
it
(6.16)
where λi is the ith eigenvalue, φi is the ith right eigenvector, ψ i is the ith left
eigenvector and Δx(0) is the initial state of the state vector Δx . Reference [34] presents
the detailed derivation of equation (6.16). The expression (6.16) defines the free motion
of a power system in terms of the n eigenvalues, and the right and left eigenvectors of
the system, from this equation the following properties of the system response can be
determined using eigenvalues [34].
(1) A real eigenvalue corresponds to a non-oscillatory mode. A negative real
eigenvalue represents a decaying mode, whereas a real positive eigenvalue
represents an unstable mode.
-93-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
(2) Complex eigenvalues always occur in conjugate pairs, and each pair corresponds
to an oscillatory mode. For example, a pair of complex eigenvalues
λi = σ i ± jωi
(6.17)
The real part of the complex eigenvalue gives the damping factor of this
oscillatory mode, and the imaginary part gives the frequency of this oscillatory
mode. A negative real part represents a damped oscillation whereas a positive
real part represents an oscillation with increasing amplitude.
The frequency of oscillatory mode is
f =
ω
(Hz)
2π
(6.18)
A practical measure for the assessment of the damping of oscillations is the
damping ratio, ζ , defined as [34]:
ζ =
−σ
σ 2 + (2πf ) 2
× 100%
(6.19)
The oscillatory modes with a damping ratio less than 3% are the critical modes
that must be improved [34]. When designing damping controls, a stability
margin should be taken into account due to the uncertainties of system operation.
Thus, a damping ratio of at least 5% should be the objective of the control
design [59].
6.3.5 Participation factors
One problem in using right and left eigenvector individually for identifying the
relationship between the states and the modes is that the elements of the eigenvectors
are dependent on the units and scaling associated with the state variables. As a solution
to this problem, a matrix called the participation matrix (P), which combines the right
and left eigenvectors, is used as the measure of the association between the state
variables and the modes.
-94-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
P = [p1 p 2 ...p n ]
(6.20)
⎡ p1i ⎤ ⎡φ1iψ i1 ⎤
⎢ p ⎥ ⎢φ ψ ⎥
p i = ⎢ 2i ⎥ = ⎢ 2i i 2 ⎥
⎢... ⎥ ⎢...
⎥
⎢ ⎥ ⎢
⎥
⎣ p ni ⎦ ⎣φ niψ in ⎦
(6.21)
with
where
φ ki is the kth entry of the right eigenvector φi .
ψ ik is the kth entry of the left eigenvector ψ i .
The element p ki = φ kiψ ik is defined as a participation factor. The product of φ ki and ψ ik
measures the net participation p ki of the kth state to ith mode. This is because φ ki
measures the activity of xk in the ith mode and ψ ik weights the contribution of this
activity to the mode. Calculated in this way, participation factors can be used as a
measure for identifying the source of an oscillatory mode.
6.3.6 Modal analysis for inter-area oscillation study
In this example, we will use the modal analysis to analyze the inter-area oscillations in
typical two-area system. The test system used for this modal analysis is the same system
which was used in Section 6.2 for the nonlinear simulations.
Concerning system modelling for modal analysis, there are twelve states in each
synchronous generator [59] [34]:
(1) Six states for modelling synchronous generator δ - rotor angle, ω -rotor speed,
ψ fd -flux of the excitation system, ψ 1d - flux of the damper winding on d-axis,
ψ 1q - flux of the damper winding 1 on q-axis, ψ 2 q - flux of the damper winding 2
on q-axis.
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Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
(2) Three states for modelling Automatic Voltage Regulator (AVR); vt -voltage
transducer state, v ph -phase shift state and va -amplifier state.
(3) Three states for modelling the Turbine Governor (TG); tg ser -governor servo state,
tg hp -high pressure turbine state and tg rh -reheat stage state.
In steady state, a classic modal analysis is executed. All the eigenvalues corresponding
to the system state matrix are presented in Table 6.1. There are 48 eigenvalues in the
system, the same number as the system state variables. As seen in Table 6.1 there are 8
pairs of complex eigenvalues (shaded), which implies that 8 oscillatory modes exist in
the system.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Table 6.1: Eigenvalues of the two-area system.
Real part
Imaginary Part No.
Real part
Imaginary Part
0
0
25
-10.15465
0
-100.0867
0
26
-5.587707
0
-100.0726
0
27
-5.641435
0
-100.0439
0
28
0.02665295
3.375048
-100.0426
0
29
0.02665295
-3.375048
-37.08784
0
30
-3.539402
0
-37.02837
0
31
-1.668693
1.61424
-35.27151
0
32
-1.668693
-1.61424
-34.43338
0
33
-0.9635185
1.056211
-32.24181
0
34
-0.9635185
-1.056211
-32.37108
0
35
-1.937562
0
-26.28765
0
36
-1.933964
0
-25.23291
0
37
-1.81263
0
-18.74816
0
38
-1.675042
0
-18.78778
0
39
-0.3302784
0.9980652
-17.36206
0
40
-0.3302784
-0.9980652
-16.44011
0
41
-1.108677
0
-0.473808
6.257372
42
-0.4201453
0.644802
-0.473808
-6.257372
43
-0.4201453
-0.644802
-0.4706583
6.30193
44
-0.4050254
0.6372564
-0.4706583
-6.30193
45
-0.4050254
-0.6372564
-10.21898
0
46
-0.1901362
0
-10.20276
0
47
-0.195777
0
-10.15399
0
48
-0.1958579
0
-96-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
The oscillatory modes and their information are presented in Table 6.2. There are three
electromechanical oscillatory modes, two of which have a satisfactory damping ratio (1
and 2) (>5%), and a third that is unstable (shaded). The other five oscillatory modes are
excitation and governor control modes. As shown in Table 6.2, the frequency of the two
local modes is 1Hz, and the frequency of the inter-area mode is 0.54Hz.
Table 6.2: Oscillation modes in the two-area system.
No of oscillatory
mode
No of
Eigenvalue (λ)
1
2
3
4
5
6
7
8
18,19
20,21
28,29
31,32
33,34
39,40
42,43
44,45
Real
imaginary
Frequency
(Hz)
Damping ratio
(%)
-0.4706584 ±6.30193
1.002983
-0.4738081 ±6.257372 0.9958917
0.0266525 ±3.375049 0.5371557
-1.668693
±1.61424 0.2569142
-0.3302784 ±0.9980652 0.1681012
-0.9635178 ±1.056211 0.158847
-0.4201452 ±0.6448019 0.1026234
-0.4050253 ±0.6372563 0.1014225
7.447738
7.550383
-0.78966
71.87365
67.39455
31.41638
54.59233
53.64027
The layouts of the eigenvalues that are associated with the oscillatory modes are
presented in a complex panel (see Figure 6.10). Here, only the eigenvalues that have
positive imaginary part are presented, as the complex eigenvalues always occur in
conjugate pairs.
7
6
local modes
imaginary
5
damping ratio=5%
4
3
2
1
0
-2
inter-area
modes
governor
modes
exciter
modes
exciter
modes
-1.5
-1
-0.5
0
real
Figure 6.10: Oscillatory modes in the two-area system.
-97-
0.5
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
The eigenvalues and the system state matrix are now used to calculate the eigenvectors
and participation factors that correspond to the inter-area oscillatory modes. The
elements of the right eigenvector corresponding to the 28th eigenvalue, which is
associated with the inter-area mode, are given in Table 6.3.
Table 6.3: Right eigenvector for eigenvalue 28 (associated with inter-area mode).
State
State
No.
Magnitudes Phase angles No.
Magnitudes Phase angles
variables
variables
1 G1 δ
0.000
107.24
25 G3 δ
0.514
-4.48
ω
ω
2 G1
0.001
-124.43
26 G3
0.005
90.82
0.027
43.75
27 G3 ψ 1d
0.022
121.14
3 G1 ψ 1d
4
G1 ψ 1q
0.025
162.25
28
G3 ψ 1q
0.054
150.66
5
G1 ψ fd
0.023
74.92
29
G3 ψ fd
0.017
85.03
6
G1 ψ 2 q
0.017
145.31
30
G3 ψ 2 q
0.037
133.71
7
G1 v ph
0.002
101.16
31
G3 v ph
0.000
111.40
8
G1 va
0.052
9.01
32
G3 va
0.015
19.25
9
G1 vt
0.809
164.68
33
G3 vt
0.229
174.92
10
G1 tg ser
0.045
36.97
34
G3 tg ser
0.223
-107.78
11
G1 tg hp
0.023
-22.05
35
G3 tg hp
0.113
-166.80
12
G1 tg rh
0.001
-108.20
36
G3 tg rh
0.007
107.04
13
14
0.032
0.001
-24.28
-129.78
37
38
-4.94
90.90
0.034
44.97
39
G4 δ
G4 ω
G4 ψ 1d
0.472
0.004
15
G2 δ
G2 ω
G2 ψ 1d
0.022
108.72
16
G2 ψ 1q
0.034
154.12
40
G4 ψ 1q
0.054
150.55
17
G2 ψ fd
0.030
71.89
41
G4 ψ fd
0.02
81.26
18
G2 ψ 2 q
0.023
137.17
42
G4 ψ 2 q
0.037
133.61
19
G2 v ph
0.002
98.91
43
G4 v ph
0.001
105.22
20
G2 va
0.065
6.76
44
G4 va
0.023
13.07
21
G2 vt
1.000
162.42
45
G4 vt
0.347
168.73
22
G2 tg ser
0.029
31.62
46
G4 tg ser
0.201
-107.71
23
G2 tg hp
0.015
-27.40
47
G4 tg hp
0.102
-166.72
24
G2 tg rh
0.001
-113.55
48
G4 tg rh
0.006
107.12
-98-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
Figure 6.11 gives the compass plot of the right eigenvector elements associated with
generator speeds. As seen in the compass plot, the speed changes in Area 1 are
approximately in anti-phase with the speed changes in Area 2. Furthermore, the
magnitudes of the right eigenvector components are larger in Area 2, than they are in
Area 1. These characteristics of the inter-area oscillatory mode given by the right
eigenvector are confirmed by the nonlinear simulation results (see Figure 6.4).
90
120
0.004
G3
60
0.003
G4
150
0.005
30
0.002
0.001
180
0
G2
G1
210
330
240
300
270
Figure 6.11: Right eigenvector (mode shape) of inter-area mode.
To obtain more information about the inter-area oscillatory mode, the participation
factors are calculated, as shown in Table 6.4. The participation factors have all been
normalized, so that the largest element is 1.00. This allows the source of the oscillatory
mode to be identified. The states associated with the rotor speed and phase angle of the
generators dominates the inter-area oscillatory mode. The participation factors
associated with the rotor angles and generator speeds are much higher than those
participation factors associated with the other state variables. However, since generator
1 is considered as the reference machine, the participation factor associated with the
rotor angle of generator 1 is zero.
-99-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
Table 6.4: Participation vector for Eigenvalue 28 (associated with inter-area mode).
No.
State variables
Magnitudes
Phase angles
No.
State variables
Magnitudes
Phase angles
0.000
166.68
25
0.00
0.563
-176.82
26
0.496
-177.31
3
G1 ψ 1d
0.009
145.82
27
0.007
42.94
4
G1 ψ 1q
0.011
41.45
28
0.025
-148.78
5
G1 ψ
fd
0.113
-126.54
29
0.082
63.31
6
G1 ψ 2 q
0.012
41.45
30
δ
G3 ω
G3 ψ 1d
G3 ψ 1q
G3 ψ fd
G3 ψ 2 q
1.00
2
δ
ω
G1
0.027
-148.78
7
G1 v ph
0.038
-2.88
31
G3 v ph
0.011
-172.91
8
G1
va
0.025
-27.22
32
G3
va
0.007
162.76
9
G1
vt
0.005
13.82
33
G3
vt
0.001
-156.20
10
G1
tg ser
G1 tg hp
0.009
36.95
34
G3
0.044
71.97
0.024
-40.67
35
tg ser
G3 tg hp
0.118
-5.65
0.005
-109.60
36
G3
-74.59
0.102
144.67
37
0.59
3.32
0.374
-175.00
38
tg rh
G4 δ
G4 ω
0.024
14
tg rh
G2 δ
G2 ω
0.257
-173.44
15
G2 ψ 1d
0.011
148.39
39
G4 ψ 1d
0.007
32.04
16
G2 ψ 1q
0.017
46.94
40
G4 ψ 1q
0.028
-135.88
17
G2 ψ
0.14
-128.22
41
G4 ψ
fd
0.091
61.05
18
G2 ψ 2 q
0.019
46.94
42
G4 ψ 2 q
0.031
-135.88
19
G2 v ph
0.045
-3.78
43
G4 v ph
0.016
-177.58
20
G2
va
0.029
-28.12
44
G4
va
0.01
158.09
21
G2
vt
0.006
12.92
45
G4
vt
0.002
-160.87
22
G2
0.004
34.25
46
G4
75.30
0.011
-43.37
47
tg ser
G4 tg hp
0.028
23
tg ser
G2 tg hp
0.075
-2.32
24
G2
0.002
-112.31
48
G4
0.015
-71.25
1
11
12
13
G1
G1
fd
tg rh
G3
tg rh
6.4 The origin of lightly damped/unstable inter-area
oscillations
Actually, a number of factors influence the inter-area oscillatory mode, such as the type
of excitation control, power flow conditions, transmission network structure and load
characteristics [59] [60]. Since the primary task of excitation control is to ensure voltage
stability or transient stability, once the controller is installed its parameters are rarely
changed [4]. The loads in a power system are distributed all across the entire power
network; this means that it is impossible and not practical to introduce control measures
that use load management to enhance small signal stability. Therefore, this work focuses
upon analyzing the effect of power flow and transmission network parameters on the
inter-area oscillatory mode.
-100-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
To investigate the effect of the inter-area active power flow on the inter-area mode,
modal analysis was executed for a range of inter-area active power flow conditions. The
frequency and damping ratio of the inter-area mode for the different inter-area power
flow conditions are given in Table 6.5. As seen from Table 6.5, the frequency and
damping ratio of the inter-area mode are reduced as the inter-area active power flow is
increased. Figure 6.12 shows how eigenvalues of the system’s oscillatory modes change
with the power flow condition. The arrows represent the direction of the movement of
each eigenvalue that occurs as the inter-area power flow is increased.
Table 6.5: The effect of inter-area power flow on inter-area mode.
Active power flow
(area 1 to area 2, MW)
100
Load in area 2(MW)
Frequency
Damping ratio (%)
1467
0.587
1.235
150
1517
0.586
0.855
200
1567
0.583
0.540
250
1617
0.577
0.262
300
1667
0.567
-0.012
350
1717
0.554
-0.345
400
1767
0.537
-0.789
7
6
local modes
imaginary
5
damping ratio=5%
4
3
inter-area
mode
2
governor
mode
exciter modes
1
0
-1.8
exciter
modes
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
real
Figure 6.12: The effect of inter-area power flow on system oscillatory mode.
0.2
In addition, the effect of the impedance of the inter-tie lines on the inter-area mode was
investigated. The inter-tie lines’ impedance was varied by changing the number of tie
lines. Under the same inter-area power flow conditions but with a different number of
inter-tie lines in service, modal analysis was once more applied to the system. The
frequencies and damping ratios of the inter-area mode in the different cases are given in
-101-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
Table 6.6. In Table 6.6, “0” denotes the scenario in which all four of the inter-tie lines
were in service; whereas “-1” denotes the scenario in which one inter-tie line (line 6)
was out of service due to maintenance. As seen from the results of modal analysis in
Table 6.6, the frequency and damping ratio of the inter-area mode were reduced as the
impedance was increased.
Table 6.6: Effect of inter-tie line impedance on inter-area mode.
0
Power flow
(area 1 to area 2, MW)
100
0.587
1.235
-1
100
0.524
0.634
0
150
0.586
0.855
-1
150
0.522
0.416
0
200
0.583
0.540
-1
200
0.515
0.210
0
250
0.577
0.262
-1
250
0.503
-0.026
Operation scenario
Frequency
Damping ratio (%)
0
300
0.567
-0.012
-1
300
0.487
-0.372
0
350
0.554
-0.345
-1
350
0.463
-2.853
0
400
0.537
-0.789
-1
400
0.428
-2.140
From above analyses, it is clear to conclude that increasing long-distance power
transfers and impedance of the transmission corridor causes the inter-area oscillation to
become lightly damped or even unstable. Here, the increased impedance of a long
transmission corridor is considered as the consequence of the outage of a transmission
line due to maintenance.
6.5 Conclusions
In this chapter, the physical nature of power system oscillations has been investigated in
both the time domain and the frequency domain. In the time domain, a series of
nonlinear simulations were carried out. By using different types of disturbances, the
local modes and the inter-area mode were excited, and the characteristic of each
oscillatory mode was clearly observed. The generator speed and system frequency
response to disturbances are the essential signals for confirming different modes of
oscillations. Whilst the active power flows across different transmission corridors can
be monitored to identify oscillation modes (oscillatory frequency and damping factor).
-102-
Chapter 6 The Physical Nature of Inter-area Oscillations in Electrical Power Systems
In terms of system operation monitoring, these oscillatory signals, such as system
frequencies, active power flows and voltage angles between different buses, can be
directly captured by PMUs installed in substations.
To understand the physical phenomenon of the inter-area oscillation accurately, modal
analysis was applied to the two-area system. Using modal analysis, the information
behind the physical phenomena of inter-area oscillations, such as oscillatory frequency,
damping factor, mode shape and the source of the oscillatory mode, was obtained.
As observed from the modal analysis, the inter-area mode is influenced by inter-area
active power flow conditions and transmission network parameters. A significant
increase of inter-area active power flow and the loss of an inter-tie line will result in
previously stable inter-area oscillations becoming lightly damped or unstable. Therefore,
a real time monitoring and warning system is a key requirement to detect if a power
system is experiencing lightly damped or unstable inter-area oscillations.
-103-
Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
Chapter 7 Inter-area Oscillation Monitoring
Using Newton-Type Algorithm
7. 1 Introduction
Low frequency electromechanical oscillations commonly occur in electrical power
systems, as a consequence of various disturbances and are closely related to generators’
rotor speed oscillations. As presented in Chapter 6, the oscillations associated with a
group of generators in one area swinging against a group of generators in another area
are called inter-area oscillations; and the frequency of inter-area oscillation is typically
in the range of 0.1-0.8 Hz [34]. The observation model of the inter-area oscillations, y(t),
can be represented through the following nonlinear parameter model with three
unknown model parameters:
y (t ) = A ⋅ e (σ + j 2πf ) t
(7.1)
where A is the amplitude of the oscillation, σ is the damping factor and f is the
oscillation frequency. The magnitude of the oscillations decays if σ is negative,
whereas it increases if σ is positive. A practical measure for the assessment of
oscillations is the damping ratio, ζ , defined as:
ζ =
−σ
σ + ( 2πf ) 2
2
× 100%
(7.2)
In order to ensure a sufficient stability margin in the system, the damping ratio ζ
should be greater than 5% [59]. Poorly damped, or unstable oscillations ( ζ smaller than
5%) are a risk since they can lead to undesirable system conditions such as instabilities,
cascading events, or ultimately a catastrophic system blackout. A typical example is the
August 1996 blackout of the western US/Canada interconnected power system [62].
In large interconnected power systems, poorly damped or unstable inter-area
oscillations usually occur between power grids which are weakly connected. Here, the
weak connection refers to two adjacent power grids connected over high impedance
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
transmission lines, or a transmission corridor that was subjected to a sudden, and
substantial change in power flow [59]. To mitigate such catastrophic scenarios, system
operators require reliable, high quality monitoring to establish the presence and
emergence of inter-area oscillations. A SMT-based Wide Area Monitoring System
(WAMS), provide a great opportunity to monitor inter-area oscillations and inform the
operator when the system experiences poorly damped or unstable inter-area oscillations.
Considerable research has been undertaken into developing real-time techniques for
identifying power oscillation modes. The Prony method is one of the most widely used
methods for identification of oscillation modes [63], however, in practical applications
noise elimination and determination of the model order are still a challenge [64], [65],
[66]. The Kalman Filter (KF) has been also utilized for real-time detection of the
dominant oscillation modes [67]. References [68], [69], [70] and [71] present algorithms
associated with the Least Square (LS) method based applications. Fourier Transform
based solutions are proposed in [65] and [72].
This Chapter introduces and tests a new numerical algorithm, Newton Type Algorithm
(NTA), for the real-time estimation of the dominant inter-area oscillation mode [73]. It
has been demonstrated that the NTA provides a robust estimation technique for
processing input signals corrupted by random noise, and in addition the algorithm can
successfully process multiple signals. This is very important for obtaining the inter-area
oscillation mode shape (to detect inter-area oscillations between groups of generators),
which is very important to ensure stability for future bulk interconnected power systems.
The determination of the inter-area oscillation mode shape is a prerequisite for a
advanced control scheme e.g. intelligent controlled islanding.
7.2 Signal Model Representation
The free motion of a power system around an operating point, after a small disturbance,
can be described by the following matrix equation [34]:
x& = Ax
where A is the n × n system state matrix and x is an
(7.3)
n ×1
system state vector. The
solution of (7.3) for the i-th state variable, xi , in terms of the eigenvalues
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
λk = σ k ± jωk (the oscillatory mode) of the system state matrix can be represented as
follows:
n
x i (t ) = A0 + ∑ Ak ⋅ e σ k ⋅t ⋅ sin(ω k t + φ k )
(7.4)
k =1
where A0 is a DC component, Ak is the magnitude of the k-th oscillatory component,
σ k and ω k = 2π f k are the damping factor and the oscillatory frequency, respectively
and φ k is the phase angle of the component. The DC component is included in the
signal model because the signal processed can oscillate around a non-zero value, this
will be shown in the algorithm testing and processing of real data records.
Given a system disturbance, the observation of the response of the i-th state variable xi
can be mathematically modelled through the following general nonlinear equation:
y (t ) = h(x(t ), t ) + ξ (t )
(7.5)
in which ξ (t ) is a zero mean Gaussian random noise, x(t ) is a suitable selected timevarying parameter vector and h(x(t ), t ) is the suitable parameter model of the processed
signal. In this particular case, the model is:
n
h(x(t ), t ) = A0 (t ) + ∑ Ak (t ) ⋅ eσ k (t )t ⋅ sin(ωk (t )t + φk (t ))
(7.6)
k =1
The parameter model (7.6) is obviously highly nonlinear, so to estimate the unknown
model parameters, the nonlinear estimation techniques must be used. Let us define the
following 4n +1 vector of the unknown model parameters, x(t ) , for the signal model
(7.6):
x ( t ) = [ A0 ( t ) A1 ( t ) σ 1 ( t ) ω1 ( t ) φ1 ( t )... Ak ( t ) σ k ( t ) ω k ( t ) φ k ( t )... An ( t ) σ n ( t ) ω n ( t ) φ n ( t )] (7.7)
From the sampled values of the input signal, the following discrete representation of the
above signal model (7.6) can be created:
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
y i = h( x i , t i ) + ξ i
(7.8)
where:
n
h(xi , ti ) = A0,i + ∑ Ak ,i e
σ k , i ⋅t i
k =1
⋅ sin(ωk ,iti + φk ,i ) i = 1,2,...
(7.9)
In (9) A0 ,i , Ak ,i , σ k ,i , ω k ,i , φk,i , ξ k,i and t i refer to the values of A0 (t ) , Ak (t ) , σ k (t ) ,
ω k (t ) , φk (t ) , ξk (t ) and t at the discrete time index i.
If the signal observed ( y (t ) ) is uniformly sampled with the sampling frequency
fs=1/T Hz during a finite period of time (defined as a data window), the value of t at a
discrete time index i is given by ti = iT. From m samples taken during a data window,
with the size Tdw = m × T , a set of the following m nonlinear equations with
4n + 1
unknown parameters can be determined:
y i = h( x i , t i ) + ξ i
(7.10)
where
n
h(xi , ti ) = A0, i + ∑ Ak , i ⋅ e
σ k , i ⋅t i
k =1
⋅ sin(ωk , i ti + φk , i ) i = 1,2,..., m
(7.11)
In the case of m samples belonging to the data window at ti = m × T , (10) can be
expressed in the following vector form:
y = h ( x) + ξ
(7.12)
where y = [ y (1),... y ( m )]T is an m×1 measurement vector, h ( x ) = [ h ( x1 , t1 ),...h( x m , t m )]T
is an m × 1 vector of nonlinear functions given by (7.11) and ξ = [ξ1 ,..., ξ m ]T is an m×1
error vector. The vector equation (7.12) represents a set of m nonlinear equations with
4n + 1 unknowns. It can be solved if m ≥ 4n + 1 using different numerical approaches.
This Chapter demonstrates the use of the NTA for solving the problem stated in (7.12).
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
The solution (the estimates of the unknown model parameters) can be obtained
iteratively, or through a sequential update of estimates obtained from a single data
window. This is presented in the next Section.
7.3 Newton Type Algorithm Derivation
For simplicity, the error vector ξ in (7.12) is temporarily neglected and this expression
has been modified to the following matrix equation:
F ( x) = h ( x) − y = 0
(7.13)
where F(x) is an m×1 vector of a set of suitable selected nonlinear equations (the
processed signal model) and 0 is a m×1 zero vector. The parameter vector x can be
iteratively calculated by solving the nonlinear matrix equation (7.13). The initial guess
xi must be used to initialize the iterative procedure, as presented later. Therefore, in the
first iteration the following can be assumed:
F (x) ≠ 0
(7.14)
There exists an unknown correction vector Δx i , which has to be determined so that the
following holds:
F ( x i + Δx i ) = 0
(7.15)
From the Taylor series expansion of F(x) , linearized in the neighbourhood of xi, the
following expression is obtained:
F(xi + Δxi ) ≅ F(xi ) + J (xi )Δxi
(7.16)
where J ( x i ) is an m × (4n + 1) Jacobian matrix containing the partial derivatives
∂ Fp / ∂ xk (p = 1,...,m and k = 1,…,4n+1). The Jacobian matrix J ( x i ) is defined as:
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
⎡ ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ∂F1 ⎤
⎥
⎢ ∂A ∂A ∂σ ∂ω ∂φ .. ∂A ∂σ ∂ω ∂φ .. ∂A ∂σ ∂ω ∂φ
k
k
k
k
n
n
n
n
⎥
⎢ 0 1 1 1 1
J ( xi ) = ⎢
...
...
...
⎥
⎥
⎢
⎢ ∂Fm ∂Fm ∂Fm ∂Fm ∂Fm .. ∂Fm ∂Fm ∂Fm ∂Fm .. ∂Fm ∂Fm ∂Fm ∂Fm ⎥
⎢⎣ ∂A0 ∂A1 ∂σ1 ∂ω1 ∂φ1 ∂Ak ∂σ k ∂ωk ∂φk ∂An ∂σ n ∂ωn ∂φn ⎥⎦
(7.17)
where
∂F p ∂A 0 = 1
(7.18)
∂Fp ∂Ak = eσ k t ⋅ sin(ωk t + φk )
(7.19)
∂Fp ∂σ k = t ⋅ Ak ⋅ eσ kt ⋅ sin(ωk t + φk )
(7.20)
∂Fp ∂ωk = t ⋅ Ak ⋅ eσ k t ⋅ cos(ωk t + φk )
(7.21)
∂Fp ∂ φk = Ak ⋅ eσ k t ⋅ cos(ωk t + φk )
(7.22)
(k=1,…,n), where n is the number of oscillatory components existing in the estimation
model. For simplicity the notation for J(x i ) and F ( x i ) can be simplified to J i and Fi ,
respectively. Taking into consideration the vector ξ , (7.16) can be rewritten as:
J i Δxi ≅ −Fi = −[h(xi ) − y + ξ ] = y − h(xi ) − ξ
(7.23)
Taking into account the error that occurred by neglecting the higher order terms in the
Taylor series expansion, it further follows that:
J i Δx i = y − h(x i ) + ς
where
ς
is an
m ×1
(7.24)
error vector that includes the error vector ξ and the errors produced
by neglecting the higher order terms in Taylor’s series expansion. By minimizing the
sum of the square of the errors in (7.24), the following unknown correction vector Δxi
can be obtained:
Δx i = ( J Ti J i ) −1 J Ti [ y − h ( x i )] = J i# [ y − h ( x i )]
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(7.25)
Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
where J i# is the left pseudo-inverse of J i . By adding the corrective vector to the
original guess, xi, one obtains:
x i +1 = x i + Δx i = x i + J i# [ y − h ( x i )]
(7.26)
The above equation is essential to the NTA. Typically, the iterative procedure should
stop when all of the unknown parameters in the (i+1)th iteration do not differ from
those in the i-th iteration by more than a specific tolerance, ε, that is defined in advance
by the user, this condition indicates that the optimal solution has been reached.
The algorithm presented in this thesis, like any other nonlinear estimator, may
prematurely converge to a local minimum. Therefore, it is important to make sure that
the initial estimate lies close to the true solution. If the initial estimate from which the
iteration begins is far away from the global minimum, the method may reach one of the
local minima or, in the worst case, totally diverge. To find an appropriate initial starting
point for the NTA, the Fast Fourier Transform (FFT) algorithm is used. The FFT is used
to find the number of dominant oscillatory components, n, in the samples captured in
the initial data window; after that the Least Square (LS) method [74] is used to estimate
the parameters of each oscillatory component, A0 , Ak , σ k , ωk = 2πf k , φk , k = 1,..., n .
Furthermore, the algorithm requires appropriate choice of the following algorithm
parameters: data window size Tdw and the sampling frequency f s . In the next Section the
algorithm’s sensitivity to the selection of data window size and sampling frequency will
be discussed.
7.4 Computer Simulated Tests
In this Section, the NTA is tested by means of the input signals obtained through
computer simulations. In Figure 7.1 the block diagram of the test procedure is given.
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
xk '
xk '
xk
δk
Figure 7.1: A global block diagram of the test procedure.
As shown in Figure 1, Block 1 generates groups of test signals with the signal
parameters x k defined in the INPUT Block. Block 2 represents the NTA applied for the
estimation of unknown parameters. The results of the estimation xk ' (saved in Block 3)
are compared to the actual values of x k and then the error vector δ k = x k − x k ' is
analyzed in Block 4. The results of the error analysis are saved in Block 5. The
computer simulation tests comprise Static tests, Noise tests and Dynamic tests.
7.4.1 Static tests
The test signals were generated in advance using known parameters. The first
representative signal generated for the static tests is described by the following equation:
y (t ) = A0 + A1 ⋅ e σ 1 t ⋅ sin( 2πf 1t + φ1 )
(7.27)
where A0 = 10 , A1 = 5 , σ 1 = −0 .2 , f1 = 0.5 and φ1 = 60 . This signal consists of a DC
component and a single damped oscillatory component, as presented in Figure 7.2. In
this test, the sampling frequency fs = 100 Hz and data window size Tdw = 2 s. Figures
7.3-7.7 present the estimation results of the unknown parameters. Figure 7.8 shows the
comparison between the original signal and the signal that was constructed with
estimated parameters. The estimation errors are practically negligible in all cases,
leading to the conclusion that the algorithm is suitable for the processing of steady state
signals.
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
y(t)
15
10
5
0
2
4
6
8
10
time [s]
Figure 7.2: Computer generated test signal.
A0
Actual
Esti.
10
9.8
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.3: Estimation results of the magnitude of DC component, A0.
Actual
Esti.
A1
5.2
5
4.8
2
3
4
5
6
time [s]
7
8
9
10
damping factor
Figure 7.4: Estimation results of the magnitude of oscillatory component A1.
Actual
Esti.
-0.15
-0.2
-0.25
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.5: Estimation results of the damping factor of oscillatory component, σ .
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
0.52
f [Hz]
Actual
Esti.
0.5
0.48
2
3
4
5
6
time [s]
7
8
9
10
phase angle [deg]
Figure 7.6: Estimation results of the frequency of oscillatory component, f.
60.2
60
Actual
Esti.
59.8
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.7: Estimation results of the phase angle of oscillatory component, φ .
Actual
Esti.
y(t)
15
10
5
0
1
2
3
4
time [s]
5
6
7
8
Figure 7.8: Computer generated test signal and estimated signal.
7.4.2 Noise tests
In this Subsection, the NTA algorithm is tested using computer generated test signals
corrupted by a white zero-mean Gaussian random noise, which was superimposed on to
the magnitude of the input test signal. The random noise standard deviations are
selected to obtain a prescribed value of the Signal-to-Noise-Ratio (SNR), defined as
follows:
SNR = 20 log
-113-
A0
2σ
(dB)
(7.28)
Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
where A0 is the magnitude of the DC component, and σ is the noise standard deviation.
Here, three series of noise tests are performed. In all cases the mean error vector δ k of
the estimation results for the unknown parameters is defined as:
n
δk =
∑x
i =1
k
− xk '
n xk
×100%
(7.29)
where x k represents the actual unknown parameters, and xk ' is the estimated values of
the unknown parameters, n is the number of estimation results.
7.4.2.1 Sensitivity to noise
To test the sensitivity of the NTA to random noise, signals with different white noise
level (i.e. different SNRs) were processed. The SNR was varied in the range 30-90 dB.
In all tests the sampling frequency used was f s = 100Hz and the data window size was
Tdw = 3s . The results of the sensitivity analysis are presented in Table 7.1. The results
suggest that larger errors are obtained for a higher noise level.
Table 7.1: Sensitivity analysis for random noise.
Mean error in the estimation results (%)
Parameters SNR=30 dB SNR= 50dB SNR=70 dB SNR=90 dB
0.6088
0.31985
0.0826
0.0317
A0
A1
58.0023
25.62634
14.8779
5.0705
σ1
39.5772
17.74586
8.7892
3.0651
f1 (Hz)
3.7504
1.55972
0.5360
0.2177
φ1 (deg)
92.0565
36.4835
13.2939
5.2441
7.4.2.2 Sensitivity to sampling frequency
The second test considers the impact of the data sampling frequency on the quality of
the NTA estimation. The test signal was corrupted by an additive white noise with
SNR = 50 dB . The data window size was set to Tdw = 3s . The results (summarized in
Table 7.2) indicate that for a higher sampling frequency better estimation results are
obtained. However, in practice, the improved accuracy obtained by increasing the
sampling frequency would need to be balanced against the processing time requirements.
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
Table 7.2: Sensitivity analysis for sampling for frequency.
Mean error in the estimation results (%)
fs =100 Hz
fs =200 Hz
fs =500 Hz
Parameters
fs =50 Hz
fs =1000 Hz
A0
0.38549
0.31985
0.17782
0.1412
0.10415
A1
39.34897
25.62634
18.96515
14.54942
12.31657
σ1
22.08241
17.74586
14.90845
9.40634
8.12717
f1 (Hz)
2.60918
1.55972
1.00475
0.52258
0.50971
φ1 (deg)
62.29959
36.4835
23.87996
12.32148
11.9796
7.4.2.3 Sensitivity to data window size
The impact of the data window size, Tdw , on the quality of the estimation was also
studied with a test signal corrupted by a random noise with SNR = 50 dB and sampled
with f s = 100Hz . The results obtained are presented in Table 7.3 and indicate that the
selection of the data window size must be carefully considered, particularly since very
short/long data windows (e.g. 3, or 6 seconds) produce unsatisfactory estimates.
Table 7.3: Sensitivity analysis for data window size.
Parameter
A0
Mean error in the estimation results (%)
Tdw =3 s Tdw =4 s Tdw =5 s
Tdw =6 s
0.31985 0.25163 0.21066
0.19179
A1
25.62634 24.22365
7.45586
7.06324
σ1
17.74586 12.88686
6.91787
5.09057
1.55972
0.75748
0.58151
0.43645
36.4835
15.44149
11.7549
7.3249
f 1 (Hz)
φ1 (deg)
In Figure 7.9, both the estimated and processed noisy signals are presented
( SNR = 50 dB , f s = 100 Hz , Tdw = 3s ), suitably demonstrating that the algorithm is
capable of processing noisy signals.
Actual
Esti.
y(t)
15
10
5
0
1
2
3
4
5
6
7
time [s]
Figure 7.9: Algorithm tracking capabilities in presence of noise.
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
7.4.3 Dynamic tests
In this Section the results from the dynamic testing will be presented. Here the NTA
properties during step changes of signal parameters are investigated. The test signal
defined in (27) had a step change of the damping factor σ (from -0.2 to 0) of the
oscillatory mode at t = 5 s. In this test a sampling frequency of f s = 100Hz was selected,
whereas the data window size was changed in the range of 2-4 seconds. Figure 7.10
illustrates the original test signal. As the damping factor of the oscillatory component
approaches zero at t=5 s, the magnitude of the signal remains constant (undamped
oscillations).
Figures 7.11-15 present the estimation results of the unknown parameters for different
data window sizes. The fastest convergence was obtained with the shortest window size
( Tdw = 2 s ), but with a large estimation deviation during convergence period. As the data
window size was increased accuracy improved, but with slower convergence. Figure
7.16 provides a comparison between the real test signal and the estimated signal
( Tdw = 2 s ).A very high level of correlation can be observed, confirming the algorithm
accuracy.
y(t)
15
10
5
0
2
6
8
10
time [s]
Figure 7.10: Computer generated signal with step change of σ .
12
4
Actual
Tdw=2s
Tdw=3s
Tdw=4s
A0
10
8
6
2
3
4
5
6
7
8
9
10
time [s]
Figure 7.11: Estimation results of the magnitude of DC component, A0, for different Tdw.
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
Actual
A1
15
Tdw=2s
Tdw=3s
Tdw=4s
10
5
0
2
3
4
5
6
7
8
9
10
Figure 7.12: Estimation results of the magnitude of oscillatory component, A1, for different Tdw.
1.5
damping factor
Actual
Tdw=2s
Tdw=3s
Tdw=4s
1
0.5
0
-0.5
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.13: Estimation results of damping factor, σ , for different Tdw.
f [Hz]
0.5
0.4
Actual
Tdw=2s
0.3
Tdw=3s
Tdw=4s
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.14: Estimation results of the frequency of oscillatory component, f, for different Tdw.
phase angle [deg]
400
Actual
Tdw=2s
200
Tdw=3s
Tdw=4s
0
2
3
4
5
6
time [s]
7
8
9
10
Figure 7.15: Estimation results of the phase angle of oscillatory component, φ , for different
Tdw.
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
Actual
y(t)
15
Esti.
10
5
0
1
2
3
4
5
6
7
8
time [s]
Figure 7.16: Dynamic testing: comparison between the actual and estimated signal.
7.5 Dynamic Simulation of a Multi-machine System
More realistic testing of the new algorithm was carried out using a dynamic simulation
of a multi-machine power system. Figure 7.17 presents a block diagram of this test
procedure. The power system was modelled and simulated using the simulation
software ‘DIGSILENT PowerFactory’ [75] (see Block 1). Block 2 represents the
oscillatory signal obtained through the DIGSILENT simulation of a large disturbance in
the test system. The dominant inter-area oscillatory mode estimated by the NTA
(represented by Block 3) is stored in Block 4 and compared with the results obtained
using the Eigenvalue analysis performed by Block 5.
λ =σ ± jω
λ'=σ'±jω'
δ
Figure 7.17: A block diagram of the testing procedure based on dynamic simulation of a multimachine test system.
The simulated two-area power system consists of two active networks in which each
one has two generators (see Figure 7.18). The two active areas are connected via four
AC transmission lines and one HVDC transmission link. The full set of the system
parameters are given in Appendix B.
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
Figure 7.18: Two-area test system with HVDC link.
To provoke inter-area oscillations, at t = 2 s a transient three-phase short circuit fault
was simulated in the middle of the line 5. This transient fault lasted for 0.1 s.
Consequently, after the disturbance, the two groups of generators started to oscillate
against each other, as seen in the generator rotor speed changes presented in Figure 7.19.
rotor speed (p.u.)
1.006
G1
G2
G3
G4
1.004
1.002
1
0.998
0.996
0.994
0
5
10
15
time [s]
20
25
30
Figure 7.19: Generator rotor speed changes after the disturbance.
The generator rotor speed variations are simultaneously analysed using the NTA. These
oscillatory signals were processed with a sampling frequency f s = 100Hz and a data
window size Tdw = 5s . In order to obtain a clear mode shape of the inter-area oscillation
mode and to avoid the influence of the other oscillation modes (e.g. local modes and
control modes), only the oscillatory signals in the range of 10-30 s are considered. In
Figure 7.20, the estimated magnitudes and phase angles of the dominant oscillatory
component of each processed signal are presented in a polar diagram. The estimation
results were updated every two seconds and the polar diagram provides a very clear
view of the shape of the dominant inter-area oscillatory mode. The phase angles of the
oscillatory speeds of the generators in area 1 are in anti-phase with respect to the
oscillatory speeds of the generators in area 2.
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
90
120
60
G2
150
30
G1
180
0.001 0.002 0.003 0
G3
210
330
G4
240
300
270
Figure 7.20: Inter-area oscillatory mode shape estimated by NTA.
For the fault described above, the oscillatory active power flow over one of the AC
inter-tie lines (line 2) is presented in Figure 7.21. This oscillatory signal (from 5 s to
30 s) was processed with the sampling frequency f s = 100Hz and the data window size
Tdw = 5s . In Figures 22-23, the estimated dominant inter-area oscillation mode (damping
factor and frequency) obtained from the oscillatory active power flow is presented. The
estimation results obtained by using the NTA were compared with the Prony method
and Eigenvalue analysis (performed under steady state). In the Prony analysis, an
estimation model with 21 orders was used for better fitting the original oscillatory signal.
As seen from Figures 7.22-23, the results obtained using the NTA are practically the
same as the results obtained using the classical Eigenvalue analysis. Furthermore, it is
demonstrated that the NTA algorithm delivered more accurate and stable estimation
results, compared to the Prony method. This is because the Prony method is based on a
linear approximation technique and the oscillation modes are calculated by solving
independent approximated polynomial equations with the data captured by individual
data windows. In the case of the NTA method, the oscillation unknown parameters are
calculated by the continuous iteration procedure based on a set of partial differential
equations. In the iteration procedure, the estimation results obtained from the previous
sliding data window are the initial points for the next iteration using the data from the
next data window.
In order to eliminate the effects of the weaker high order components in the estimation
model used for Prony method, the sampling frequency of original oscillatory signal was
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
reduced to f s = 5 Hz (data window size Tdw = 5s ); the Prony estimation model was
reduced to have 3 orders, i.e., one DC component and one oscillatory component. The
dominant inter-area oscillation mode (damping factor and frequency) estimated by the
Prony method are shown in Figures 7.24-25. As seen from these plots, the quality of the
estimation of the dominant inter-area oscillation mode was significantly improved. The
estimation results obtained from NTA algorithm are still more accurate and stable than
the results obtained from Prony method. Figure 7.26 presents the reconstructed signal
based on the NTA estimated parameters.
P (MW)
200
100
0
0
5
10
15
time [s]
20
25
30
Figure 7.21: Oscillatory active power (on line 2) after the disturbance.
frequency [Hz]
0.54
0.52
0.5
10
Prony
NTA
Eigen
20
25
30
time [s]
Figure 7.22: Estimated frequency of the inter-area oscillatory mode by NTA and Prony method.
damping factor
15
0
-0.1
-0.2
10
Prony
15
NTA
Eigen
20
25
30
time [s]
Figure 7.23: Estimated damping factor of the inter-area oscillatory mode by NTA and Prony
method.
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Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
frequency (Hz)
0.53
Reduced-order Prony
NTA
Eigen
0.52
0.51
10
15
20
25
30
time [s]
Figure 7.24: Estimated frequency of the inter-area oscillatory mode by reduced-order Prony
damping factor
method and NTA.
0
Reduced-order Prony
NTA
Eigen
-0.05
-0.1
10
15
20
25
30
time [s]
Figure 7.25: Estimated damping factor of the inter-area oscillatory mode by reduced-order
Prony method and NTA.
P (MW)
200
100
Actual
0
0
5
10
15
time [s]
20
Esti.
25
30
Figure 7.26: Estimated oscillatory active power from estimated parameters.
7.6 Real-life Conditions Tests
This Section considers an example of the off-line assessment of the inter-area
oscillations in the GB power network using NTA. On November 8th 2010 at 07:24:00
the sudden disconnection of a large generating unit caused a significant mismatch
between the active power generated and the active power consumed by the system. The
phase angle difference measured between two remote locations in the network
(Glasgow and London) is shown Figure 7.27, along with the system response through
damped inter-area oscillations. The angular differences were recorded by the FlexNet
Wide Area Monitoring System installed in the GB network [76].
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
A post-mortem analysis of the event was performed using the NTA with the sampling
frequency f s = 100 Hz and the data window size Tdw = 5 s , which estimates the
dominant oscillatory frequency and the damping ratio defined to the values illustrated in
Figures 7.28-7.29.
The estimation results from NTA were compared to those of the Prony method. For the
Prony analysis, the sampling frequency was reduced to f s = 5 Hz and the data window
size was Tdw = 5s . Here, the Prony estimation model has 5 orders, i.e., one DC
component and two oscillatory components. As seen from Figures 7.28-7.29, both
methods delivered similar estimation results of the dominant inter-area oscillation mode;
however, the results from the NTA more accurately present the dynamic characteristic
of the system. This can be attributed to the NTA estimating the oscillation parameters
based on the real oscillatory signal rather than a decimated signal. The results have been
validated through a comparison between the real and the estimated signal as given in
Figure 7.30. From this exercise it can be concluded that the NTA is capable of tracking
phase angle [deg.]
the unknown inter-area oscillations parameters.
59
58
57
56
0
2
4
6
8
10
time [s]
frequency [Hz]
Figure 7.27: Oscillatory voltage phase angle difference between Glasgow and London.
Reduced-order Prony
NTA
0.6
0.5
0.4
0.3
5
6
7
8
9
10
time [s]
Figure 7.28: Estimated frequency of inter-area oscillatory mode in the GB network.
-123-
damping ratio [%]
Chapter 7 Inter-area Oscillations Monitoring using Newton-Type Algorithm
40
20
0
Reduced-order Prony
5
6
7
8
NTA
9
10
time [s]
Figure 7.29: Estimated damping ratio of inter-area oscillatory mode in the GB network.
59
Actual
Esti.
y(t)
58
57
56
0
1
2
3
4
5
t (s)
Figure 7.30: Oscillatory signal based on estimated oscillatory parameters.
7.7 Conclusions
This Chapter has presented an NTA algorithm developed for the estimation of inter-area
oscillatory modes. In the static tests, the NTA has been shown to reliably identify the
oscillatory mode in a computer generated signal. The robust nature of the NTA has been
further demonstrated to perform the same duty in the presence of white noise, if the
sampling frequency and data window size are selected properly.
The dynamic capability of the NTA has also been successfully demonstrated by
capturing the dynamic oscillatory mode when the parameters of the test signal
experienced a step change. The performance of the NTA to estimate inter-area
oscillatory modes has been shown to not only corresponded to the results of the
Eigenvalue analysis, but it was also more accurate and stable than the well know
conventional Prony method for both laboratory tests and real condition tests.
The NTA enables the inter-area oscillation mode shape to be observed by processing the
generator rotor speeds, which is an essential application for confirming the swing modes
between different parts of a large system. This work has not been possible from existing
oscillation monitoring methods. The NTA was tested on real recorded data and
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Chapter 7 Inter-area Oscillation Monitoring Using Newton-Type Algorithm
successfully extracted the dynamic oscillation parameters from the oscillations observed
in the GB power system following a large disturbance in 2010.
In summary, the research so far suggests that the NTA is a powerful tool for analyzing
PMU data captured from Wide area monitoring and could be a key constituent of future
WAM applications.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Chapter 8 The Application of Power Electronic
Devices for Damping Inter-area oscillations
8.1 Introduction
Presently, using Power System Stabilizers (PSSs) is the most cost-effective approach for
low frequency power oscillations control [34] [77] [78] [79]. The PSS is used to add
additional damping torque to the generator rotor by controlling the generator’s
Automatic Voltage Regulator (AVR). The inputs to PSSs can be generator rotor speed,
electrical power or terminal bus frequency [80]. These PSSs are effective in stabilizing
local modes, and if accurately tuned may also be effective in stabilizing inter-area
modes. However, the effectiveness of PSSs in damping inter-area oscillations is limited
because inter-area modes are not as highly controllable and observable in the
generator’s local signals [81].
In interconnected power systems, lightly damped or unstable inter-area oscillations
usually occur between power grids which are weakly connected. Here, the weak
connection refers to the stressed transmission lines carrying heavy power flow. In
modern power transmission technology, Flexible AC Transmission Systems (FACTS)
devices and High Voltage Direct Current (HVDC) system are the competitive solutions
to enhance the power transfer capability of the currently stressed transmission lines.
Once these power electronic devices have been installed in the inter-tie lines the
additional inter-area oscillation damping controllers become available [80].
In this Chapter, a wide area inter-area oscillation control scheme designed for the future
GB power system is presented. As the long term GB’s WAMPAC strategy proposes, the
HVDC and TCSC installed in the transmission corridor between Scotland and England
can be used to control the inter-area oscillations. In this Chapter, a process for designing
inter-area oscillation damping controller using power electronic devices is presented.
The typical two-area system will be used to illustrate the damping control design
process. In the two-area system, each generator is equipped with a high gain static
excited exciter and speed governor. There is no PSS installed in the system; thus the
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
system is representative of the sort that may benefit from the use of power electronic
devices for damping inter-area oscillations.
8.2 Modal Analysis for Control
Chapter 6 introduced the process of using modal analysis for analyzing the physical
nature of the inter-area oscillations. Although electrical power systems are essentially
nonlinear systems, we have seen that the oscillation information around an operating
point can be accurately described with a linearized system model [80]. Therefore, we
can use linear control theory, and the system dynamic information obtained from modal
analysis, to control inter-area oscillations. In this section, the details behind the use of
modal analysis for inter-area oscillation control are introduced.
8.2.1 Transfer functions
As presented in Chapter 6, the power system dynamics around an equilibrium point can
be described using the following set of state equations [34]:
•
Δ x = AΔx + B Δu
(8.1)
Δy = CΔx + DΔu
(8.2)
∆x is the state vector of length n
∆u is input disturbance vector of length r
∆y is the output vector of length m
n× n
B is the input matrix of size n×r
C is the output matrix of size m× n
D is a matrix of size m× r defines the proportion of input which directly influences the
A is the state matrix of size
output, ∆y.
The frequency domain representation of these state equations can be defined by taking
their Laplace transforms, as follows:
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
sΔ x ( s ) − Δ x (0) = A Δ x ( s ) + B Δ u ( s )
(8.3)
Δy ( s ) = CΔx( s ) + DΔu ( s )
(8.4)
By rearranging Equation (8.3), we have:
( sI − A ) Δ x ( s ) = Δ x (0) + B Δ u ( s )
(8.5)
Δx(s) = (sI − A) −1[Δx(0) + BΔu(s)]
(8.6)
Thus:
Substituting Δx(s) into equation (8.4) allows the system outputs to be defined as:
Δy(s) = C(sI − A)−1[Δx(0) + BΔu(s)] + DΔu(s)
(8.7)
Since we are only concerned with the transfer function between the system inputs and
outputs, the element Δx(0) can be assumed to be zero. In addition, if we assume that the
system outputs, y (s) , are not a direct function of the inputs, Δu( s ) , (i.e., D=0) then the
open loop transfer function of the system is:
G (s) =
Δy ( s)
= C ( s I − A) − 1 B
Δu( s)
(8.8)
8.2.2 Residue based damping controller design
If we only concern the transfer function between the system single input Δu k (s ) and
single output Δy j (s ) , (8.8) can be changed to:
G(s) =
Δy j (s)
Δu k (s)
n
Ri
i =1
s − λi
= c j ( s I − A) − 1 b k = ∑
(8.9)
where
Ri = c j φi ψ i b k
-128-
(8.10)
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
is the residue of the transfer function between the input Δuk (s ) and the output Δy j (s ) .
c j is the jth row vector of the C matrix and b k is the kth column vector of the B matrix.
φi is the right eigenvector associated with the eigenvalue λi , and ψ i is the left
eigenvector associated with the eigenvalue λi .
A residue describes the sensitivity of the corresponding eigenvalue, λi , to a feedback
control. Figure 8.1 represents the open loop transfer function G ( s) and a positive
feedback control transfer function H(s). For the original open loop control, Δuk (s ) is a
single input and Δy j (s ) is a single output; whereas for the feedback control, Δy j (s ) is
used as an input signal. The output of the feedback control will be used to modify the
input of the original open loop control. When feedback control is applied, the
eigenvalues of the original system are changed according to the rule defined in (8.11)
[82]; Δλi is the shift of the eigenvalue λi caused by the closed loop feedback control.
Δλi = Ri H (λi )
Δuk (s )
+
(8.11)
Δ y j (s )
G(s)
+
H(s)
Figure 8.1: Closed loop system with feedback control.
Figure 8.2 gives a block diagram of a typical feedback damping controller. The
controller consists of an amplification block, a low-pass filter, a washout filter and
several compensation blocks [83].
umax
kd
1
1 + sTm
sTw
1 + sTw
1 + sTlead
1 + sTlag
1 + sTlead
1 + sTlag
umin
Figure 8.2: The structure of a feedback damping control.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
The transfer function of the damping control, H ( s ) , is given by:
⎛ 1
H ( s ) = k d ⎜⎜
⎝ 1 + sTm
⎞ ⎛ sTw
⎟⎜
⎟ ⎜ 1 + sT
w
⎠⎝
⎞ ⎛ 1 + sTlead
⎟⎜
⎟ ⎜ 1 + sT
lag
⎠⎝
⎞
⎟
⎟
⎠
N
(8.12)
where k d is a positive constant gain, Tm is the time constant of the low pass filter
(typically 0.1s) [83] and Tw is the washout time constant (typically 3s-10s) [84]. Tlead
and Tlag are the lead and lag time constants for the N phase-compensation blocks.
As shown in equation (8.11), the distance of the shift of the eigenvalue λi that is caused
by the feedback damping control is proportional to magnitude of the corresponding
residue and the gain of the feedback damping control. The direction of this shift of the
eigenvalue λi depends on the residue’s phase angle and the phase shift across the
feedback control transfer function, H ( s ) .
jω
Ri
Δλi = kd Ri
ϕ H (s )
θR
λi
λinew
σ
Figure 8.3: The shift of an eigenvalue caused a feedback damping control.
An ideal feedback damping control move the selected eigenvalue, λ i , directly into the
left stable area (damping ratio>5%), moving parallel with the real axis. In other words,
the residue’s phase angle, θR , and the phase shift across transfer function of the
feedback control, ϕ H ( s ) , should satisfy the relationship θ R + ϕ H ( s ) = 180 0 . The
compensation angle, ϕ H ( s ) , is predominantly determined by the phase compensation
blocks. The necessary parameter values for Tlead and Tlag , which will properly define
the phase compensation blocks, can be calculated using the following equations:
ϕ H(s) = 180o − θR
-130-
(8.13)
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
ϕH(s) ≤ 60o
⎧⎪1
N=⎨
⎪⎩2
α =
Tlead
Tlag
Tlag =
(8.14)
ϕH(s) ≤ 120o
1 − sin(
=
1 + sin(
ϕ H (s)
N
ϕ H (s)
N
)
(8.15)
)
1
(8.16)
ω α
Tlead = αTlag
(8.17)
where θ R is the phase angle of the residue, R i , and ω (rad/sec) is the oscillation
frequency of the oscillatory mode to be modified.
8.3 Inter-area Oscillation Damping Control with HVDC
In this section, the process for designing a HVDC supplementary controller for damping
inter-area oscillations is presented. For illustrating the application of HVDC damping
control, a typical two-area system with an HVDC link, shown in Figure 8.4, was
constructed using ‘DIgSILENT PowerFactory’. The details of this test system are given
in ‘Appendix C’.
Bus 2
G1
Bus 6
Tr1
Bus 3
Line 1
REC
Line 3
Line 2
Area 1
Line 8
Cap 3
Bus 1
Line 5
Line 4
Line 6
Load 1
G2
Tr2
Tr3
INV Bus 5
DC link
Cap 4
Bus 7
Line 7
Area 2
Load 2
Cap 1
Bus 4
Cap 2
Figure 8.4: A two-area system with HVDC.
-131-
Tr4
G4
G3
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
8.3.1 HVDC transmission system modelling
Generally, the modelling of HVDC transmission systems for power flow and system
stability studies consists of three main parts: 1) Power converter modelling, 2) HVDC
transmission network modelling, 3) HVDC control system modelling. In a HVDC
transmission system, power electronic converters are required to convert electric power
from the AC side to the DC side and then back from the DC side to the AC side. The
DC power flow, transferred over the DC transmission lines, is managed by the HVDC
control system by adjusting the firing angles of the power converters. The details of
HVDC system modelling are presented in the following sections.
8.3.1.1 Power converter modelling
A HVDC system uses power electronic converters to convert electric power from the
AC system to the DC system and vice versa. There are two types of power converters,
Current Source Converters (CSC) and Voltage Source Converters (VSC). The
fundamental design of these two converter technologies is shown in Figure 8.5.
Figure 8.5: Two types of power converters [85].
Modern HVDC transmission technology either uses CSC or VSC as power converters.
The proper selection of converter technology in a HVDC transmission system should be
based on a wide range of factors; a number of which are addressed in the detailed
comparison of CSC and VSC technologies given in [85]. The capacity of the current
VSC technology is currently limited to 250 MW, due to practical limitations of the
electronic switches. This limitation means that CSC technology will be more suitable
for use in the HVDC links that are expected to be installed between Scotland and central
England, as shown in Figure 5.5. This is because the power transferred over the new
HVDC links will be approximate 2000 MW [86] during heavy load condition.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Therefore, in the discussion of modelling presented in this section only the CSC based
technology is only considered.
A detailed introduction and discussion of CSC converter theory and performance is
presented in [34]. We directly move to the introduction of the equivalent circuits of
CSC power converters. A power converter has two operation modes, rectifier mode and
inverter mode. The operation mode of a converter is determined by the firing angle, α,
of the controlled valves. With a firing angle of 0°<α<90° a converter operates in
rectifier mode; whereas when the firing angle is 90°<α<180° a converter operates in
inverter mode. A rectifier converts electric power from the AC system to the DC system;
whereas an inverter converts electric power from the DC system to the AC system.
Figure 8.6 shows the equivalent circuit of a rectifier with one six-pulse bridge.
Rcr
Id
E LL
Vdor cos α
Vdr
Figure 8.6: Rectifier equivalent circuit [34].
V dor =
3 2
π
TE LL
Vdr = Vdor cosα − Rcr I d
Rcr =
3
π
X cr
where:
Vdor is the ideal open circuit direct voltage of rectifier
ELL is the line-line voltage on converter side
T is the transformer ratio
α is the ignition delay (firing) angle
-133-
(8.19)
(8.20)
(8.21)
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Rcr is the commutation resistance of rectifier
Xcr is the commutation reactance of rectifier
Vdr is the dc output voltage of rectifier
Id is the direct current
Figure 8.7 presents the equivalent circuit of an inverter with one six-pulse bridge. The
inverter operation may be described in terms of α; defined in the same way as for the
rectifier but with an ignition (firing) delay angle of between 90° and 180°. However, the
common practice is to describe an inverter using the ignition advance angle β (β=π-α),
instead of α.
Rci
E LL
Id
Vdi
Vdoi cos β
Figure 8.7: Inverter equivalent circuit [34].
V doi =
3 2
π
TE LL
Vdi = Vdoi cos β + Rc I d
Rci =
3
π
X ci
where
Vdoi is the ideal open circuit direct voltage of inverter
ELL is the line-line voltage on converter side
β=π-α is the ignition advance angle of inverter
Rci is the commutation resistance of inverter
Xci is the commutation reactance of inverter
-134-
(8.22)
(8.23)
(8.24)
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Vdi is the dc output voltage of inverter
Id is the direct voltage and current
8.3.1.2 HVDC transmission network modelling
Generally, there are three types of HVDC links: Monopolar links, Bipolar links and
Homopolar links, these are shown in Figures 8.8-8.10. The characteristics of these links
are introduced in [34] and [85]. As shown in Figure 8.8, the Monopolar link uses a main
power transfer conductor and another metallic conductor as the return path. Such a
system has the advantage of low investment costs and offers a reliable return path,
particularly for underground/underwater cable systems [34]. As the UK power system is
planning to use submarine cable technology to implement the new HVDC links between
Scotland and central England, shown in Figure 5.5, this section only studies the
modelling of a Monopolar HVDC transmission system.
Figure 8.8: Monopolar HVDC link [34].
Figure 8.9: Bipolar HVDC link [34].
-135-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Figure 8.10: Homopolar HVDC link [34].
Figure 8.8 shows the three main parts of a Monopolar HVDC transmission network: the
rectifier at the power sending terminal, the inverter at the power receiving terminal and
the DC transmission line. Combining this configuration with the equivalent circuits of
power converters allows the equivalent circuit of a Monopolar HVDC link to be formed.
This equivalent circuit is shown in Figure 8.11 alongside a typical voltage profile of the
equivalent circuit in Figure 8.12.
Rcr
Vdor cos α
RL
Rci
Id
Vdr
Vdi
Vdoi cos β
Figure 8.11: Equivalent circuit of HVDC link [34].
Vdor cos α
Vdr
Vdi
Vdoi cos β
Figure 8.12: Voltage profile of the equivalent circuit of HVDC link [34].
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
The direct current flow in the equivalent circuit of a closed HVDC circuit can be
described by:
Id =
V dor cos α − V doi cos β
Rci + R L + Rci
(8.25)
The sending power at the rectifier terminal is:
Pdr = Vdr I d
(8.26)
The receiving power at the inverter terminal is:
Pdi = Vdi I d = Pdr − R L I d2
(8.27)
8.3.1.3 HVDC control system modelling
From the given equivalent circuit of a HVDC link (see Figure 8.11), it can be seen that
the voltages at the two terminals of the link, and the current across the DC line, can be
controlled by the converters’ internal voltages ( Vdor cosα ) and ( Vdoi cos β ). Thus, if the
open circuit voltages of rectifier and converter are assumed to be constant, by
controlling the firing angle of the rectifier and converter the power flow across the DC
link can be controlled. The HVDC control scheme developed in this section is a simple
form of control. In practical implementation, there are a number of different, and more
complex, control schemes for managing DC power flow; a detailed discussion of these
are given in [34]and [85].
A simplified HVDC control scheme is given in Figure 8.13. In this scheme the amount
of active power to be transferred over the DC link is first determined by the system
operators. Then, the direct voltage at the power receiving terminal is held at 1.0 p.u.
through ‘β control’ of the inverter (see Figure 8.14). In ‘β control’ of the inverter, the
input signal is the error between the voltage reference, Vref , and the real time voltage
measurement, Vmeas . This error is processed using a Proportional-Integral (PI) regulator
to calculate a new value for the firing angle.
-137-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
With the predetermined power transfer and a constant voltage at the inverter terminal,
the direct current through the DC link can be directly calculated. Using this calculated
value as a current reference, the rectifier’s ‘α control’ acts to hold the direct current at
the reference value by adjusting the firing angle α (see Figure 8.15).
β control
α control
I ref
Vref = 1.0 p.u.
Figure 8.13: Basic control scheme of HVDC system.
β max
kp
1
1 + sT f
Vref
Vmeas
ki
s
β
β min
Figure 8.14: Inverter’s β control for constant voltage [80].
α max
kp
1
1 + sT f
I ref
I meas
ki
s
α min
Figure 8.15: Rectifier’s α control for constant current [80].
-138-
α
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
8.3.2 System performance without HVDC damping controller
At a steady state, modal analysis was used to find the system’s oscillatory modes. The
eigenvalues associated with all of the oscillatory modes are shown in Figure 8.16. As
seen from Figure 8.16, there are 8 oscillatory modes in this system and they are all well
damped except for the inter-area oscillatory mode ( λint er = −0.0128 ± j3.212 , damping
ratio = 0.3%).
7
6
local modes
imaginary
5
damping ratio=5%
4
3
inter-area mode
2
exciter modes
1
0
-2
governor modes
exciter modes
-1.5
-1
-0.5
0
0.5
real
Figure 8.16: Oscillatory modes in the two-area system with HVDC.
A nonlinear simulation was performed to show that the inter-area oscillatory mode
under which the generators in the areas swing against each other after disturbances. For
exciting the inter-area mode, the mechanical torque of generator 2 was increased by
0.01 p.u. at 0s, the mechanical torque of generator 4 was simultaneously reduced by
0.01 p.u.. Figure 8.17 shows the generator rotor speed responses to this pair of small
disturbances. The shape of the inter-area mode can be clearly observed in the responses,
i.e. the change of the generator rotor speeds in area 1 are always in anti-phase with the
change of the generator rotor speeds in area 2. Figure 8.18 shows the frequency
response at two locations in the system; one is measured in area 1 (at bus 3) and the
other is measured in area 2 (at bus 5). As seen from Figures 8.17-8.18, the inter-area
mode is not damped.
-139-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
1.0003
G1
speed [p.u.]
1.0002
G2
G3
G4
1.0001
1
0.9999
0.9998
0
5
10
time [s]
15
20
Figure 8.17: Generator rotor speed responses to the small disturbances without HVDC damping
control.
Frequency [Hz]
fre-bus3
fre-bus5
50.005
50
49.995
0
5
10
time [s]
15
20
Figure 8.18: System frequency responses to the small disturbances without HVDC damping
control.
8.3.3 Residue based HVDC damping controller design
Figure 8.19 gives a block diagram of a supplementary damping controller for HVDC.
The input of the supplementary HVDC damping controller is the frequency difference
between area 1 and area 2; one frequency is measured at bus 3 and the other one is
measured at bus 5. The output of this damping controller is used to modify the current
reference of the rectifier’s ‘α control’. Since the DC voltage at the inverter terminal is
held constant by the inverter’s ‘β control’, modifying the current reference of the
rectifier control allows corresponding changes to be made to the active power transfer
over the DC line.
Actually, the input signal selection for the damping controller is not unique. Other
oscillatory signals, such as the power angle and active power across the AC inter-tie
lines; and the voltage magnitude at the ends of the AC inter-tie lines, can also be used.
The inter-area oscillation is associated with the differences between the rotor speed
changes of different groups of generators; these differences can be clearly observed by
-140-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
monitoring system frequencies at different locations (see Figure 8.18). Therefore, the
frequency difference between the two areas is a logical choice for the input signal of the
damping controller.
I ref
α max
kp
1
1 + sT f
I meas
ki
s
α
α min
u max
1
1 + sTm
kd
1 + sTlead
1 + sTlag
sTw
1 + sTw
1 + sTlead
1 + sTlag
umin
Figure 8.19: Rectifier control with supplementary damping control.
Figure 8.20 represents such closed loop system, in which the feedback control has two
input signals, Δy j (s ) and Δyl (s) . Then based on the equation (8.10), the residue of the
open loop transfer function between the system input Δuk (s ) and the system outputs
Δy j (s ) and Δyl (s) can be represented by equation (8.28).
Δuk (s )
+
+
Δ y j (s )
G(s)
H(s)
Δyl (s )
+
−
Figure 8.20: Feedback control with multiple input signals.
Ri = c j φi ψi bk − cl φi ψi bk
(8.28)
where c j and cl is the jth and lth row vector of the C matrix and b k is the kth column
vector of the B matrix. φi is the right eigenvector associated with the eigenvalue λi , and
ψ i is the left eigenvector associated with the eigenvalue λi .
-141-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
As introduced in Section 8.2.2, the phasor angle of the shift of the selected eigenvalue
λi caused by the feedback control should be equal to the sum of θR and ϕ H ( s ) (see Fig.
8.3). Therefore, if the phase shift across the transfer function of the feedback damping
control, at the frequency associated with λi is zero (no phase compensation block is
used in the feedback control), and then the feedback control will move the eigenvalue
λi in the same direction as the residue. Hence, the corresponding movement of the
eigenvalue λi caused by such feedback control can be described by the following
equations:
Δλi = Ri H (λi ) = Δσ + jΔω
(8.29)
Δω
)
Δσ
(8.30)
θ R = ac tan(
where Δλi is the shift of the eigenvalue λi caused by the transfer function of the
feedback control H (λi ) and the residue Ri . Δσ and Δω represent the change of the real
part and imaginary part of Δλi , respectively. This approach for estimating the phase
angle of the residue is illustrated in Figure 8.21.
2
λishift
2
Δλi
Δω
8
6
λi
λ
θ R = ac tan
Δω
Δσ
Δσ
Figure 8.21: An illustration of the estimation of the phase angle of the residue.
In this case, the method shown in Figure 8.21 was used to estimate the phase angle of
the residue. First of all, a simple feedback damping controller was integrated into the
system. This damping controller only consisted of a low pass filter and a washout filter;
no phase compensation blocks are included. Modal analysis was applied for both
k d = 0 and k d = 100 (see Figure 8.14); for both of these gain values the locations of
the eigenvalues that are associated with the inter-area mode are presented in Figure 8.22.
With the shift of the eigenvalue, the phase angle of the residue was estimated to be
68.48 0.
-142-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
3.218
3.217
λint er = −0.01105942 + j3.216411 K d = 100
imaginary
3.216
3.215
3.214
3.213
3.212
3.211
θ shift = 68.480
Kd = 0
λint er = −0.0127485 + j 3.212157
-0.0125
-0.012
-0.0115
-0.011
real
Figure 8.22: An estimation of the residue’s phase angle for HVDC damping control design.
Therefore, to implement an ideal feed back controller (according to equation (8.14))
phase compensation blocks should be included to introduce a phase shift of 111.52 0 at
0.5 Hz (the frequency of inter-area mode). Using equations (8.15-8.19) suitable
parameter values for the tuning of a set of phase compensation blocks can be found; in
this case they are Tlead = 0.1s , T lag = 1 .03 s . The transfer function of the modified
feedback damping controller is represented by the following equation:
⎛ 1 ⎞ ⎛ 10s ⎞ ⎛ 1 + 0.1s ⎞ ⎛ 1 + 0.1s ⎞
H (s) = K d ⎜
⎟⎜
⎟⎜
⎟⎜
⎟
⎝ 1 + 0.1s ⎠ ⎝ 1 + 10s ⎠ ⎝ 1 + 1.03s ⎠ ⎝ 1 + 1.03s ⎠
(8.31)
8.3.4 System performance with a HVDC damping controller
Having integrated the HVDC damping controller into the system, the modal analysis
was repeated and 9 oscillatory modes were found in the system. Analysis of the
participation factors shows that the new oscillatory mode is a HVDC control mode.
Figure 8.23 shows the eigenvalues of the system’s oscillatory modes for different
controller gains. The inter-area oscillatory mode and HVDC control mode are quite
sensitive to the gain of the HVDC feedback damping control; whereas the other modes
are relatively insensitive. As the gain of the HVDC damping controller increases the
poorly damped inter-area oscillatory mode moved directly to the left; whereas the
HVDC control mode moved directly to the right. When the damping controller’s gain
increased to 1600, the inter-area mode started to move back to the right; this means that
the damping ratio of the inter-area mode starts to decrease.
-143-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
7
local
modes
6
damping
ration=5%
imaginary
5
kd=400
kd=800
kd=1400
HVDC control mode
4
3
inter- area
mode
kd=1600
2
governor
mode
1
0
-4
exciter
modes
-3.5
-3
-2.5
-2
exciter
modes
-1.5
-1
-0.5
0
0.5
real
Figure 8.23: Oscillatory modes versus the gain of HVDC damping controller.
Nonlinear time-domain simulations were used to check the ability of the HVDC
damping controller to properly damp inter-area oscillations. At 0 s, the mechanical
torque of generator 2 was increased by 0.01 p.u.; simultaneously the mechanical torque
of generator 4 was reduced by 0.01 p.u.. Figure 8.24 presents the responses of generator
rotor speeds to the pair of disturbances with and without the HVDC damping controller.
In addition, Figure 8.25 presents the responses of the inter-area power flow (line 3) to
these small disturbances with different damping controller gains. These results show
that the larger controller gain is used the larger damping is obtained.
1.0003
1.0003
no control
1.0002
rotor speed [p.u.]
rotor speed [p.u.]
no control
kd=1600
1.0001
1
0.9999
G1
0.9998
0
5
10
15
1.0002
kd=1600
1.0001
1
0.9999
G2
0.9998
20
0
5
time [s]
10
1.0003
20
1.0003
no control
1.0002
no control
rotor speed [p.u.]
rotor speed [p.u.]
15
time [s]
kd=1600
1.0001
1
0.9999
G3
0.9998
0
5
10
15
1.0002
kd=1600
1.0001
1
0.9999
G4
0.9998
20
time [s]
0
5
10
15
20
time [s]
Figure 8.24: Generator rotor speed responses to the small disturbances with and without HVDC
damping control.
-144-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
160
without control
with control kd=400
with control kd=800
with control kd=1600
P [MW]
155
150
145
0
5
10
time [s]
15
20
Figure 8.25: Active power flow (line 3) responses to the small disturbances with and without
HVDC damping control.
The behaviour of the HVDC damping controller during large disturbances was also
tested. At 1 s a permanent three-phase short-circuit fault was simulated at the mid-point
of line 6, after 100 ms the faulted line was disconnected. The response of the generator
rotor speeds to the three-phase fault with, and without a HVDC damping controller are
presented in Figure 8.26. As seen from the simulation results, the HVDC damping
controller has shown its robustness in damping inter-area oscillations after the system is
subject to a large disturbance. In addition, Figure 8.27 presents the responses of the
inter-area power flow (line 3) to the large disturbance with different damping controller
gains. As before, when the controller gain is increased the damping is also increased;
no control
1.005
rotor speed [p.u.]
rotor speed [p.u.]
this allows the system to be stabilized more quickly from the large disturbance.
kd=1600
1
G1
0.995
0
5
10
15
no control
1.005
kd=1600
1
G2
0.995
20
0
5
time [s]
1.015
15
20
1.015
no control
G3
1.01
rotor speed [p.u.]
rotor speed [p.u.]
10
time [s]
kd=1600
1.005
1
0.995
no control
G4
1.01
kd=1600
1.005
1
0.995
0
5
10
15
20
time [s]
0
5
10
15
20
time [s]
Figure 8.26: Generator rotor speed responses to a three-phase fault with and without HVDC
damping control.
-145-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
400
without control
with control kd=400
with control kd=800
300
P [MW]
with control kd=1600
200
100
0
-100
0
5
10
time [s]
15
20
Figure 8.27: Active power flow (line 3) responses to a three-phase fault with and without
HVDC damping control.
8.4 Inter-area Oscillation Control with TCSC
In this section, we will present a process for designing a controller that uses TCSC to
damp inter-area oscillations. The system used for illustrating this application of TCSC
supplementary damping control is given in Figure 8.28. It is similar to the two-area
system used in the previous section (see Figure 8.4). In the mid-point of the additional
AC line there is a TCSC that provides 40% compensation of the line reactance. This test
system was modelled using ‘DIgSILENT PowerFactory’ and further details are given in
Appendix D.
Figure 8.28: Typical two-area system with TCSC.
8.4.1 TCSC modelling
A Thyristor Controlled Series Capacitor (TCSC) is an impedance compensator. It is
added in series to an AC transmission line for the purpose of increasing the power
transfer capability of that transmission line, and controlling power flow [87] [88]. A
-146-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
typical TCSC consists of a series capacitor bank, C, in parallel with a thyristorcontrolled reactor, L, as shown in Figure 8.29.
Figure 8.29: A structure of a typical TCSC.
For power flow and power system stability studies, the effect of the thyristor operation
can be neglected in the simulations. Therefore, for these studies, a TCSC can be
represented using the ideal model shown in Figure 8.30; that consists of a fixed
capacitor in parallel with a variable reactor.
Figure 8.30: An ideal model of TCSC for power system stability study.
Using this ideal model the equivalent circuit of a transmission corridor with TCSC
shown in Figure 8.31 is constructed. In the equivalent circuit the resistance of the
transmission line is neglected. As the equivalent reactance of “line 1” can now be
smoothly changed, by adjusting the reactance of the TCSC, the active power flow
across the two transmission lines can be dynamically regulated.
xTCSC
Pline1
xline1
xline 2
VS
Pline 2
VR
Figure 8.31: An equivalent circuit of the transmission corridor with TCSC.
-147-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
Figure 8.32 gives a block diagram of basic TCSC control. Based on off line power flow
study (see Figure 8.31), the reactance of the variable reactor is calculated to obtain an
expected power flow condition (see Figure 8.30). In addition, TCSC can also play an
important role in improving the damping of low frequency power oscillations. This can
be achieved by adding a damping control that provides a damping signal to change the
reactance dynamically.
xmax
xC ⋅ xTCSC
xC + xTCSC
xTCSC
1
1 + sT f
xreactor
xmin
Figure 8.32: A block diagram of TCSC control.
8.4.2 System performance without TCSC damping controller
At a steady state, modal analysis was used to find the system’s oscillatory modes. The
eigenvalues associated with all of the oscillatory modes are presented in Figure 8.33.
These eigenvalues show that the system is stable, as all of the eigenvalues’ real parts are
negative. However, the damping ratio of the inter-area oscillatory mode (λinter-area = 0.0203107±j4.09283) is only 0.4%, which does not satisfy the requirements of practical
power system operation.
7
6
local modes
imaginary
5
damping
ratio=5%
4
inter-area
modes
3
2
1
0
-2
governor
mode
exciter
modes
-1.5
-1
exciter modes
-0.5
0
0.5
real
Figure 8.33: Oscillatory modes in the two-area system with TCSC.
-148-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
After the modal analysis, a nonlinear simulation was executed in the time domain to
show the inter-area oscillatory mode under which the generators in the areas swing
against each other after disturbances. For exciting the inter-area mode, the mechanical
torque of generator 2 was increased by 0.01 p.u. at 0s, the mechanical torque of
generator 4 was reduced simultaneously by 0.01 p.u.. Figure 8.34 shows the generator
rotor speed responses to this pair of small disturbances. The shape of the inter-area
mode can be clearly observed in the responses, i.e. the change of the generator rotor
speeds in area 1 are always in anti-phase with the change of the generator rotor speeds
in area 2. Figure 8.35 shows the frequency response at two locations in the system; one
is measured in area 1 (at bus 3) and the other is measured in area 2 (at bus 5).
1.0002
speed [p.u.]
G1
G2
G3
G4
1.0001
1
0.9999
0.9998
0
5
10
15
20
time [s]
Figure 8.34: Generator rotor speed responses to the small disturbances without TCSC damping
control.
Frequency [Hz]
50.006
fre-bus3
fre-bus5
50.004
50.002
50
49.998
49.996
0
5
10
time [s]
15
20
Figure 8.35: System frequency responses to the small disturbances without TCSC damping
control.
8.4.3 Residue based TCSC damping controller design
Figure 8.36 gives the block diagram of a TCSC supplementary damping controller. The
input of the damping controller is the frequency difference across the AC transmission
corridor; one is measured in area 1 (at bus 3) and the other is measured in area 2 (at bus
-149-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
5). The output of this damping controller is used to modify the reactance reference of
the TCSC.
xmax
xC ⋅ xTCSC
xC + xTCSC
+
xTCSC
+
1
1 + sT f
xreactor
xmin
u max
Freq area 1
+
1
1 + sTm
kd
-
1 + sTlead
1 + sTlag
sTw
1 + sTw
Freq area 2
1 + sTlead
1 + sTlag
N stages
Limit
u min
Figure 8.36: A block diagram TCSC supplementary damping control.
In this case, the method shown in Figure 8.21 is used to estimate the phase angle of the
residue of the inputs and the output of the system’s open loop transfer function. First of
all, a feedback damping controller is integrated into the system. This damping controller
only consists of a low pass filter and a washout filter; there are no phase compensation
blocks. Modal analysis was applied for two gain values, k d = 0 and k d = 100 . Figure
8.37 presents the locations of the eigenvalues associated with the inter-area mode
obtained from this modal analysis. Using the shift of the eigenvalue, the phase angle of
the residue was estimated to -42.417 0.
4.0932
4.093
imaginary
4.0928
4.0926
k d = 0 λint er = −0.02031065 + j 4.09283
θ shift = −42.417 0
4.0924
4.0922
4.092
4.0918
4.0916
λinter = −0.01913188
+ j4.09175 k = 100
d
-0.0204 -0.0202 -0.02 -0.0198 -0.0196 -0.0194 -0.0192 -0.019
real
Figure 8.37: An estimation of the residue’s phase angle for TCSC damping control design.
In this case, a negative feedback control is used to produce an ideal feed back controller,
based on equation (8.14) the phase compensation blocks of the feedback control should
produce a phase shift of 42.417° at 0.65 Hz (the frequency of the inter-area mode). The
parameters values that produce the necessary compensation were calculated by using
-150-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
equations (8.15-8.19); these values are Tlead = 0.11s , Tlag = 0 .556 s . Hence, we have a
transfer function for the negative feedback damping controller:
⎛ 1 ⎞ ⎛ 10 s ⎞ ⎛ 1 + 0.22 s ⎞
⎟⎟ ⎜⎜
⎟⎟ ⎜⎜
⎟⎟
H (s) = Kd ⎜⎜
⎝ 1 + 0.1s ⎠ ⎝ 1 + 10 s ⎠ ⎝ 1 + 1.38 s ⎠
(8.32)
8.4.4 System performance with TCSC damping controller
Modal analysis was again applied to the two-area system with the addition of the new
TCSC damping controller; the oscillatory modes are shown in Figure 8.38. There were
now 9 oscillatory modes identified in the system. Using participation factor analysis this
new oscillatory mode was confirmed to be a TCSC control mode. Figure 8.38 shows the
changes that occur in system’s oscillatory modes when the gain of TCSC damping
controller is varied. As the gain of the damping controller is increased the poorly
damped inter-area oscillatory mode moves to the left; whereas the TCSC control mode
moves to the right. When the damping controller’s gain, kd , is increased to
approximately 22000 the inter-area mode begin to move back to the right; this means
the damping ratio of the inter-are mode has begun to decrease.
7
local
modes
6
damping
ratio =5%
imaginary
5
4
Kd=22000
Kd=18000
Kd=12000
Kd=6000
TCSC control mode
3
2
governor
mode
exciter modes
1
inter-area
mode
exciter modes
0
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
real
Figure 8.38: Oscillatory modes versus the gain of TCSC damping controller.
Nonlinear simulations were used to demonstrate that the ability of the TCSC damping
controller to move the inter-area mode eigenvalue corresponds to an ability to damp the
inter-area oscillation. At 0 s, the mechanical torque of generator 2 was increased by 0.01
p.u.; simultaneously the mechanical torque of generator 4 was reduced by 0.01 p.u..
Figure 8.39 presents the responses of generator rotor speeds to these small disturbances
-151-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
with and without the TCSC damping control. These results confirmed the TCSC
damping controller’s ability in damping inter-area oscillations. In addition, Figure 8.40
presents the responses of the inter-area power flow (line 3) to these small disturbances
with different damping controller gains. These results show that the larger controller
gain was used the larger damping was obtained.
1.0002
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.0002
kd=22000
1.0001
1
no control
kd=22000
1.0001
1
G1
0.9999
0
5
10
15
0.9999
20
G2
0
5
time [s]
15
20
1.0003
no control
1.0002
rotor speed [p.u.]
rotor speed [p.u.]
1.0003
kd=22000
1.0001
1
0.9999
0.9998
10
time [s]
G3
0
5
10
15
no control
1.0002
kd=22000
1.0001
1
0.9999
G4
20
0.9998
0
5
time [s]
10
15
20
time [s]
Figure 8.39: Generator rotor speed responses to the small disturbances with and without TCSC
damping control.
112
111
110
P [MW]
109
108
107
without control
with control kd=6000
106
with control kd=12000
105
104
with control kd=22000
0
5
10
time [s]
15
20
Figure 8.40: Active power flow (line 3) responses to small disturbance with and without TCSC
damping control.
Furthermore, the damping effect of the TCSC damping controller was also verified for a
large disturbance. At 1 s a permanent three-phase short-circuit fault was simulated at the
mid-point of line 6, after 100 ms the faulted line was disconnected. The response of the
-152-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
generator rotor speeds to the three-phase fault with, and without a TCSC damping
controller are presented in Figure 8.41. As seen from the simulation results, the TCSC
damping controller has shown its robustness in damping inter-area oscillations after the
system is subject to a large disturbance. In addition, Figure 8.42 presents the responses
of the inter-area power flow (line 3) to the large disturbance with different damping
controller gains. As before, when the controller gain is increased the damping is also
increased; this allows the system to be stabilized more quickly from the large
disturbance.
1.003
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.003
kd=22000
1.002
1.001
1
G1
0.999
0
5
10
15
no control
kd=22000
1.002
1.001
1
G2
0.999
20
0
5
no control
1.004
kd=22000
1.002
1
0.998
G3
0
5
10
15
20
time [s]
rotor speed [p.u.]
rotor speed [p.u.]
time [s]
10
15
no control
1.004
kd=22000
1.002
1
0.998
20
G4
0
time [s]
5
10
15
20
time [s]
Figure 8.41: Generator rotor speed responses to a three-phase fault with and without TCSC
damping control.
110
100
90
P [MW]
80
70
60
without control
50
with control kd=6000
with control kd=12000
40
with control kd=22000
30
20
0
5
10
time [s]
15
20
Figure 8.42: Active power flow (line 3) responses to a three-phase fault with and without TCSC
control.
-153-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
8.5 Inter-area Oscillation Control with SVC
In this section, a fundamental study of using SVC for damping inter-area oscillations
will be presented. The system used for testing the SVC damping control is shown in
Figure 8.43. There is a SVC connecting to Bus 5. The SVC acts to hold the voltage
magnitude of Bus 5 close to 1.0 p.u.. This test system was modelled using ‘DIgSILENT
PowerFactory’ and details of it are given in Appendix E.
Figure 8.43: Modified two-area system with SVC.
8.5.1 SVC modelling
A Static Var Compensator (SVC) is a shunt-connected static reactive power
compensation component that is originally designed to ensure that the bus voltage is
held close to a set value. Here, the term ‘static’ is used to indicate that an SVC, unlike
synchronous machines, has no rotating components [34] [88]. Figure 8.44 shows the
structure of a typical SVC: it consists of a shunt capacitor bank and a thyristor
controlled shunt reactor.
Figure 8.44: A structure of a typical SVC.
-154-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
For power flow, and power system stability studies, a SVC can be modelled using the
circuit diagram shown in Figure 8.45. This model represents an ideal SVC; which
consists of a fixed capacitor connected in parallel with a variable reactor. By controlling
the reactance value of the reactor, the SVC releases or absorbs reactive power
dynamically to ensure the voltage stays in an acceptable range.
Figure 8.45: An ideal model of SVC.
Figure 8.46 gives a block diagram of SVC control. Under steady states, the SVC
controller uses the difference in magnitude between the reference voltage and the
measured voltage to determine the adjustment of the reactive power (Q) output of the
SVC. These adjustments act to hold the local voltage close to the reference voltage;
however, SVC can also be used to improve the system’s small signal stability if the
parameters of the controller are set properly.
Vref
VSVC
Qmax
Qfixed
k
1
1 + sT f
1 + sTa
1 + sTb
QSVC
Qmin
Figure 8.46: Block diagram of SVC control [34].
8.5.2 System performance without SVC damping controller
At a steady state, modal analysis was applied to find the system’s oscillatory modes.
The eigenvalues associated with all of these oscillatory modes are presented in Figure
-155-
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
8.47. As shown in Figure 8.47, the system is unstable as the there is an unstable interarea oscillatory mode (λinter-area = 0.02996345 ± j3.416078) in the system.
7
6
local modes
imaginary
5
damping ratio= 5%
4
inter-area
mode
3
2
governor
mode
exciter modes
1
0
-2
exciter modes
-1.5
-1
-0.5
0
0.5
real
Figure 8.47: Oscillatory modes in the two-area system with SVC.
A nonlinear simulation was used to demonstrate that the inter-area mode, identified by
the modal analysis, would cause the system to become unstable. At 0s, the mechanical
torque of generator 2 was increased by 0.01 p.u., simultaneously the mechanical torque
of generator 4 was reduced by 0.01 p.u.. Figure 8.48 shows the generator rotor speed
responses to this pair of small disturbances. Figure 8.49 shows the voltage angle
difference across the inter-are transmission corridor (line 3 and line 5) during the
disturbances. As seen from the simulation results, the inter-area mode was not damped.
G1
speed [p.u.]
1.0004
G2
G3
G4
1.0002
1
0.9998
0.9996
0
5
10
time [s]
15
20
Figure 8.48: Generator rotor speed responses to the small disturbances without SVC damping
control.
-156-
phase angle [deg]
Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
phase angle (between bus3&bus5)
26
25
24
23
0
5
10
time [s]
15
20
Figure 8.49: Oscillatory voltage angle difference between bus3 and bus5 caused by the
disturbances.
8.5.3 Residue based SVC damping controller design
Figure 8.50 gives a block diagram of a SVC supplementary damping controller. In this
case, the voltage angle difference between bus3 and bus5 (see Figure 8.49) was selected
to be the input of the damping controller. The output of this damping controller was
used to modify the local voltage reference of the primary SVC control.
Vref
VSVC
Qmax
Qfixed
1
1 + sT f
1 + sTa
1 + sTb
k
QSVC
Qmin
u max
kd
1
1 + sTm
sTw
1 + sTw
1 + sTlead
1 + sTlag
1 + sTlead
1 + sTlag
u min
Figure 8.50: A block diagram of a SVC damping controller.
For the SVC damping control design, the method presented in Figure 8.20 was used to
estimate the phase angle of the residue of the system’s open loop transfer function
between the inputs and the output. First of all, a feedback damping controller was
integrated into the system; this damping controller only consisted of a low pass filter
and a washout filter, no phase compensation blocks were used at this time. Modal
analysis was performed twice, once with k d = 0 and again with k d = 0.01 . Figure 8.51
presents the locations of the eigenvalues associated with the inter-area mode obtained
from the modal analysis. With the shift of the eigenvalue, the phase angle of the residue
was estimated to be -46.095°.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
3.42
k d = 0 λinter −area = 0.02996345 + j 3.4116078
3.415
θ shift = −46.095 0
imaginary
3.41
3.405
3.4
3.395
kd = 0.01
3.39
λinter −area = 0.05412006 + j 3.39098
3.385
3.38
0.025
0.03
0.035
0.04 0.045
real
0.05
0.055
0.06
Figure 8.51: An estimation of the residue’s phase angle for SVC damping control design.
In this case, we used negative feedback control. To implement an ideal feedback
controller, according to equation (8.12), the phase compensation blocks of the feedback
control should introduce a phase shift of 46.095 0 at 0.54 Hz (the frequency of the interarea mode). The parameters values that deliver such a phase shift were and Tlead = 0.22 s ,
Tlag = 1.38 s , these were determined using equations (8.13-8.17). Hence, the transfer
function of the negative feedback damping controller is:
⎛ 1 ⎞ ⎛ 10 s ⎞ ⎛ 1 + 0.22 s ⎞
⎟⎟ ⎜⎜
⎟⎟ ⎜⎜
⎟⎟
H (s) = K d ⎜⎜
+
s
+
s
+
s
1
0
.
1
1
10
1
1
.
38
⎝
⎠⎝
⎠⎝
⎠
(8.33)
8.5.4 System performance with SVC damping controller
Modal analysis was again performed for the two-area system, but the new SVC
damping controller was used. There were now 9 oscillatory modes in the system.
Participation factor analysis confirms that this new oscillatory mode was a SVC control
mode. Figure 8.52 shows the changes that occurred in the system’s oscillatory modes
when the gain of the SVC damping controller was varied.
As seen in Figure 8.52, when the gain of the damping controller is increased the
unstable inter-area oscillatory mode moves to the left; whereas the SVC control mode
moves to the right. Furthermore, two exciter modes move to the left as well as the interarea mode. However, when the damping controller’s gain, kd , is increased to
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
approximately 1.0, the two exciter modes begin to move back to the right, and the
damping factor of the SVC control mode becomes less than the damping factor of the
inter-area mode. Therefore, to obtain an optimum set of parameters for the existing
system controllers the gain of the SVC damping controller was set to kd = 1.0 .
7
6
local
modes
imaginary
5
4
kd =1.2
kd =1.0
3
inter-area mode
kd =0.8
2
0
-4
exciter
modes
kd =0.8 kd =1.0
kd =0.8
kd =1.0
-3.5
-3
-2.5
kd =0.2
kd =0.5
SVC control mode
1
damping
ratio=5%
governor
mode
exciter
modes
kd=1.0
-2
-1.5
-1
-0.5
0
0.5
real
Figure 8.52: Oscillatory modes versus the gain of SVC damping controller.
To confirm that the SVC damping controller can prevent the system from becoming
unstable, by damping the inter-area oscillations, nonlinear simulations were used. At 0s,
the mechanical torque of generator 2 was increased by 0.01 p.u.; simultaneously the
mechanical torque of generator 4 was reduced by 0.01 p.u.. Figure 8.53 presents the
responses of generator rotor speeds to these small disturbances with and without the
SVC damping controller. These simulation results confirmed the SVC supplementary
controller’s ability in damping inter-area oscillations. In addition, Figure 8.54 presents
the responses of the inter-area power flow (line 3) to these small disturbances with
different damping controller gains. These results show that the larger controller gain
was used the larger damping was obtained.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
1.0003
no control
1.0003
G1
rotor speed [p.u.]
rotor speed [p.u.]
1.0004
kd=1
1.0002
1.0001
1
0.9999
0
5
10
15
no control
1.0002
kd=1
1.0001
1
0.9999
20
G2
0
5
no control
1.0005
G3
kd=1
1
0.9995
0
5
10
10
15
20
time [s]
rotor speed [p.u.]
rotor speed [p.u.]
time [s]
15
20
no control
1.0005
G4
kd=1
1
0.9995
0
5
time [s]
10
15
20
time [s]
Figure 8.53: Generator rotor speed responses to the small disturbances with and without SVC
damping control.
215
P [MW]
210
205
200
without control
195
with control kd=0.2
with control kd=0.5
with control kd=1.0
190
0
5
10
time [s]
15
20
Figure 8.54: Active power flow (line 3) responses to small disturbance with and without SVC
damping control.
The robustness of the SVC damping controller to large disturbances was also tested. At
1 s a permanent three-phase short-circuit fault was simulated at the mid-point of line 6,
after 100 ms the faulted line was disconnected. The response of the generator rotor
speeds to the three-phase fault with and without a SVC damping controller are
presented in Figure 8.55. As seen from the simulation results, the SVC damping
controller has shown its robustness in damping inter-area oscillations after the system is
subject to a large disturbance. In addition, Figure 8.56 presents the responses of the
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
inter-area power flow (line 3) to the large disturbance with different damping controller
gains. As before, when the controller gain was increased the damping was also
increased; this allowed the system to be stabilized more quickly from the large
no control
G1
1.005
rotor speed [p.u.]
rotor speed [p.u.]
disturbance.
kd=1
1
0.995
0
5
10
15
kd=1
1
0.995
20
no control
G2
1.005
0
5
time [s]
15
20
time [s]
1.02
1.02
no control
G3
rotor speed [p.u.]
rotor speed [p.u.]
10
kd=1
1.01
1
0.99
no control
G4
kd=1
1.01
1
0.99
0
5
10
15
20
0
5
time [s]
10
15
20
time [s]
Figure 8.55: Generator rotor speed responses to a three-phase fault with and without SVC
damping control.
350
300
250
P [MW]
200
150
100
without control
50
with control kd=0.2
with control kd=0.5
0
-50
with control kd=1.0
0
5
10
time [s]
15
20
Figure 8.56: Active power flow (line 3) responses to a three-phase fault with and without SVC
damping control.
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Chapter 8 The use of Power Electronic Devices for Damping Inter-area oscillations
8.6 Conclusions
In this Chapter, a process for designing inter-area oscillation damping controller using
power electronic devices is presented. The results of the damping analyses performed
here, in both the frequency and time domain, demonstrate that the proper control of
HVDC, TCSC and SVC installed in the inter-area power transmission corridor can
significantly improve the damping of the inter-area oscillation mode. The conventional
modal analysis carried out in the frequency domain can be used to find the optimum set
of parameters for the system controllers, i.e. the operation point with maximum
damping. Nonlinear simulations can be used to assist the conventional eigenvalue
analysis. These simulations confirm the ability of the damping controllers, designed in
the frequency domain, to provide additional damping to the system robustly.
The selection of the input signals that feed the damping controllers is not unique; it is
dependent on the observability of the inter-area oscillation mode extracted from the
selected input signals. In this chapter, the frequency difference and voltage angle
difference across the inter-area power transmission corridor were tested as the input
signals for the damping controllers. In practical implementation, these wide area signals
can be successfully captured by PMUs and sent to the centralized control centre via high
speed communication network.
The robustness of the damping controllers was only tested through a single large
disturbance at one operating condition. However, the damping controllers designed
based on the conventional linear control theory often only work within a limited
operating range. For real power system operation, variable operating conditions and
different contingencies may reduce the effect of the existing damping controllers, and
allow lightly damped or even unstable inter-area oscillations to exist. Therefore, for real
implementations, a large number of simulations should be performed to confirm the
robustness of the damping controllers at variable operating conditions and for different
contingencies.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Chapter 9 Wide Area Monitoring and Control
System (WAMCS) in a Future GB Power System
9.1 Introduction
In this Chapter, a proposed Wide Area Monitoring and Control System (WAMCS) for a
future GB power system is presented. This WAMCS is designed to enhance the
system’s small signal stability, i.e. monitor and improve the damping of the inter-area
oscillatory mode between Scotland and England. The motivation to establish such a
system was introduced in Chapter 5 (Strategies of GB WAMPAC project).
This WAMCS combines the applications of Wide Area Monitoring (WAM) and Wide
Area Control (WAC). It consists of two real time applications, 1. real time inter-area
oscillation monitoring using Newton Type Algorithm (NTA), 2. real time inter-area
oscillation damping control using HVDC. These two applications were introduced and
tested using a typical two-area system in Chapters 7 and 8.
In this Chapter, the operation of the proposed WAMCS will be demonstrated using a
full model of the future GB power system (vision 2015). This model was created in the
DIgSILENT PowerFactory software package. In addition to the demonstration of the
major applications, some key factors that will influence the operation of the wide area
inter-area oscillation damping control scheme will be tested and discussed in this
Chapter. These factors include the time delay involved in wide area data transmission,
and the reactions between the additional HVDC damping controller and conventional
Power System Stabilizers (PSSs).
9.2 Assessment of the Inter-area Oscillations in GB Power
System
9.2.1 GB power system modelling
A GB power system model (vision 2015) used for the GB WAMPAC study was
constructed in DIgSILENT PowerFactory. This system consists of three areas, the
Scottish Power Transmission Network (SPTN), the Scottish Hydro-Electric
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Transmission Network (SHETN) and the National Grid Electricity Transmission
Network (NGETN). There are 201 synchronous generators in the system. Of the 201
synchronous generators, 196 are equipped with AVRs, 121 are equipped with
Governors and 98 are equipped with PSSs. 20 wind farms consisting of fixed speed
wind turbines are modelled as groups of induction machines, and the 170 wind farms
consisting of doubly feed wind turbines are modelled as static generators with AVR. In
addition, 38 substations in NGETN have dynamically-controlled SVCs intended for the
purpose of maintaining the bus voltages at an acceptable level. All of the 627 loads in
the system model are modelled as constant impedance loads for all operation conditions.
Figure 9.1: 500 kV HVDC links and 400 kV Series Compensators that are installed in the GB
power system (vision 2015).
As part of vision 2015, two Monopolar 500 kV CSC-HVDC links are installed between
the 400 kV Substations at Hunterston and Deeside, to enhance the power transfer
capability of the transmission corridors between Scotland and England. In addition,
eight Series Compensators (SCs) are installed into the 400 kV AC transmission lines
connecting SHETL and NGETL. At heavy load condition, these two HVDC links
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
transfer 1900 MW of active power from Southern Scotland to Northern Wales, whilst
2400 MW of active power is transferred over the AC transmission lines. Figure 9.1
presents the layouts of the 500 kV HVDC links and 400 kV SCs. The two CSC-HVDC
links use the control system introduced in Chapter 8, i.e., constant current control for the
rectifier (power sending terminal) and constant voltage control for the inverter (power
receiving terminal). The block diagrams and parameters of the HVDC control system
are included in Appendix F.
9.2.2 Inter-area oscillations study in GB power system
In order to excite the inter-area oscillatory mode in the GB power system, a large
disturbance was initiated in the power transmission corridor between SPTN and
NGETN. This disturbance was a permanent three-phase short-circuit fault simulated at
the mid-point of one of the transmission lines connecting the substations at Torness and
Eccles. This fault was simulated at 1s and after 100 ms the faulted line was
disconnected. The inter-area power flow on one of the transmission lines connecting the
Harker and Hutton substations was used for the inter-area oscillation damping
assessment. Figure 9.2 gives the locations of the faulted transmission line and the line
selected for monitoring the inter-area oscillations.
Figure 9.2: Inter-area oscillation monitoring SPTN and NGETN.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
To observe the inter-area oscillations associated with the generators in Scotland
swinging against the generators in England the system frequencies across the GB power
transmission network were monitored. These system frequencies were measured at the
terminals of some of the large generators (>500 MVA) that are operating at different
locations in GB. The locations of the large generators selected for the monitoring of
inter-area oscillations are presented in Figures 9.3-9.5.
Figure 9.3: Three large generators selected in Scotland for monitoring inter-area oscillations.
Figure 9.4: Three large generators selected in central England for monitoring inter-area
oscillations.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Figure 9.5: Two large generators selected in the South of England for monitoring inter-area
oscillations.
Figure 9.6 presents the oscillatory inter-area power flow (over the Harker-Hutton line)
caused by the large disturbance. As seen from the response of the inter-area power flow
to the disturbance, the inter-area oscillatory mode is well damped in the GB power
system. Figure 9.7 shows the system frequency responses to the large disturbance. The
frequencies measured in Scotland (PEHE, LOAN and HUER) were closely coupled and
swinging around the frequencies measured in England.
1300
line Harker-Hutton
1200
1100
P [WM]
1000
900
800
700
600
500
0
2
4
6
time [s]
8
10
12
Figure 9.6: The oscillatory inter-area power flow on the Harker-Hutton line after a large
disturbance.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
PEHE
system frequencies [Hz]
50.3
LOAN
HUER
50.2
EGGB
WBUR
RUGE
SIZE
50.1
DUNG
50
49.9
0
1
2
3
4
time [s]
5
6
7
8
Figure 9.7: The system frequency variations caused by a large disturbance.
To create more oscillatory behaviour for observing the inter-area oscillations between
Scotland and England, 68 conventional PSSs were removed from service. Appendix F
lists the PSSs that are in the service. The same disturbance (a three-phase short-circuit
fault on the Torness-Eccles line occurring at 1 s and cleared after 100ms) was simulated
to provoke a lightly damped inter-area oscillation. Figure 9.8 presents the oscillatory
inter-area power flow transferred over the Harker-Hutton line. Comparing this response
to that of the original system, it was seen that the damping of the inter-area oscillation
mode was significantly reduced.
P (line Harker-Hutton) [WM]
1300
original system
PSSs-reduced system
1200
1100
1000
900
800
700
600
500
0
5
10
time [s]
15
20
Figure 9.8: The oscillatory inter-area power flow caused by a large disturbance in the original
and PSSs-reduced GB system.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Figure 9.9 presents the system frequency variations caused by the large disturbance in
the PSSs-reduced system. As seen from the simulation results, the inter-area mode
dominated the system frequency variations, i.e. the system frequency variations in
Scotland were nearly in anti-phase with the frequency variations in England. The interarea oscillation associated with the generators in Scotland swinging against the
generators in England was clearly observed, even though the inter-area oscillation was
also influenced by local oscillation modes at the beginning of the dynamic period.
Figure 9.10 presents the system frequency variations measured from the substations
Hunterston (HUNT) and Deeside (DEES). The inter-area oscillation mode was also
clearly observed i.e., the frequency variation measured in the HUER substation was
more or less anti-phase to the frequency variation measured in the DEES substation.
PEHE
LOAN
HUER
system frequencies [Hz]
50.3
EGGB
50.2
WBUR
RUGE
SIZE
50.1
DUNG
50
49.9
49.8
0
5
10
time [s]
15
20
Figure 9.9: System frequency variations caused by the large disturbance in the PSSs-reduced
system.
HUER
DEES
frequency [Hz]
50.2
50.1
50
49.9
49.8
0
5
10
time [s]
15
20
Figure 9.10: System frequency variations measured in substations HUER and DEES in the
PSSs-reduced system.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
As seen from these simulation results (Figures 9.8-9.10), after a number of PSSs were
removed from service, the damping of the inter-area oscillatory mode was significantly
reduced. This operational condition will probably emerge in the future as the system
inertia will be significant reduced due to the integration of a large mount of offshore
wind farms [57]. Because offshore wind farms will connect to the power grid using
back-to-back Voltage Source Converters [63], they will not provide inertia to the system.
Coupled with the increasing replacement of conventional generators with the offshore
wind farms the inertia of the future UK power system will be largely reduced.
A number of power electronic devices such as HVDC and TCSC will be installed to
strengthen the Scotland-England interconnection (see Figure 9.1), there is an essential
need to establish a wide-area inter-area oscillation control system to extract maximum
benefit from these power electronic devices and improve the system damping.
9.3 Wide Area Monitoring and Control System (WAMCS) in
a Future GB Power System
9.3.1 Architecture of WAMCS in GB power system
Figure 9.11 presents architecture of a proposed WAMCS in a future GB power system.
The GB WAMCS has two major applications: 1. real time inter-area oscillation
monitoring using the Newton Type Algorithm (NTA), 2. real time inter-area oscillation
damping control with HVDC. The WAMCS consists of three parts: ⑴ a synchronized
data acquisition system, ⑵ a real time monitoring and control centre and ⑶ a real time
control execution system [89].
⑴ Synchronized data acquisition system
There are twelve PMUs in the synchronized data acquisition system. Two PMUs are
installed in the 400 kV substations Harker (HARK) and Hutton (HUTT). The inter-area
active power flow over one of the transmission lines connecting the two substations can
be captured by the two PMUs. The NTA is used to process the active power flow for the
real time inter-area oscillation damping assessment. Eight power stations (See Figures
9.3-9.5) are equipped with PMUs to measure system frequencies. The mode shape of
the inter-area oscillation mode can be obtained by processing the system frequencies
with NTA.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Another two PMUs are installed in the substations/HVDC converter stations,
Hunterston (HUER) and Deeside (DEES) to monitor the DC power flow over the
HVDC link. Furthermore, the frequency difference between the two substations is used
as the input signals for the wide-area HVDC damping control system.
The synchronized data is directly transmitted to the monitoring and control centre
through a dedicated fibre optic communication network. To further reduce the effect of
the time delay involved in the data transmission in WAMCS, it is recommended that a
Data Concentrator (DC) is not applied.
⑵ Real time monitoring and control centre
The monitoring and control centre is the core of the WAMCS. It receives synchronized
data streams and processes the data to serve real time applications. For real time interarea oscillation damping assessment, the wide-area oscillatory signals are collected in
WAMCS centre. This real time data is then processed by the NTA-based small signal
stability assessment software. The software alerts system operators by issuing an alarm
when the oscillatory damping is unsatisfactory. Then system operators will not allow
the inter-area transmission lines to carry more active power flow. For the real time interarea oscillation damping control scheme, the WAMCS centre uses the real time interarea oscillatory signals to calculate the parameters of the firing angle control of the
HVDC system, then the DC power flow is modulated to stabilise the inter-area
oscillations.
⑶ Real time control execution system
The real time control execution system consists of several execution units installed at
the AC/DC and DC/AC converter stations of the HVDC link. An execution unit is a
GPS-synchronized device, which receives commands regarding the adjustments to the
HVDC converter firing angles from WAMCS centre and transmits these commands to
the power converters. In addition, the start/stop of the whole damping control system is
controlled by the execution units.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Figure 9.11: Architecture of the wide-area inter-area oscillation monitoring and control system
in GB.
9.3.2 Inter-area oscillation monitoring using NTA
For the assessment of the small signal stability, the lightly damped oscillatory active
power flow over the AC transmission line HARK-HUTT (see Figure 9.8) was processed
using NTA. This oscillatory signal (from 3 s to 20 s) was processed with a sampling
frequency f s = 100Hz and a data window size Tdw = 5s . Figure 9.12 presents the
dominant inter-area oscillatory information estimated by the NTA. The frequency of the
inter-area mode is approximately 0.6 Hz, and the damping ratio is approximately 5 %.
To show the inter-area oscillation mode shape, the system frequency variations caused
by the disturbance (see Figure 9.9) were simultaneously processed using NTA. These
oscillatory signals were processed with a sampling frequency f s = 100Hz and a data
window size Tdw = 3s . To obtain a clear mode shape of the inter-area mode, and remove
the influence of the other oscillatory modes, only the oscillatory signals in the range of
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
6 s-20 s were processed. In Figure 9.13, the magnitudes and phase angles of the
dominant oscillatory component of each oscillatory signal are presented in a polar
diagram. Here, the estimation results were updated every one second. The polar diagram
provides a very clear view of the shape of the inter-area oscillatory mode in the GB
system. The phase angles of the change of system frequencies (measured at PEHE,
LOAN and HUER) in Scotland are nearly in anti-phase with the change of system
0.65
0.6
0.55
Damping ratio (%)
Frequency (Hz)
frequencies in England.
6
8
10
12
14
16
18
20
14
16
18
20
t [s]
10
5
0
6
8
10
12
t [s]
Figure 9.12: Inter-area oscillation mode identified by NTA in GB system.
90
0.4
120
60
150
30
0.3
0.2
0.1
180
0
330
210
PEHE
LOAN
HUER
EGGB
WBUR
RUGE
SIZE
DUNG
300
240
270
Figure 9.13: Estimated inter-area oscillation mode shape of GB system.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
9.3.3 Wide area inter-area oscillation damping control with HVDC in GB
The damping ratio of the inter-area mode was reduced to approximately 5% after a
number of PSSs were removed from service (see Figure 9.12). With this level of
damping it is essential to develop an additional control system that uses the two HVDC
links to improve the damping of the inter-area mode. The fundamentals of HVDC
supplementary control design were introduced in Chapter 8. Figure 9.14 gives a
schematic diagram of the HVDC damping control system. The frequency oscillation between
the HUER and DEES substations allowed clear observation of the inter-area mode (see
Figure 9.10). Therefore, the difference between the two frequencies was used as the
input signals for the HVDC damping control system. The signals, Δ I s, generated by
the damping controllers were added to the current references of the rectifier controllers
to dynamically modulate the DC power. Expression (9.1) gives a transfer function of the
HVDC damping controllers. In this case, the parameters of the HVDC supplementary
damping controllers were determined by trial and error method.
I max
kd
1
1 + sTm
sTw
1 + sTw
1 + sTlead
1 + sTlag
1 + sTlead
1 + sTlag
I meas
I max
f DEES
kd
1
1 + sTm
sTw
1 + sTw
1 + sTlead
1 + sTlag
kp
ΔI
I min
f HUNT
I ref
1 + sTlead
1 + sTlag
I ref
ki
s
kp
ΔI
I min
I meas
ki
s
α max
1
1 + sT f
α min
α max
1
1 + sT f
α min
Figure 9.14: Schematic diagram of HVDC damping system.
⎛ 1 ⎞ ⎛ 10s ⎞ ⎛ 1 + 0.05s ⎞ ⎛ 1 + 0.05s ⎞
H ( s) = 100⎜
⎟⎜
⎟⎜
⎟⎜
⎟
⎝ 1 + 0.1s ⎠ ⎝ 1 + 10s ⎠ ⎝ 1 + 1.8s ⎠ ⎝ 1 + 1.8s ⎠
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(9.1)
Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
To check the abilities of the HVDC damping controllers to improve the damping of the
inter-area mode, a same disturbance was used as before. At 1 s, a permanent three-phase
short-circuit fault was simulated at the mid-point of one of the transmission lines
connecting substations Torness and Eccles; after 100 ms the faulted line tripped.
Figures 9.15-9.16 present the responses of the generator rotor speeds to the large
disturbance with and without the additional HVDC damping control system. Figure 9.17
shows the response of the inter-area active power flow over the AC transmission line
Harker–Hutton to the large disturbance. As confirmed by these simulation results, the
HVDC damping controllers allow the system to be stabilized much more quickly after
the inception of the large disturbance.
1.005
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.005
with control
1
PEHE
0.995
0
5
10
15
with control
1
LOAN
0.995
20
no control
0
5
time [s]
10
15
20
time [s]
1.002
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.005
with control
1
HUER
no control
with control
1.001
1
0.999
EGGB
0.995
0
5
10
15
20
time [s]
0
5
10
15
20
time [s]
Figure 9.15: Responses of the generator rotor speeds (PEHE, LOAN, HUER and EGGB) to the
large disturbance with and without the wide area HVDC damping control.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
1.002
rotor speed [p.u.]
rotor speed [p.u.]
no control
with control
1.001
1
WBUR
0.999
0
5
10
15
with control
1.001
1
RUGE
0.999
20
no control
1.002
0
5
time [s]
10
15
20
time [s]
1.002
no control
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.002
with control
1.001
1
0.999
0.998
SIZE
0
5
10
15
with control
1.001
1
0.999
20
DUNG
0
5
time [s]
10
15
20
time [s]
Figure 9.16: Responses of the generator rotor speeds (WBUR, RUGE, SIZE and DUNG) to the
large disturbance with and without the wide area HVDC damping control.
P (line Harker-Hutton) [WM]
1600
without HVDC damping control
with HVDC damping control
1400
1200
1000
800
600
400
200
0
5
10
time [s]
15
20
Figure 9.17: The response of the inter-area power flow on the Harker-Hutton line to the large
disturbance, with and without HVDC damping control.
The oscillatory power flow (from 3 s to 10 s) over the Harker-Hutton line was processed
using NTA with the sampling frequency f s = 100Hz and the data window size Tdw = 3s .
The estimated inter-area oscillation mode, shown in Figure 9.18 has confirmed that the
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
damping of the inter-area oscillatory mode has been significantly improved by
integrating the new HVDC damping control system.
Frequency (Hz)
0.65
0.6
0.55
Damping ratio (%)
0.5
without HVDC damping control
with HVDC damping control
6
6.5
7
7.5
8
time [s]
8.5
9
9.5
10
8.5
9
9.5
10
40
without HVDC damping control
with HVDC damping control
30
20
10
0
6
6.5
7
7.5
8
time [s]
Figure 9.18: Inter-area oscillation mode identified by NTA in the GB system, with and without
HVDC damping control.
9.3.4 The impact of time delays on wide-area control
Wide area closed loop control systems use remote signals as feedback input signals. The
dependence of the control system on wide area signals makes the time delay involved in
their transmission of significant concern. The time delay of the data transmission can
vary from tens to hundreds of milliseconds. It depends on the communication distance,
protocols and time consumed by numerical calculations [90]. In this Section, the effect
of time delay in the wide area damping control system is tested.
The delays involved in the transmission of a wide area signal can be defined as follows,
with reference to Figure 9.19. A packet of measurements (real time oscillatory signal)
produced by a PMU is tagged with a time stamp defined as ‘T1’, and then the
measurements are transmitted to the WAMCS centre. With this real time oscillatory
signal, the WAMCS centre calculates the corresponding commands for the HVDC
converter control and sends these commands to the remote HVDC rectifier station. The
time when the execution units in the HVDC converter stations receive these commands
is defined as ‘T2’. The difference between ‘T2’ and ‘T1’ is defined as the time delay of
the data transmission in the wide area control system.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
Figure 9.19: An illustration of the time delay involved in the data transmission in GB WAMCS.
Figure 9.20 gives a block diagram of HVDC damping controllers, in which the time
delay of the transmission of the input signals is taken into account. The element e − sT
represents the effect of time delay; T represents the time delay in seconds [91]. In these
tests, the time delays in different signal transmission channels are assumed to be
constant.
I max
f HUER
kd
e − sT
1
1 + sTl
sTw
1 + sTw
1 + sTlead
1 + sTlag
1 + sTlead
1 + sTlag
ΔI
I min
I max
e − sT
kd
f DEES
1
1 + sTl
sTw
1 + sTw
1 + sTlead
1 + sTlag
1 + sTlead
1 + sTlag
ΔI
I min
Figure 9.20: A block diagram of HVDC damping controllers (with time delay).
Figure 9.21 presents the effects of different time delays in the wide area control system,
ranging from 50 milliseconds to 200 milliseconds. The effect of wide area HVDC
control was gradually reduced when the delay time increased. In addition, when the
time delay increased to 150 ms, a high frequency oscillatory component appeared [91].
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
P (line Harker-Hutton) [WM]
800
790
780
770
760
no latency
latency=50ms
latency=100ms
750
latency=150ms
740
730
latency=200ms
10
12
14
16
18
20
time [s]
Figure 9.21: The effect of time delay in the wide area damping controllers (50 milliseconds to
200 milliseconds).
Figure 9.22 presents the effect of the time delay in wide area control system, from
300 milliseconds to 700 milliseconds. As seen from the simulations, when the time
delay increased to 300 ms, the high frequency oscillatory component disappeared [91];
and the inter-area oscillation became unstable as the time delay approached 700 ms.
1300
latency=300ms
P (line Harker-Hutton) [WM]
1200
latency=400ms
latency=500ms
1100
latency=600ms
1000
latency=700ms
900
800
700
600
500
0
5
10
time [s]
15
20
Figure 9.22: The effect of time delay in the wide area damping controllers (300 milliseconds to
700 milliseconds).
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
9.3.5 Interaction between PSSs and HVDC damping control system
As seen from the simulation results (Figures 9.15-9.17), the HVDC damping control
system has shown its powerful capability to stabilize inter-area oscillations when a
number of PSSs are removed from the GB power system. This capability exists because
the additional damping control system has very strong influence on the dynamic
behaviour of the system, this strong influence could also have unforeseen negative
effects. To ensure that the new HVDC damping control system does not have negative
effects on the GB power system, the interaction between the PSSs that were removed
form service and the new HVDC damping controllers was investigated.
With all of the PSSs in service the same simulations was used, with and without the
HVDC damping control. In these tests, the effect of time delay was not taken into
account. Figures 9.23-9.24 present the responses of the generator rotor speeds to the
large disturbance.
1.005
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.005
with control
1
PEHE
0.995
0
5
10
with control
1
LOAN
0.995
15
no control
0
5
no control
1.005
with control
1
0.995
HUER
0
5
15
time [s]
rotor speed [p.u.]
rotor speed [p.u.]
time [s]
10
10
15
time [s]
no control
1.001
with control
1
0.999
EGGB
0
5
10
15
time [s]
Figure 9.23: Responses of the generator rotor speeds (PEHE, LOAN, HUER and EGGB) to the
large disturbance (all PSSs in service).
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.0015
with control
1.001
1.0005
1
WBUR
0.9995
0
5
10
no control
1.002
with control
1.001
1
0.999
15
RUGE
0
5
time [s]
10
15
time [s]
no control
rotor speed [p.u.]
rotor speed [p.u.]
1.0015
with control
1.001
1.0005
1
0.9995
SIZE
0
5
10
15
time [s]
no control
1.0015
with control
1.001
1.0005
1
0.9995
DUNG
0
5
10
15
time [s]
Figure 9.24: Responses of the generator rotor speeds (WBUR, RUGE, SIZE and DUNG) to the
large disturbance (all PSSs in service).
As seen from the simulations results, the new wide area damping control system has
changed the dynamics of the original system (all PSSs in service). However, the
responses of the system are still well damped. The new HVDC damping control system
slightly improves the damping of the generators in Scotland (PEHE, LOAN and HUER).
The new HVDC damping control system did not introduce negative effects to other the
generators.
The oscillatory inter-area active power flows (over the Harker-Hutton line) caused by
the disturbance in the scenario with, and without HVDC damping control are shown in
Figure 9.25. The HVDC additional damping control has changed the response of the
inter-area power flow during disturbances. A larger deviation of the inter-area power
flow was introduced by the HVDC damping control system; the system with HVDC
damping control took longer time to stabilize at a new steady state after the large
disturbances.
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
P (line Harker-Hutton) [WM]
1300
without HVDC damping control
with HVDC damping control
1200
1100
1000
900
800
700
600
500
0
2
4
6
time [s]
8
10
12
Figure 9.25: The influence of HVDC damping control on the inter-area power flow in complete
GB system.
9.4 Conclusions
In this Chapter, a proposed Wide Area Monitoring and Control System (WAMCS),
designed for enhancing the small signal stability of a future GB power system, has been
presented.
A permanent three-phase fault was introduced to one of the inter-tie lines between
Scotland and England, to investigate the inter-area oscillations associated with the
generators in Scotland swinging against the generators in England. As seen from the
system response (inter-area active power flow) to the disturbances, the inter-area mode
was well damped in the original GB power system. However, after a number of PSSs
were removed from service, the damping of the inter-area mode was significantly
reduced.
To improve the small signal stability of the PSSs-reduced GB power system, two real
time SMT applications were introduced and tested through dynamic simulation with a
full GB system model. The NTA has successfully extracted the inter-area oscillatory
mode from the lightly damped oscillatory power flow transferred between Scotland and
England. The inter-area mode shape has been obtained through NTA processing of the
system frequencies across the GB power system. With this application, system operators
will be more confident to utilize the inter-area transmission lines, and to ensure the
system stay at secure level when they increase the inter-area power flow. The wide area
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Chapter 9 Wide Area Monitoring and Control System (WAMCS) in the Future GB Power System
HVDC damping control system has shown that by dynamically modulating the DC
power flow it can be powerful tool for improving the damping of the inter-area
oscillatory mode. With this application, the power transfer capacity of the inter-area
transmission lines can be increased.
The influence of the time delay on the wide area control system has been discussed. The
effect of the wide area HVDC control system was gradually reduced when the time
delay increased. When the time delay increased to a certain range (approximately
150 ms-200 ms), a high frequency oscillatory component was introduced into the interarea oscillations.
Finally, the interactions between the HVDC wide area damping control system and the
conventional PSSs were investigated. The new wide area damping control system has
changed the dynamics of the original system. However, the responses of the system to a
large disturbance were still well damped. The damping of some of the generators has
been further improved by the wide area damping control system; and it did not
introduce obvious negative effects to other the generators.
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Chapter 10 Conclusions and future work
Chapter 10 Conclusions and Future Work
10.1 Conclusions
This thesis describes key work needed to overcome the challenges involved in the
development of the future GB WAMPAC system. This includes the provision of a
thorough study of Synchronized Measurement Technology (SMT), the development of
a roadmap to guide the GB WAMPAC project, and the proposal and evaluation of SMT
applications and algorithms in the DIgSILENT simulator.
SMT is the most essential element and enabler of WAMPAC. To develop a roadmap for
the practical implementation of WAMPAC in the GB network, the state of the art and
worldwide experience with SMT applications are provided. This thorough study of
SMT helps power system operators become more confident that the deployment of SMT
will significantly improve the stability of future power systems, and that a SMT-based
WAMPAC system will be the only choice for monitoring and managing the future
power systems.
A proposed architecture of the future GB WAMPAC system, which is presented in this
thesis, was based on international experience with existing WAMPAC systems and
includes the core building blocks of a WAMPAC system (PMUs, DCs and
communication technologies). The future GB WAMPAC system will predominantly
serve three power utilities, SPTN, SHETN and NGETN. Therefore, each power utility
has a single DC to serve regional applications, and one Super-DC that collect
synchronized data from the three regional DCs and support wide area applications.
WAMPAC systems involve significant financial investment and long project lead times.
Therefore, to ensure the efficient development of the GB WAMPAC system, a roadmap
that guides the GB WAMPAC project is required. In this thesis, a methodology of
designing a roadmap to guide the GB WAMPAC project is introduced. This
methodology takes into account the international experience with WAMPAC project
management and the practical challenges faced in the future GB electric power network.
Based on this methodology, the roadmap to the future GB WAMPAC system has been
devised.
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Chapter 10 Conclusions and future work
The roadmap is divided into a short term and a long term strategy. In the short term, a
few (5-6) PMUs will be deployed in the GB power system. This is due to the
uncertainties related to the project and the financial limitations. These PMUs will be
distributed across the entire UK transmission network to form a wide area power angle
and frequency monitoring system, or the transmission corridor between Scotland and
England to monitor inter-area oscillations. In the long term, the methodology introduced
for increasing the number of PMUs deployed in the GB power system will allow a new
generation of real time wide area monitoring system to become available. Furthermore,
several SMT-based smart protection and control schemes have been proposed. For
example, a wide area inter-area oscillation control system is introduced. This new
control system uses wide area oscillatory signals as input signals, and produces dynamic
parameters for the control of HVDC or TCSC to stabilize inter-area oscillations. This
application has the potential to allow the conventional EMS-based open loop control to
be upgraded to a sophisticated wide-area closed loop control system.
The study performed to develop the GB WAMPAC roadmap highlighted that an
application that can perform real time inter-area oscillation monitoring and control
would be a valuable component of the future GB WAMPAC system. As a result of this,
the thesis moves to focus on using WAMPAC to enhance the small signal stability i.e.,
inter-area oscillation stability. For this purpose, a fundamental study of inter-area
oscillations is provided. Two classical methods were used to investigate the nature of
inter-area oscillations i.e., nonlinear simulations and modal analysis. Different types of
disturbance were used in the nonlinear simulations to observe the physical
characteristics of local modes and the inter-area mode. To accurately understand the
physical phenomenon behind inter-area oscillations, i.e. oscillation frequency, mode and
source, modal analysis was introduced. From this modal analysis, it was found that the
inter-area oscillatory mode is strong influenced by the inter-area power flow and
transmission network parameters. This means that the large increase in inter-area active
power flow caused by permanent faults may lead to inter-area oscillations becoming
unstable, particularly due to the increased loading of future power systems. Therefore, a
real time monitoring and warning system will become increasingly desirable to detect if
a lightly damped/unstable inter-area oscillation exists in the system.
The core of the research described in this thesis is to establish a real time inter-area
oscillation monitoring platform for estimating the dominant inter-area oscillatory mode
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Chapter 10 Conclusions and future work
(frequency and damping) using the real time oscillatory signals captured by PMUs. This
thesis presented a novel NTA for the real time estimation of the dominant inter-area
oscillation mode. Two data sets were tested using the new algorithm; one data set was
taken from simulated models and the other from real-life data records. These tests have
shown that the NTA can reliably identify the oscillatory mode in static conditions for
both data sets and in the presence of white noise. The dynamic capability of the NTA
has also been successfully demonstrated by capturing the dynamic oscillatory mode
when the parameters of the test signal experienced a step change. In both cases the NTA
results were more accurate and stable than these using conventional Prony methods.
The NTA-based real time inter-area oscillation monitoring can be considered as a
suitable SMT application for deployment during the short-term phase of the GB
WAMPAC strategy proposed in this thesis. As part of the long term GB WAMPAC
strategy, this monitoring application could be extended into a real time wide area closed
loop control application. Detailing how this oscillation control application could be
created formed a key part of this thesis. Modal analysis-based linear control theory was
used to design a wide area damping control system that uses HVDC, TCSC and SVC
installed in an inter-area power transmission corridor, to stabilize inter-area oscillations.
Conventional modal analysis in the frequency domain was used to find the optimum set
of parameters for the system controllers, i.e. the operation point with maximum
damping. Nonlinear simulations were used to confirm the new controllers’ ability to
damp the inter-area oscillations.
The final part of this thesis proposes a Wide Area Monitoring and Control System
(WAMCS), designed to enhance the small signal stability of a future GB power system.
The operation of this WAMCS was evaluated using a full GB power system model
(vision 2015). When this system was in a vulnerable state, e.g. several PSS equipped
generators were removed from service; the WAMCS developed here was capable of
significantly increasing the damping of the lightly damped inter-area mode in the
system. This loss of PSS control, and the associated lightly damped inter-area
oscillation, will occur as the number of synchronous generators will be replaced by offshore wind generation that cannot provide inertia to the system.
Two real applications i.e. inter-area oscillation monitoring with New Type Algorithm
(NTA) and inter-area oscillation damping control with HVDC, were tested using
dynamic simulation with a full GB power system model. The NTA has successfully
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Chapter 10 Conclusions and future work
extracted the inter-area oscillatory mode from a lightly damped inter-area oscillatory
power flow between Scotland and England. In addition, the inter-area mode shape was
obtained through NTA processing of the frequencies across the GB power system. A
wide area damping control system was added to the submarine HVDC link between the
SPTN and NGETN, to improve the damping of the inter-area mode. The input signal to
these HVDC supplementary damping control system is the frequency difference
between Scotland and England. This new damping control system modulated the DC
power flow to stabilize the inter-area oscillations. Simulation results have shown that
the damping of the inter-area mode has been significantly improved by the inclusion of
the supplementary damping control system.
One of most important issues in wide area control is the effect of any time delays. Here,
the influence of time delay in the range of 50 ms to 500 ms was investigated. It has been
concluded that the effect of wide area HVDC control system in damping inter-area
oscillations is gradually reduced when the delay time is increased. A time delay in a
certain range (approximately 150 ms-200 ms) introduces a high frequency oscillatory
component into the inter-area oscillations.
The additional HVDC damping control system has significantly changed the system’s
dynamics and the interactions between this control system and the existing PSSs cannot
be ignored. Simulation results have shown that the additional HVDC damping control
system increased the damping of some generators and didn’t introduce a negative effect
on the other generators. However, in a practical implementation the parameters of the
PSSs should be tuned to coordinate with the HVDC damping controllers to ensure
optimal system control.
10.2 Future Work
The research described in this thesis represents the initial stage of tailoring a WAMPAC
system for the needs of a future GB power system. Significant further research is
needed before the proposed GB WAMCS can be implemented in the real GB power
system.
This thesis presents several wide area control schemes that can use individual power
electronic devices i.e. HVDC, TCSC and SVC to damp inter-area oscillations. Here,
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Chapter 10 Conclusions and future work
only the use of HVDC in damping inter-area oscillations has been analyzed in a full GB
power system model. In the future GB power system, several TCSC and SVC will be
installed in the transmission corridors between Scotland and England to enhance the
power transfer capability of the existing transmission lines. The potential opportunity to
use TCSC and SVC to damp inter-area oscillations should also be evaluated in the full
GB power system model. Coordination between all of the controllers in a power system
is essential if system damping is to be optimized. Achieving this coordination should
form part of any future work. This will require the development of optimised methods
for the coordinated design and tuning of controllers; these methods should be evaluated
in the full GB power system model.
In this thesis, the wide area damping control schemes were designed using conventional
linear control theory. Therefore, these control schemes often only work within a limited
operating range. During power system operation, variable operating conditions and
different contingencies can reduce the effect of the damping controllers, and allow
lightly damped or even unstable inter-area oscillations to exist. Therefore, for practical
implementations, a robust control design method is needed to ensure that the damping
controllers are viable under a sufficiently wide range of operating conditions. A large
number of simulations should be performed in the full GB power system model to
confirm the robustness of the controllers for variable operating conditions and for
different contingencies.
As this thesis presents, the inevitable time delay of the wide area signal transmission is
the main operational challenge for the implementation of a real time wide area control
system. It has been shown that the time delay can reduce the damping effect of the wide
area HVDC damping control system on inter-area oscillations, even allowing unstable
system operation to occur. The time delay is usually caused by a number of variables,
such as measurement processing times, the bandwidth of the communication medium
and geographic distance, the time delay of in different channels may be different and
variable. Therefore, another main aspect of the future work is developing a method for
compensating the negative effect introduced by time delay. The time delay
compensation method should be robust and flexible to deal with the variables;
furthermore, the compensation method should also concern the issues related to the
reliability of the
communication
network, GPS
communication challenges.
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synchronization
and
other
Chapter 10 Conclusions and future work
This research has developed the essential applications and algorithms of wide area
monitoring and control for improving the inter-area oscillatory stability of the future GB
power system. As the other essential part of the future GB WAMPAC system, SMTbased system protection schemes should also be developed to optimize the existing
system emergency protection schemes, e.g. intelligent controlled islanding and wide
area adaptive under-frequency load shedding. In the future work, the essential
algorithms required for supporting these wide area protection schemes should be
developed; and the performance of these wide area protection schemes i.e., the key
factors that influence the performance of wide area protection schemes should be
evaluated in full GB system model.
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-195-
Appendices
Appendices
10.1 Appendix A
Figure A-1: A single line diagram of two-area system.
Table A-1: Synchronous machine parameters of G1, G2 and G3 and G4.
No. of Generator
1
2
3
4
Rotor type
Round
Rotor
Round
Rotor
Round
Rotor
Round
Rotor
Inertia time constant H (rated to Sgn)
Mechanical damping
Stator resistance ra
Stator leakage reactance xl
Synchronous reactance xd d-axis
Synchronous reactance xq q-axis
Transient reactance xd’ d-axis
Transient reactance xq’ q-axis
Sub-transient reactance xd’’ d-axis
Sub-transient reactance xq’’ q-axis
Transient time constant Td0’ d-axis
Transient time constant Tq0’ q-axis
Sub-transient time constant Td0’’ daxis
Sub-transient time constant Tq0’’ qaxis
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
0.05
0.05
0.05
0.05
Table A-2: Power generation conditions of G1, G2 and G3 and G4.
Gen
1
2
3
4
Bus
type
SL
PV
PV
PV
Rated power
(MVA)
900
900
900
900
Nominal voltage
(L-L kV)
20
20
20
20
Active power
output
750
700
719
700
-196-
Reactive power
output
185
235
176
202
Terminal
voltage (p.u.)
1.03
1.01
1.03
1.01
Appendices
Vref
Vmeas
+
1
1 + sTr
-
Vmax
K
1 + sTe
1 + sTb
1 + sTa
Vmin
Figure A-2: Block diagram of static exciter of G1, G2 and G3 and G4.
1
2
3
4
5
6
7
Table A-3: Parameters of static exciter.
0.01
Transducer filter time constant Tr
Voltage regulator gain K
150
Voltage regulator time constant Te
0.05
Transient gain reduction time constant Ta
1
Transient gain reduction time constant Tb 10
Maximum voltage regulator output Vmax
3
Minimum voltage output Vmin
-3
second
p.u.
second
Second
Second
p.u.
p.u.
Tmax
1. 0
K
ωrotor
Pref
1
1 + sTs
1 + sT3
1 + sTc
1 + sT4
1 + sT5
Tmin
Figure A-3: Block diagram of speed governor of G1, G2, G3 and G4.
1
2
3
4
5
6
7
8
Table A-4: Parameters of speed governor.
Governor gain K
50 p.u.
Servo time constant Ts
0.1 second
Transient gain time constant T3
0
Second
HP turbine time constant Tc
0.5 Second
Time constant to set HP ratio T4 1.25 Second
Reheat time constant T5
5
Second
Maximum power Pmax
1
p.u.
Minimum power Pmin
0
p.u.
Table A-5: Transformer parameters.
No. of Transformer
Rated power (MVA)
Rated voltage (HV)
Rated voltage (LV)
Short circuit voltage (positive sequence %)
Short circuit voltage (zero sequence. %)
Winding connection (HV)
Winding connection (LV)
-197-
1
900
230
20
15
3
YN
YN
2
900
230
20
15
3
YN
YN
3
900
230
20
15
3
YN
YN
4
900
230
20
15
3
YN
YN
Appendices
Table A-6: AC transmission line parameters.
No. of line
1
2
3
4
5
6
Rated voltage (L-L kV) 230
230
230
230
230
230
Length (km)
25
10
110
110
110
110
0.0529 0.0529 0.0529 0.0529 0.0529 0.0529
Resistance (Ohm/km)
Reactance (Ohm/km)
0.529 0.529 0.529 0.529 0.529 0.529
3.3075 3.3075 3.3075 3.3075 3.3075 3.3075
Susceptance (µs/km)
7
230
10
8
230
25
0.0529
0.0529
0.529
0.529
3.3075
3.3075
Table A-7: Load data.
Load
Active power (MW)
Reactive power (MVar)
Load 1
967
100
Load 2
1667
100
The active load is modeled as 50% constant and 50% constant impedance.
The reactive load is modeled as constant impedance.
No. of
Capacitor
1
2
3
Nominal
voltage
(kV)
230
230
230
Table A-8: Shunt capacitors.
Connected
Reactive power
bus
output
(MVar)
3
215.34
4
246.73
5
378.38
-198-
Minimum
output
(MVar)
Maximum
output
(MVar)
100
100
50
600
500
500
Appendices
10.2 Appendix B
Figure B-1: A single line diagram of the two-area system with HVDC.
Table B-1: Synchronous machine parameters of G1, G2 and G3 and G4.
No. of Generator
1
2
3
4
Rotor type
Round
Rotor
Round
Rotor
Round
Rotor
Round
Rotor
Inertia time constant H (rated to Sgn)
Mechanical damping
Stator resistance ra
Stator leakage reactance xl
Synchronous reactance xd d-axis
Synchronous reactance xq q-axis
Transient reactance xd’ d-axis
Transient reactance xq’ q-axis
Sub-transient reactance xd’’ d-axis
Sub-transient reactance xq’’ q-axis
Transient time constant Td0’ d-axis
Transient time constant Tq0’ q-axis
Sub-transient time constant Td0’’ daxis
Sub-transient time constant Tq0’’ qaxis
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
0.05
0.05
0.05
0.05
Table B-2: Power generation conditions of G1, G2 and G3 and G4.
Gen
1
2
3
4
Bus
type
SL
PV
PV
PV
Rated power
(MVA)
900
900
900
900
Nominal voltage
(L-L kV)
20
20
20
20
Active power
output
750
700
719
700
-199-
Reactive power
output
185
235
176
202
Terminal
voltage (p.u.)
1.03
1.01
1.03
1.01
Appendices
Vref
Vmeas
1
1 + sTr
Vmax
1 + sTc
1 + sTb
1
sTe
Ka
1 + sTa
Vmin
Ke
f ( E1 , Se1 , E2 , Se 2 )
Kf
1 + sT f
Figure B-2: Block diagram of DC exciter of G1, G3 and G4.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Table B-3: Parameters of DC exciter.
Transducer filter time constant Tr
0.02
Voltage regulator gain Ka
20
Voltage regulator time constant Ta
0.005
Filter derivative time constant Tc
3.1
Filter delay time constant Tb
40
Exciter time constant Te
0.05
Exciter constant Ke
0.5
Stabilization path gain Kf
0.01
Stabilization path time constant Tf
0.3
Saturation factor 1E1
3.9
Saturation factor 2Se1
0.0001
Saturation factor 3E2
5.2
Saturation factor 4Se2
0.001
Maximum voltage regulator output Vmax
5
Minimum voltage regulator output Vmin
-5
Vref
Vmeas
1
1 + sTr
second
p.u.
second
second
second
second
p.u.
p.u.
second
p.u.
p.u.
p.u.
p.u.
p.u.
p.u.
Vmax
1 + sTb
1 + sTa
K
1 + sTe
Vmin
Figure B-3: Block diagram of static exciter of G2.
-200-
Appendices
1
2
3
4
5
6
7
Table B-4: Parameters of static exciter.
Transducer filter time constant Tr
0.01
Voltage regulator gain K
200
Voltage regulator time constant Te
0.05
Transient gain reduction time constant Ta
1
Transient gain reduction time constant Tb 10
Maximum voltage regulator output Vmax
3
Minimum voltage output Vmin
-3
second
p.u.
second
Second
Second
p.u.
p.u.
Tmax
1.0
K
ωrotor
Pref
1
1 + sTs
1 + sT3
1 + sTc
1 + sT4
1 + sT5
Tmin
Figure B-4: Block diagram of speed governor of G1, G2, G3 and G4.
1
2
3
4
5
6
7
8
Table B-5: Parameters of speed governor.
Governor gain K
50 p.u.
Servo time constant Ts
0.1 second
Transient gain time constant T3
0
Second
HP turbine time constant Tc
0.5 Second
Time constant to set HP ratio T4 1.25 Second
Reheat time constant T5
5
Second
Maximum power Pmax
1
p.u.
Minimum power Pmin
0
p.u.
Table B-6: Transformer parameters.
No. of Transformer
1
2
Rated power (MVA)
900 900
Rated voltage (HV)
230 230
Rated voltage (LV)
20 20
Short circuit voltage (positive Sequence %) 15 15
Short circuit voltage (zero Sequence %)
3
3
Winding connection (HV)
YN YN
Winding connection (LV)
YN YN
3
900
230
20
15
3
YN
YN
Table B-7: AC transmission line parameters.
No. of line
1
2
3
4
5
6
Rated voltage (L-L kV) 230
230
230
230
230
230
Length (km)
25
10
110
110
110
110
0.0529 0.0529 0.0529 0.0529 0.0529 0.0529
Resistance (Ohm/km)
Reactance (Ohm/km)
0.529 0.529 0.529 0.529 0.529 0.529
3.3075 3.3075 3.3075 3.3075 3.3075 3.3075
Susceptance (µs/km)
-201-
4
900
230
20
15
3
YN
YN
7
230
10
8
230
25
0.0529
0.0529
0.529
0.529
3.3075
3.3075
Appendices
Table B-8: DC transmission line parameters.
DC transmission line 1
Rated DC voltage (kV) 56
Rated current (kA)
3.6
Length (km)
200
Overhead line
Line type
0.0075
Resistance (Ohm/km)
Inductance (mH/km)
1
Figure B-5: Rectifier operation condition (DIgSILENT interface).
α max
kp
1
1 + sT f
I ref
I meas
ki
s
α min
Figure B-6: Rectifier’s α control for constant current.
1
2
3
4
5
6
Table B-9: Parameters of rectifier control.
Current reference for current control 1.8 kA
Proportional gain Kp
0.001 p.u.
Output gain Ko
1.0 p.u.
Rectifier time constant Tf
0.001 second
Integral gain Ki
0.01 p.u.
5
Minimum firing angle αmin
degree
90
Maximum firing angle αmax
degree
-202-
α
Appendices
Figure B-7: Inverter operation condition (DIgSILENT interface).
β max
kp
1
1 + sT f
Vref
Vmeas
ki
s
β
β min
Figure B-8: inverter’s β control for constant voltage.
1
2
3
4
5
6
7
Table B-10: Parameters of inverter control.
Voltage reference for voltage control 1.0 p.u.
Proportional gain Kp
0.001 p.u.
Output gain Ko
1
p.u.
Rectifier time constant Tf
0.001 second
Integral gain Ki
0.01 p.u.
30
Minimum advance firing angle βmin
degree
90
Maximum advance firing angle βmax
degree
Table B-11: Load data.
Load
Active power (MW)
Reactive power (MVar)
Load 1
967
100
Load 2
1667
100
The active load is modeled as 50% constant and 50% constant impedance.
The reactive load is modeled as constant impedance.
-203-
Appendices
No. of
Capacitor
1
2
3
Nominal
voltage
(kV)
230
230
230
4
230
Table B-12: Shunt capacitors.
Connected bus
Reactive power
output
(MVar)
3
189.88
5
341.61
Rectifier AC
118.67
terminal
Rectifier AC
122.00
terminal
-204-
Minimum
output
(MVar)
100
50
0
Maximum
output
(MVar)
600
500
125
0
125
Appendices
10.3 Appendix C
Figure C-1: A single line diagram of the two-area system with HVDC.
Table C-1: Synchronous machine parameters of G1, G2 and G3 and G4.
No. of Generator
1
2
3
4
Rotor type
Round
Rotor
Round
Rotor
Round
Rotor
Round
Rotor
Inertia time constant H (rated to Sgn)
Mechanical damping
Stator resistance ra
Stator leakage reactance xl
Synchronous reactance xd d-axis
Synchronous reactance xq q-axis
Transient reactance xd’ d-axis
Transient reactance xq’ q-axis
Sub-transient reactance xd’’ d-axis
Sub-transient reactance xq’’ q-axis
Transient time constant Td0’ d-axis
Transient time constant Tq0’ q-axis
Sub-transient time constant Td0’’ daxis
Sub-transient time constant Tq0’’ qaxis
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
0.05
0.05
0.05
0.05
Table C-2: Power generation conditions of G1, G2 and G3 and G4.
Gen
1
2
3
4
Bus
type
SL
PV
PV
PV
Rated power
(MVA)
900
900
900
900
Nominal voltage
(L-L kV)
20
20
20
20
Active power
output
750
700
719
700
Reactive power
output
185
235
176
202
Vref
Vmeas
1
1 + sTr
Vmax
1 + sTb
1 + sTa
K
1 + sTe
Vmin
Figure C-2: Block diagram of static exciter of G1, G2 G3 and G4.
-205-
Terminal
voltage (p.u.)
1.03
1.01
1.03
1.01
Appendices
1
2
3
4
5
6
7
Table C-3: Parameters of static exciter.
Transducer filter time constant Tr
0.01
Voltage regulator gain K
200
Voltage regulator time constant Te
0.05
Transient gain reduction time constant Ta
1
Transient gain reduction time constant Tb 10
Maximum voltage regulator output Vmax
3
Minimum voltage output Vmin
-3
second
p.u.
second
Second
Second
p.u.
p.u.
Tmax
1.0
K
ωrotor
Pref
1
1 + sTs
1 + sT3
1 + sTc
1 + sT4
1 + sT5
Tmin
Figure C-3: Block diagram of speed governor of G1, G2, G3 and G4.
1
2
3
4
5
6
7
8
Table C-4: Parameters of speed governor.
Governor gain K
50 p.u.
Servo time constant Ts
0.1 second
Transient gain time constant T3
0
Second
HP turbine time constant Tc
0.5 Second
Time constant to set HP ratio T4 1.25 Second
Reheat time constant T5
5
Second
Maximum power Pmax
1
p.u.
Minimum power Pmin
0
p.u.
Table C-5: Transformer parameters.
No. of Transformer
1
2
Rated power (MVA)
900 900
Rated voltage (HV)
230 230
Rated voltage (LV)
20 20
Short circuit voltage (positive Sequence %) 15 15
Short circuit voltage (zero Sequence %)
3
3
Winding connection (HV)
YN YN
Winding connection (LV)
YN YN
No. of
line
1
2
3
4
5
6
7
8
Rated voltage
(L-L kV)
230
230
230
230
230
230
230
230
3
900
230
20
15
3
YN
YN
Table C-6: AC transmission line parameters.
Length
Resistance
Reactance
(km)
(Ohm/km)
(Ohm/km)
0.0529
25
0.529
0.0529
10
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
10
0.529
0.0529
25
0.529
-206-
4
900
230
20
15
3
YN
YN
Susceptance
(µs/km)
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
Appendices
Table C-7: DC transmission line parameters.
DC transmission line 1
Rated DC voltage (kV) 56
Rated current (kA)
3.6
Length (km)
200
Overhead line
Line type
0.0075
Resistance (Ohm/km)
Inductance (mH/km)
1
Figure C-4: Rectifier operation condition (DIgSILENT interface).
α max
kp
1
1 + sT f
I ref
I meas
ki
s
α min
Figure C-5: Rectifier’s α control for constant current.
1
1
2
3
4
5
6
Table C-8: Parameters of rectifier control.
Current reference for current control 1.0 p.u.
Proportional gain Kp
0.001 p.u.
Output gain Ko
1.0 p.u.
Rectifier time constant Tf
0.001 second
Integral gain Ki
0.01 p.u.
5
Minimum firing angle αmin
degree
90
Maximum firing angle αmax
degree
-207-
α
Appendices
Figure C-6: Inverter operation condition (DIgSILENT interface).
β max
kp
1
1 + sT f
Vref
Vmeas
ki
s
β
β min
Figure C-7: inverter’s β control for constant voltage.
1
2
3
4
5
6
7
Table C-9: Parameters of inverter control.
Voltage reference for voltage control 1.0
Proportional gain Kp
0
Output gain Ko
1
Rectifier time constant Tf
0.001
Integral gain Ki
0.01
30
Minimum advance firing angle βmin
90
Maximum advance firing angle βmax
-208-
p.u.
p.u.
p.u.
second
p.u.
degree
degree
Appendices
I ref
+
I meas
-
α max
kp
+
1
1 + sT f
+
-
ki
s
α
(rectifier)
α min
umax
Freq area 1
+
1
1 + sTm
kd
-
1 + sTlead
1 + sTlag
sTw
1 + sTw
1 + sTlead
1 + sTlag
Limit
umin
Freq area 2
Figure C-8: Rectifier control with supplementary damping control.
1
2
3
4
5
6
7
Table C-10: Parameters of HVDC supplementary control.
Damping control gain Kd
1600 p.u.
Low pass filter time constant Tm
0.1 second.
Washout time constant Tw
10 second
Lead phase compensation time constant Tlead 0.1 second
1.03 second
Lag phase compensation time constant Tlag
-5
Minimum damping controller output umin
second
5
Maximum damping controller output umax
second
Table C-11: Load data.
Load
Active power (MW)
Reactive power (MVar)
Load 1
967
100
Load 2
1667
100
The active load is modeled as 50% constant and 50% constant impedance.
The reactive load is modeled as constant impedance.
No. of
Capacitor
1
2
3
Nominal
voltage
(kV)
230
230
230
4
230
Table C-12: Shunt capacitors.
Connected bus
Reactive power
output
(MVar)
3
189.88
5
341.61
Rectifier AC
118.67
terminal
Inverter AC
122.00
terminal
-209-
Minimum
output
(MVar)
100
50
0
Maximum
output
(MVar)
600
500
125
0
125
Appendices
10.4 Appendix D
Figure D-1: A single line diagram of the two-area system with TCSC.
Table D-1: Synchronous machine parameters of G1, G2 and G3 and G4.
No. of Generator
1
2
3
4
Rotor type
Round
Rotor
Round
Rotor
Round
Rotor
Round
Rotor
Inertia time constant H (rated to Sgn)
Mechanical damping
Stator resistance ra
Stator leakage reactance xl
Synchronous reactance xd d-axis
Synchronous reactance xq q-axis
Transient reactance xd’ d-axis
Transient reactance xq’ q-axis
Sub-transient reactance xd’’ d-axis
Sub-transient reactance xq’’ q-axis
Transient time constant Td0’ d-axis
Transient time constant Tq0’ q-axis
Sub-transient time constant Td0’’ daxis
Sub-transient time constant Tq0’’ qaxis
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
0.05
0.05
0.05
0.05
Table D-2: Power generation conditions of G1, G2 and G3 and G4.
Gen
1
2
3
4
Bus
type
SL
PV
PV
PV
Rated power
(MVA)
900
900
900
900
Nominal voltage
(L-L kV)
20
20
20
20
Active power
output
750
700
719
700
reactive power
output
185
235
176
202
Terminal
voltage (p.u.)
1.03
1.01
1.03
1.01
Vmax
Vref
1
1 + sTr
1 + sTb
1 + sTa
Vmeas
K
1 + sTe
Vmin
Figure D-2: Block diagram of static exciter of G1, G2 and G3 and G4.
-210-
Appendices
Table D-3: Parameters of Static Exciter.
Transducer filter time constant Tr
0.01
Voltage regulator gain K
150
Voltage regulator time constant Te
0.05
Transient gain reduction time constant Ta
1
Transient gain reduction time constant Tb 10
Maximum voltage regulator output Vmax
3
Minimum voltage output Vmin
-3
1
2
3
4
5
6
7
second
p.u.
second
Second
Second
p.u.
p.u.
Tmax
1.0
1
1 + sTs
K
ωrotor
1 + sT3
1 + sTc
1 + sT4
1 + sT5
Pref
Tmin
Figure D-3: Block diagram of speed governor for G1, G2, G3 and G4.
1
2
3
4
5
6
7
8
Table D-4: Parameters of Governor.
Governor gain K
50 p.u.
Servo time constant Ts
0.1 second
Transient gain time constant T3
0
Second
HP turbine time constant Tc
0.5 Second
Time constant to set HP ratio T4 1.25 Second
Reheat time constant T5
5
Second
Maximum power Pmax
1
p.u.
Minimum power Pmin
0
p.u.
Table D-5: The capacitor and reactor of TCSC under steady state.
1 Series capacitor
20 Ohm
2 Series reactor (in parallel with the capacitor) 35 Ohm.
xmax
xC ⋅ xTCSC
xC + xTCSC
xTCSC
1
1 + sT f
xreactor
xmin
u max
kd
sTw
1 + sTw
1
1 + sTm
1 + sTlead
1 + sTlag
u min
Figure D-4: TCSC with supplementary damping control.
-211-
Appendices
Table D-6: Parameters of TCSC supplementary damping control.
1 Damping control gain Kd
22000 p.u.
2 Low pass filter time constant Tm
0.1
second.
3 Washout time constant Tw
10
second
0.11
4 Lead phase compensation time constant Tlead
second
0.556 second
5 Lag phase compensation time constant Tlag
-10
6 Minimum damping controller output umin
Ohm
10
7 Maximum damping controller output umax
Ohm
Table D-7: Transformer parameters.
No. of Transformer
1
Rated power (MVA)
900
Rated voltage (HV)
230
Rated voltage (LV)
20
Short circuit voltage (pos. Sequ. %) 15
Short circuit voltage (zero Sequ. %) 3
Winding connection (HV)
YN
Winding connection (LV)
YN
No. of
line
1
2
3
4
5
6
7
8
9
10
Rated voltage
(L-L kV)
230
230
230
230
230
230
230
230
230
230
2
900
230
20
15
3
YN
YN
3
900
230
20
15
3
YN
YN
Table D-8: Transmission line parameters.
Length
Resistance
Reactance
(km)
(Ohm/km)
(Ohm/km)
0.0529
25
0.529
0.0529
10
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
110
0.529
0.0529
10
0.529
0.0529
25
0.529
0.0529
110
0.529
0.0529
110
0.529
4
900
230
20
15
3
YN
YN
Susceptance
(µs/km)
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
3.3075
Table D-9: Load data.
Load
Active power (MW)
Reactive power (MVar)
Load 1
967
100
Load 2
1667
100
The active load is modeled as 50% constant and 50% constant impedance.
The reactive load is modeled as constant impedance.
No. of
Capacitor
1
2
Nominal
voltage
(kV)
230
230
Table D-10: Shunt capacitors.
Connected
Reactive power
bus
output
(MVar)
3
193.37
5
341.78
-212-
Maximum
output
(MVar)
600
500
Appendices
10.5 Appendix E
Figure E-1: A single line diagram of the two-area system with SVC.
Table E-1: Synchronous machine parameters of G1, G2 and G3 and G4.
No. of Generator
1
2
3
4
Rotor type
Round
Rotor
Round
Rotor
Round
Rotor
Round
Rotor
Inertia time constant H (rated to Sgn)
Mechanical damping
Stator resistance ra
Stator leakage reactance xl
Synchronous reactance xd d-axis
Synchronous reactance xq q-axis
Transient reactance xd’ d-axis
Transient reactance xq’ q-axis
Sub-transient reactance xd’’ d-axis
Sub-transient reactance xq’’ q-axis
Transient time constant Td0’ d-axis
Transient time constant Tq0’ q-axis
Sub-transient time constant Td0’’ daxis
Sub-transient time constant Tq0’’ qaxis
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
6.5
0
0.0025
0.2
1.8
1.7
0.3
0.55
0.25
0.25
8
0.4
0.03
0.05
0.05
0.05
0.05
Table E-2: Power generation conditions of G1, G2 and G3 and G4.
Gen
1
2
3
4
Bus
type
SL
PV
PV
PV
Rated power
(MVA)
900
900
900
900
Nominal voltage
(L-L kV)
20
20
20
20
Active power
output
750
700
719
700
Reactive power
output
185
235
176
202
Terminal
voltage (p.u.)
1.03
1.01
1.03
1.01
Vmax
Vref
1
1 + sTr
1 + sTb
1 + sTa
Vmeas
K
1 + sTe
Vmin
Figure E-2: Block diagram of static exciter of G1, G2 and G3 and G4.
-213-
Appendices
1
2
3
4
5
6
7
Table E-3: Parameters of static exciter.
Transducer filter time constant Tr
0.01
Voltage regulator gain K
150
Voltage regulator time constant Te
0.05
Transient gain reduction time constant Ta
1
Transient gain reduction time constant Tb 10
Maximum voltage regulator output Vmax
3
Minimum voltage output Vmin
-3
second
p.u.
second
Second
Second
p.u.
p.u.
Tmax
1.0
K
ωrotor
Pref
1
1 + sTs
1 + sT3
1 + sTc
1 + sT4
1 + sT5
Tmin
Figure E-3: Block diagram of speed governor of G1, G2, G3 and G4.
1
2
3
4
5
6
7
8
Table E-4: Parameters of speed governor.
50 p.u.
Governor gain K
Servo time constant Ts
0.1 second
Transient gain time constant T3
0
Second
HP turbine time constant Tc
0.5 Second
Time constant to set HP ratio T4 1.25 Second
Reheat time constant T5
5
Second
Maximum power Pmax
1
p.u.
Minimum power Pmin
0
p.u.
Table E-5: Transformer parameters.
No. of Transformer
Rated power (MVA)
Rated voltage (HV)
Rated voltage (LV)
Short circuit voltage (pos. Sequ. %)
Short circuit voltage (zero Sequ. %)
Winding connection (HV)
Winding connection (LV)
1
900
230
20
15
3
YN
YN
2
900
230
20
15
3
YN
YN
3
900
230
20
15
3
YN
YN
4
900
230
20
15
3
YN
YN
Table E-6: Transmission line parameters.
No. of line
1
2
3
4
5
6
Rated voltage (L-L kV) 230
230
230
230
230
230
Length (km)
25
10
110
110
110
110
0.0529 0.0529 0.0529 0.0529 0.0529 0.0529
Resistance (Ohm/km)
Reactance (Ohm/km)
0.529 0.529 0.529 0.529 0.529 0.529
3.3075 3.3075 3.3075 3.3075 3.3075 3.3075
Susceptance (µs/km)
-214-
7
230
10
8
230
25
0.0529
0.0529
0.529
0.529
3.3075
3.3075
Appendices
Table E-7: Load data.
Load
Active power (MW)
Reactive power (MVar)
Load 1
967
100
Load 2
1667
100
The active load is modeled as 50% constant and 50% constant impedance.
The reactive load is modeled as constant impedance.
No. of
Capacitor
1
2
Table E-8: Shunt capacitors.
Connected
Reactive power
bus
output
(MVar)
3
197.11
5
217.53
Nominal
voltage
(kV)
230
230
Maximum
output
(MVar)
600
500
Figure E-4: SVC composite (DIgSILENT interface).
Vref
VSVC
Qmax
Qfixed
k
1
1 + sT f
1 + sTa
1 + sTb
Qmin
Figure E-5: Primary voltage control of SVC.
Table E-9: Parameters of the primary voltage control of SVC.
10 p.u.
1 Proportional gain Kp
3 Lead phase compensation time constant Tlead 0.65 second
0.2 second
4 Lag phase compensation time constant Tlead
6 SVCr time constant Tf
0.03 second
-100 Ohm
7 Minimum reactive power output Qmin
400 Ohm
8 Maximum reactive power output Qmax
-215-
QSVC
Appendices
Vref
VSVC
-
+
-
Qmax
Qfixed
k
+
1 + sTa
1 + sTb
1
1 + sT f
+
Qmin
u max
Phase angle 1
+
kd
-
1
1 + sTm
sTw
1 + sTw
1 + sTlead
1 + sTlag
u min
Phase angle 2
Figure E-6: SVC supplementary damping controller.
Table E-10: Parameters of the primary voltage control of SVC.
1 Voltage reference for voltage control
1.0 p.u.
2 Damping control gain Kd
1.0 p.u.
3 Low pass filter time constant Tm
0.1 second.
4 Washout time constant Tw
10 second
0.22
5 Lead phase compensation time constant Tlead
second
1.38 second
6 Lag phase compensation time constant Tlag
-10 p.u.
7 Minimum damping controller output umin
10 p.u.
8 Maximum damping controller output umax
-216-
QSVC
Appendices
10.6 Appendix F
Table F-1: DC transmission line parameters.
DC transmission line 1
Rated DC voltage (kV) 500
Rated current (kA)
3.6
Length (km)
200
Cable
Line type
0.0075
Resistance (Ohm/km)
Inductance (mH/km)
1
Figure F-1: Rectifier operation condition (DIgSILENT interface).
α max
kp
1
1 + sT f
I ref
ki
s
I meas
α min
Figure F-2: Rectifier’s α control for constant current.
1
2
3
4
5
6
Table F-2: Parameters of rectifier control.
Proportional gain Kp
0
p.u.
Output gain Ko
1
p.u.
Rectifier time constant Tf
0.001 second
Integral gain Ki
0.01 p.u.
5
Minimum firing angle αmin
degree
90
Maximum firing angle αmax
degree
-217-
α
Appendices
Figure F-3: Inverter operation condition (DIgSILENT interface).
β max
kp
1
1 + sT f
Vref
Vmeas
ki
s
β min
Figure F-4: inverter’s β control for constant voltage.
1
2
3
4
5
6
Table F-3: Parameters of rectifier control.
Proportional gain Kp
0
p.u.
Output gain Ko
1
p.u.
Rectifier time constant Tf
0.001 second
Integral gain Ki
0.01 p.u.
90
Minimum advance firing angle βmin
degree
Maximum advance firing angle βmax 150 degree
-218-
β
Appendices
I ref
α max
kp
1
1 + sT f
I meas
ki
s
α
α min
umax
1
1 + sTm
kd
1 + sTlead
1 + sTlag
sTw
1 + sTw
1 + sTlead
1 + sTlag
umin
Figure F-5: HVDC supplementary damping controller in GB full model.
Table F-4: Parameters of the HVDC damping controller.
1
2
3
4
5
6
7
Damping control gain Kd
100 p.u.
Low pass filter time constant Tm
0.1 second.
Washout time constant Tw
10 second
Lead phase compensation time constant Tlead 0.05 second
1.8 second
Lag phase compensation time constant Tlag
-4 p.u.
Minimum damping controller output umin
4
Maximum damping controller output umax
p.u.
-219-
Appendices
Table F-5: A list of the PSS in service.
No. of PSS PSS name
1
GRMPSS
Power gird generator name
SPTL
BPGR01_1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
NGET
ABBPSS
ABBPSS
ABBPSS
ABBPSS
ABBPSS
ABBPSS
ABBPSS
RYHPSS
RYHPSS
RYHPSS
RYHPSS
RYHPSS
RYHPSS
ST4PSS
ST4PSS
ST4PSS
ST4PSS
ST4PSS
ST4PSS
ST4PSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
ZVTPSS
-220-
DEES8A_1
DEES8B_1
DEES8S_1
KILL8A_1
KILL8B_1
KILL8C_1
KILL8F_1
KILL8D_1
KILL8E_1
RYEH8A_1
RYEH8B_1
RYEH8C_1
RYEH8S_1
BAGB8B_1
SHOS8A_1
SHOT8A_1
SHOT8B_1
SHOT8S_1
WBUR8A_1
WBUR8B_1
LITB8S_1
PEMB8A_1
PEMB8B_1
PEMB8C_1
PEMB8D_1
PEMB8E_1
SEAB8A_1
SEAB8B_1
SEAB8S_1
Appendices
10.7 Appendix G
10.7.1 Published journal papers
Paper 1. V. Terzija, D. Cai, V. Stanojevic, G. Strbac, “Frequency and Power
Components Estimation from Instantaneous Power Signal,” IEEE Transactions on
Instrumentations and Measurements. Vol. 60, no. 1, pp. 3640-3649, June 2011.
Paper 2. V. Terzija, G. Valerde, D. Cai, P. Regulski, V. Madani, J. Fitch, S. Skok,
Miroslav M. Begovic and A. Phadke, “Wide-Area Monitoring, Protection and Control
of Future Electric Power Networks”, IEEE Proceedings, vol. 99, No.1, pp. 80-93,
January. 2011.
Paper 3. S. Chakrabarti, E. Kyriakides, B. Tianshu; D. Cai, V. Terzija, “Measurements
get together,” IEEE Power and Energy Magazine, vol.7, no.1, pp.41-49, January 2009.
10.7.2 Submitted journal papers
Paper 4. D. Cai, M. Osborne, V. Terzija, “A Smart Application for Inter-area
Oscillations Monitoring based on the Newton-Type Algorithm”, submitted to IEEE
transactions on Smart Grid.
Paper 5. D. Cai, M. Osborne, V. Terzija, “Wide Area Inter-area Oscillations Monitoring
based on fast Nonlinear Estimation Algorithm”, submitted to Special Issue on Planning
and Operation of Transmission Grid with Applications to Smart Grid, IEEE
Transactions on Smart Grid.
10.7.3 Published conference papers
Paper 6. V. Terzija, D. Cai, J. Fitch, “Monitoring of inter-area oscillations in power
systems with renewable energy resources using Prony method,” The 20th International
Conference and Exhibition on Electricity Distribution - Part 2, CIRED, 2009.
Paper 7. V. Terzija, D. Cai, K. Mustafa “Power imbalance estimation in distribution
networks with renewable energy resources,” The 20th International Conference and
Exhibition on Electricity Distribution - Part 2, CIRED, 2009.
Paper 8. G. Valerde, D. Cai, J. Fitch, V. Terzija, “Enhanced state estimation with realtime updated network parameters using SMT,” IEEE Power & Energy Society General
Meeting, 2009.
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