Analysis and Damping Control of Power System Low-frequency Oscillations (eBook)
XI, 394 Seiten
Springer US (Verlag)
978-1-4899-7696-3 (ISBN)
This book presents the research and development results on power systems oscillations in three categories of analytical methods. First is damping torque analysis which was proposed in 1960's, further developed between 1980-1990, and widely used in industry. Second is modal analysis which developed between the 1980's and 1990's as the most powerful method. Finally the linearized equal-area criterion analysis that is proposed and developed recently. The book covers three main types of controllers: Power System Stabilizer (PSS), FACTS (Flexible AC Transmission Systems) stabilizer, and ESS (Energy Storage Systems) stabilizer. The book provides a systematic and detailed introduction on the subject as the reference for industry applications and academic research.
This book presents the research and development results on power systems oscillations in three categories of analytical methods. First is damping torque analysis which was proposed in 1960's, further developed between 1980-1990, and widely used in industry. Second is modal analysis which developed between the 1980's and 1990's as the most powerful method. Finally the linearized equal-area criterion analysis that is proposed and developed recently. The book covers three main types of controllers: Power System Stabilizer (PSS), FACTS (Flexible AC Transmission Systems) stabilizer, and ESS (Energy Storage Systems) stabilizer. The book provides a systematic and detailed introduction on the subject as the reference for industry applications and academic research.
Prof. Wenjuan Du is a Professor at the School of Electrical Engineering, North China Electric Power University in Beijing, China. Prof. Haifeng Wang is a Professor at the State Key Lab of Renewable Power Generation Power Systems, North China Electric Power University in Beijing, China. Dr. Siqi Bu is an Assistant Professor at the Department of Electrical Engineering, The Hong Kong Polytechnic University in Kowloon, Hong Kong.
Preface 6
Contents 7
1 Introduction 12
1.1 Power System Low-frequency Oscillations 12
1.2 Linearized Methods for the Analysis and Damping Control of Power System Oscillations 14
1.3 FACTS and Grid-Connected ESS 16
1.4 Controllers to Damp Power System Oscillations 18
1.5 Design of Damping Controllers to Suppress Power System Oscillations 21
1.6 Organization of the Book 23
References 24
2 A Single-Machine Infinite-Bus Power System Installed with a Power System Stabilizer 27
2.1 Linearized Model of a Single-Machine Infinite-Bus Power System Installed with a Power System Stabilizer 27
2.1.1 General Linearized Mathematical Model 27
2.1.1.1 Full Mathematical Model of a Synchronous Generator 27
2.1.1.2 Excitation System and the Automatic Voltage Regulator (AVR) 28
2.1.1.3 A Single-Machine Infinite-Bus Power System 32
2.1.1.4 Linearized Model of Single-Machine Infinite-Bus Power System 34
2.1.2 Heffron–Phillips Model 36
2.1.2.1 Simplification 36
2.1.2.2 A Simplified Model of Single-Machine Infinite-Bus Power System 37
2.1.2.3 Heffron–Phillips Model [1–3] 40
2.2 Modal Analysis 42
2.2.1 Basis of Modal Analysis Theory 42
2.2.1.1 Modal Decomposition 42
2.2.1.2 Stability of Open-Loop System and Closed-Loop System 45
2.2.2 Applications of Modal Analysis 47
2.2.2.1 Modal Analysis for the AVR 47
2.2.2.2 Modal Analysis for the PSS 49
2.2.2.3 Design of PSS by Pole Assignment 51
2.3 Damping Torque Analysis 52
2.3.1 Damping Torque and Synchronizing Torque 52
2.3.1.1 Damping Torque and Synchronizing Torque Derived from Heffron–Phillips Model 52
2.3.1.2 Electric Torque Contributed from the PSS 54
2.3.1.3 Damping Torque and Synchronizing Torque Derived from the General Linearized Model 55
2.3.2 Damping Torque Analysis and Design of PSS by Phase Compensation 57
2.3.2.1 Theoretical Basis of the Damping Torque Analysis 57
2.3.2.2 Graphical Explanation of the Damping Torque Analysis 58
2.3.2.3 Design of PSS by the Phase Compensation Method [4] 60
2.4 Examples 63
2.4.1 Linearized Mathematical Models of an Example Power System 63
2.4.1.1 Linearized Mathematical Model with Full Model of Generator Used 63
2.4.1.2 Heffron–Phillips Model of Example Power System 68
2.4.2 Modal Analysis of Example Power System 69
2.4.2.1 Modal Decomposition and Stability of Example Power System 69
2.4.2.2 Modal Analysis of the AVR 71
2.4.2.3 Design of the PSS by Pole Assignment for the Example Power System 73
2.4.3 Damping Torque Analysis of Example Power System 76
2.4.3.1 Damping Torque Provided by the AVR in the Example Power System 76
2.4.3.2 Design of PSS Installed in the Example Power System by the Phase Compensation Method 78
2.4.3.3 Theoretical Basis and Graphical Explanation of the Damping Torque Analysis 81
2.4.4 Equivalence Between the Damping Torque and Modal Analysis 83
2.4.4.1 Demonstration by Use of Heffron–Phillips Model of Example Power System 83
2.4.4.2 Demonstration by Use of General Linearized Model of Example Power System 85
References 89
3 Damping Torque Analysis of Thyristor-Based FACTS Stabilizers Installed in Single-Machine Infinite-Bus Power Systems 90
3.1 A Single-Machine Infinite-Bus Power System Installed with an SVC Stabilizer 90
3.1.1 Extended Heffron—Phillips Model of a Single-Machine Infinite-Bus Power System Installed with an SVC Stabilizer 90
3.1.1.1 Nonlinear Mathematical Model of a Single-Machine Infinite-Bus Power System Installed with an SVC Stabilizer 90
3.1.1.2 Extended Heffron–Phillips Model 92
3.1.1.3 Extended Heffron–Phillips Model with Both the SVC Voltage and Damping Control Function Included 94
3.1.1.4 Calculation of Initial Compensation 97
3.1.2 Damping Torque Analysis of SVC Stabilizer 99
3.1.2.1 Electric Torque Provided by the SVC Stabilizer 99
3.1.2.2 Damping Control as Affected by the Load Conditions 101
3.1.2.3 Influence of Parameters of the Generator 102
3.1.2.4 Electric Length of the Transmission Line 103
3.1.2.5 Installing Location of the SVC 105
3.2 A Single-Machine Infinite-Bus Power System Installed with a TCSC or TCPS Stabilizer 106
3.2.1 Extended Heffron–Phillips Model of a Single-Machine Infinite-Bus Power System Installed with a TCSC or TCPS Stabilizer 106
3.2.1.1 Extended Heffron–Phillips Model of a Single-Machine Infinite-Bus Power System Installed with a TCSC 106
3.2.1.2 Extended Heffron–Phillips Model of a Single-Machine Infinite-Bus Power System Installed with a TCPS 109
3.2.2 Damping Torque Analysis of TCSC and TCPS Stabilizers 112
3.2.2.1 General Expression of Damping Torque Contributed by the TCSC and TCPS Stabilizers 112
3.2.2.2 Damping Torque Provided by the TCSC Stabilizer [4] 113
3.2.2.3 Damping Torque Provided by the TCPS Stabilizer [5] 115
3.3 An Example Power System Installed with an SVC Stabilizer 116
3.3.1 Linearized Model of Example Power System 117
3.3.1.1 Linearized Model with the Transfer Function of the SVC Voltage Controller Included 117
3.3.1.2 Linearized Model of the Example Power System 121
3.3.2 Design of SVC-Based Stabilizer 123
3.3.2.1 SVC Stabilizer Designed by Using the Phase Compensation Method 123
3.3.2.2 Damping Control Effectiveness of the SVC Stabilizer as Affected by Various Factors 126
References 129
4 Single-Machine Infinite-Bus Power Systems Installed with VSC-Based Stabilizers 130
4.1 Damping Torque Analysis of a Shunt VSC-Based Stabilizer Installed in a Single-Machine Infinite-Bus Power System 130
4.1.1 Extended Heffron–Phillips Model of a Single-Machine Infinite-Bus Power System Installed with a Shunt VSC-Based Stabilizer 130
4.1.1.1 A Shunt VSC Installed in a Single-Machine Infinite-Bus Power System 130
4.1.1.2 Extended Heffron–Phillips Model 134
4.1.2 Damping Torque Analysis of Shunt VSC-Based Stabilizer Installed in Single-Machine Infinite-Bus Power System 139
4.1.2.1 Damping Torque Contributed by the Shunt VSC-Based Stabilizer [2, 3] 139
4.1.2.2 Difference of Damping Control Effectiveness Between the VSC-Based Reactive and Active Power Stabilizers 140
4.2 Damping Function of a Stabilizer Added on a Static Synchronous Series Compensator (SSSC) Installed in a Single-Machine Infinite-Bus Power System 142
4.2.1 Damping Torque Analysis of a SSSC Stabilizer Installed in a Single-Machine Infinite-Bus Power System 142
4.2.1.1 A Single-Machine Infinite-Bus Power System Installed with a Static Synchronous Series Compensator 142
4.2.1.2 Extended Heffron–Phillips Model of the Single-Machine Infinite-Bus Power System Installed with the SSSC and Damping Torque Analysis [4] 145
4.2.2 Design of a SSSC Stabilizer 148
4.3 Damping Function of a Unified Power Flow Controller (UPFC) Installed in a Single-Machine Infinite-Bus Power System 152
4.3.1 Mathematical Model of a Single-Machine Infinite-Bus Power System Installed with a UPFC 152
4.3.1.1 Dynamic Model of a UPFC 152
4.3.1.2 Nonlinear Model of the Single-Machine Infinite-Bus Power System Installed with the UPFC 155
4.3.1.3 Linearized Model of the Single-Machine Infinite-Bus Power System Installed with the UPFC 157
4.3.2 Design of a UPFC Stabilizer Installed in a Single-Machine Infinite-Bus Power System 164
4.3.2.1 Selection of Modulation Signal to Add the Damping Control Signal of the UPFC Stabilizer by Using the Controllability and Observability Index [6, 7] 164
4.3.2.2 Selection by Damping Torque Calculation 168
4.3.2.3 Robustness of the Damping Control to the Variations of Power System Operating Conditions 170
4.4 Examples 172
4.4.1 An Example Single-Machine Infinite-Bus Power System Installed with a BESS Stabilizer 172
4.4.1.1 Extended Heffron–Phillips Model of the Example Power System Installed with a BESS 172
4.4.1.2 Design of BESS Stabilizers by Use of the Phase Compensation Method 176
4.4.1.3 Robustness of the BESS Stabilizers to the Variations of Power System Loading Conditions 179
4.4.2 An Example Single-Machine Infinite-Bus Power System Installed with a UPFC Stabilizer 181
4.4.2.1 Extended Heffron–Phillips Model of Example Power System Installed with a UPFC 181
4.4.2.2 Robust Selection of a Modulation Signal to Add the Damping Control Signal of the UPFC Stabilizer by Using the Damping Torque Analysis and Residue Index 184
4.4.2.3 Design of the UPFC Stabilizer by Using the Phase Compensation Method 187
References 191
5 A Multi-machine Power System Installed with Power System Stabilizers 192
5.1 Mathematical Model of a Multi-machine Power System Installed with Power System Stabilizers 192
5.1.1 A Two-Machine Power System Installed with Power System Stabilizers 192
5.1.1.1 Network Equations 192
5.1.1.2 Linearized Model When the Classical Model of Synchronous Generators Is Used 196
5.1.1.3 Heffron–Phillips Model 198
5.1.2 A Multi-machine Power System Installed with Power System Stabilizers 201
5.1.2.1 Heffron–Phillips Model of an N-Machine Power System Installed with Power System Stabilizers 201
5.1.2.2 Linearized Model When Full Mathematical Model of Synchronous Generators Is Used 205
5.2 Modal Analysis and Control of Power System Oscillations in a Multi-machine Power System Installed with Power System Stabilizers 208
5.2.1 Eigensolution for the Analysis of Power System Oscillations 208
5.2.1.1 Participation Factor, Correlation Ratio of Electromechanical Loop, Modal Shape, and Eigensolution 208
5.2.1.2 Selective Reduced-Order Calculation of Electromechanical Oscillation Modes 211
5.2.2 Design of Power System Stabilizers in Multi-machine Power System 213
5.2.2.1 Coordinated Design of Multiple Power System Stabilizers 213
5.2.2.2 Parameter Tuning Algorithm for the Design of Multiple Power System Stabilizers 215
5.2.3 Fixed Modes Associated with PSS Control 218
5.3 An Example Three-Machine Power System 223
5.3.1 Example Power System and Its Linearized Heffron–Phillips Model 223
5.3.1.1 System Parameters and Operating Conditions 223
5.3.1.2 Calculation of Initial Values of State Variables 224
5.3.1.3 Linearized Heffron–Phillips Model 226
5.3.2 Modal Analysis of Example Power System 230
5.3.2.1 Electromechanical Oscillation Modes of Example Power System 230
5.3.2.2 Selective Reduced-Order Calculation of Electromechanical Oscillation Modes of Example Power System 233
5.3.2.3 Coordinated Design of PSSs 238
References 243
6 Multi-machine Power System Installed with Thyristor-Based FACTS Stabilizers 244
6.1 Mathematical Model of a Multi-machine Power System Installed with Thyristor-Based FACTS Stabilizers 244
6.1.1 Heffron–Phillips Model [1] 244
6.1.1.1 Heffron–Phillips Model of an N-Machine Power System Installed with an SVC Stabilizer 244
6.1.1.2 Heffron–Phillips Model of an N-Machine Power System Installed with a TCSC or TCPS Stabilizer 247
6.1.2 General Linearized Model of an N-Machine Power System Installed with Multiple Thyristor-Based FACTS Stabilizers 251
6.1.2.1 Linearized Model of Generators 251
6.1.2.2 Linearized Model of an SVC Installed in the N-Machine Power System 255
6.1.2.3 Linearized Model of a TCSC Installed in the N-Machine Power System 259
6.1.2.4 Linearized Model of a TCPS Installed in the N-Machine Power System 264
6.1.2.5 General Linearized Model of the N-Machine Power System Without the PSSs and Thyristor-Based FACTS Stabilizers Installed 268
6.1.2.6 General Linearized Model of the N-Machine Power System with the PSSs and Thyristor-Based FACTS Stabilizers Installed 273
6.2 Analysis and Damping Control of Thyristor-Based FACTS Stabilizers Installed in a Multi-machine Power System 275
6.2.1 Damping Torque Analysis in a Multi-machine Power System 275
6.2.1.1 Damping Torque Contribution from a Stabilizer Derived from the Heffron–Phillips Model 275
6.2.1.2 Damping Torque Contribution from a Stabilizer Derived from the General Linearized Model of an N-Machine Power System 278
6.2.2 Selection of Installing Location and Feedback Signal of a Stabilizer in a Multi-machine Power System 281
6.2.2.1 Selection of Installing Location of a PSS by Participation Factor and Sensitivity Index 281
6.2.2.2 Selection of Installing Locations and Feedback Signals of a Stabilizer by Damping Torque Analysis [2] 283
6.2.2.3 Residue Index and Its Connection with the Damping Torque Analysis [3] 285
6.2.3 Selection of Robust Installing Locations and Feedback Signals of a Stabilizer by an Eigensolution-Free Method 288
6.2.3.1 Robust Selection of Installing Locations and Feedback Signals of a Stabilizer [4] 288
6.2.3.2 An Equivalent Residue Index and Eigensolution-Free Selection of Robust Installing Location and Feedback Signal of the Stabilizer 289
6.2.4 Stabilizer Design in a Multi-machine Power System Considering Robustness and Interaction of Stabilizers 291
6.2.4.1 Selection of an Operating Condition for the Robust Coordinated Design of Multiple Stabilizers in a Multi-machine Power System 291
6.2.4.2 Non-negatively Interactive Design of a Stabilizer in a Multi-machine Power System [5] 294
6.3 An Example Two-Area Four-Machine Power System 298
6.3.1 Linearized Model 298
6.3.1.1 System Parameters and Operating Conditions 298
6.3.1.2 Linearized Heffron–Phillips Model 301
6.3.1.3 Linearized Heffron–Phillips Model of the System with an SVC Stabilizer to Be Installed 306
6.3.2 Selection of Installing Locations of Stabilizers 310
6.3.2.1 Selection of the PSS Installing Locations 310
6.3.2.2 Selection of Installing Location of the SVC Stabilizer 313
6.3.2.3 Robust Installing Locations and Feedback Signals of the SVC Stabilizer 323
6.3.2.4 Design of Robust SVC Stabilizer 325
6.4 Example Three-Machine Power System 329
6.4.1 Dynamic Interactions Among PSSs Installed in Example Three-Machine Power System 329
6.4.2 Design of Non-negatively Interactive PSSs Installed in the Example Power System 333
References 337
7 Multi-machine Power Systems Installed with VSC-Based Stabilizers 338
7.1 Mathematical Model of a Multi-machine Power System Installed with VSC-Based Stabilizers 338
7.1.1 Mathematical Model of a Multi-machine Power System Installed with a Shunt VSC-Based Stabilizer 338
7.1.1.1 Heffron–Phillips Model of an N-Machine Power System Installed with a Shunt VSC-Based Stabilizer 338
7.1.1.2 General Linearized Model of an N-Machine Power System Installed with a Shunt VSC-Based Stabilizer 345
7.1.2 Mathematical Model of a Multi-machine Power System Installed with a UPFC-Based Stabilizer 348
7.1.2.1 Heffron–Phillips Model of an N-Machine Power System Installed with a UPFC-Based Stabilizer [4, 5] 348
7.1.2.2 General Linearized Model of an N-Machine Power System Installed with a UPFC-Based Stabilizer 355
7.2 Design of a Shunt VSC-Based Stabilizer by Localized Phase Compensation Method to Suppress Inter-area Line Power Oscillations 358
7.2.1 Localized Small-Signal Model of a VSC-Based Unit in a Multi-machine Power System 359
7.2.1.1 Line Power Small-Signal Oscillation [6] 359
7.2.1.2 Control Function Model of the VSC 361
7.2.1.3 Dynamic Equation of the VSC 363
7.2.1.4 Localized Small-Signal Model of the VSC-Based Unit 364
7.2.2 Design of VSC-Based Stabilizer by Localized Phase Compensation Method 367
7.2.3 Robustness of an ESS-Based Stabilizer to Variation of Line-Loading Conditions 371
7.2.3.1 Localized Small-Signal Model of an Energy Storage System [7] 371
7.2.3.2 Robustness of the ESS-Based Stabilizer to the Variations of Line-Loading Conditions 372
7.3 An Example of Multi-machine Power System with a Grid-Connected FC Power Plan 376
7.3.1 Mathematical Model of a Multi-machine Power System with a Grid-Connected FC Power Plant 376
7.3.1.1 Dynamic Model of the SOFC Power Plant 376
7.3.1.2 Linearized Model of the SOFC Power Plant 379
7.3.1.3 Linearized Model of Multi-machine Power System with SOFC Power Plant 381
7.3.2 Design of a Stabilizer Attached to the VSC of FC Power Plant by Localized Phase Compensation Method 384
7.3.2.1 Localized Design of the Stabilizer 384
7.3.2.2 An Example 386
7.4 Damping of Multi-mode Oscillations by Multiple Stabilizers Attached to a Single UPFC 389
7.4.1 Coordinated Design of Multiple Stabilizers by Artificial Fish Swarm Algorithm (AFSA) [8] 390
7.4.1.1 Objective Function 390
7.4.1.2 The Artificial Fish Swarm Algorithm 391
7.4.2 Examples 392
7.4.2.1 An Example of Damping Two-Mode Oscillations by Stabilizers Added on a UPFC 392
7.4.2.2 An Example of Damping Three-Mode Oscillations by Stabilizers Added on a Multi-terminal UPFC 395
References 400
Index 402
| Erscheint lt. Verlag | 30.3.2016 |
|---|---|
| Reihe/Serie | Power Electronics and Power Systems |
| Zusatzinfo | XI, 394 p. 149 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Technik ► Elektrotechnik / Energietechnik |
| Schlagworte | BSS • damping torque • ESS • HVCC • LEAC • multi-machine • SSMP • stabilizer |
| ISBN-10 | 1-4899-7696-5 / 1489976965 |
| ISBN-13 | 978-1-4899-7696-3 / 9781489976963 |
| Haben Sie eine Frage zum Produkt? |
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