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ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES PhD THESIS Ahmet Mete VURAL MODELING OF MULTI-CONVERTER FACTS (FLEXIBLE ALTERNATING CURRENT TRANSMISSION SYSTEMS) DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING ADANA, 2012 ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES MODELING OF MULTI-CONVERTER FACTS (FLEXIBLE ALTERNATING CURRENT TRANSMISSION SYSTEMS Ahmet Mete VURAL PhD THESIS DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING We certify that the thesis titled above was reviewed and approved for the award of degree of the Doctor of Philosophy by the board of jury on 24/12/2012. ……………….................................. Assoc. Prof. Dr. K. Çağatay BAYINDIR SUPERVISOR …………….……........... Prof. Dr. Mehmet TÜMAY CO-SUPERVISOR …………………...……... Assoc. Prof. Dr. İlyas EKER MEMBER ………............................... Assoc. Prof. Dr. Ulus ÇEVİK MEMBER ……………………….…... Prof. Dr. Tankut YALÇINÖZ MEMBER This Ph.D. Thesis is written at the Institute of Natural and Applied Sciences of Çukurova University. Registration Number: Prof. Dr. Selahattin SERİN Director Institute of Natural and Applied Sciences Note: The usage of the presented specific declarations, tables, figures and photographs either in this thesis or in any other reference without citation is subject to "The law of Arts and Intellectual Products" number of 5846 of Turkish Republic. ABSTRACT PhD THESIS MODELING OF MULTI-CONVERTER FACTS (FLEXIBLE ALTERNATING CURRENT TRANSMISSION SYSTEMS) Ahmet Mete VURAL ÇUKUROVA UNIVERSITY INSTITUTE OF NATURAL AND APPLIED SCIENCES DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING Supervisor: Assoc. Prof. Dr. K. Çağatay BAYINDIR Co-Supervisor: Prof. Dr. Mehmet TÜMAY Year: 2012, Pages: 249 Jury: Prof. Dr. Mehmet TÜMAY Prof. Dr. Tankut YALÇINÖZ Assoc. Prof. Dr. İlyas EKER Assoc. Prof. Dr. Ulus ÇEVİK Assoc. Prof. Dr. K. Çağatay BAYINDIR Multi-converter FACTS devices can increase control flexibility of power systems by providing independent and simultaneous control of multi-power system parameters. In this thesis, the following multi-converter FACTS devices are modeled and analyzed at transmission level: Generalized Unified Power Flow Controller (GUPFC), Interline Power Flow Controller (IPFC), and Back-to-Back Static Synchronous Compensator (BtB-STATCOM). The steady-state PSCAD models of these devices are proposed for power flow studies without requiring programming coding. A quasi multi-pulse voltage source converter with low harmonic content is designed for converter-level modeling of the aforementioned devices. The magnitude and the phase angle of the voltage of the designed converter are controlled efficiently despite triggering the power semiconductors at fundamental system frequency. The dynamic control characteristics of GUPFC, IPFC, and BtB-STATCOM are extensively studied and analyzed using the developed PSCAD based converter-level models in various test power systems. A novel fuzzy-rule based control scheme for IPFC to decouple real and reactive power flow control loops is designed and tested through miscellaneous and comparative simulation studies. Using converter-level models of these devices, transient stability studies of the power systems are also addressed in this thesis. A novel self-tuning fuzzy damping controller for GUPFC is designed to damp synchronous generator oscillations and to increase speed stability of induction generators which are located in a wind farm. The same controller is adapted for IPFC to suppress inter-area mode of oscillations. Key Words: FACTS Devices, Modeling, Simulation. I ÖZ DOKTORA TEZİ ÇOK KONVERTÖRLÜ ESNEK ALTERNATİF AKIM İLETİM SİSTEMLERİNİN MODELLENMESİ Ahmet Mete VURAL ÇUKUROVA ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ ELEKTRİK ELEKTRONİK MÜHENDİSLİĞİ ANABİLİM DALI 1. Danışman: Doç. Dr. K. Çağatay BAYINDIR 2. Danışman: Prof. Dr. Mehmet TÜMAY Yıl: 2012, Sayfa: 249 Jüri: Prof. Dr. Mehmet TÜMAY Prof. Dr. Tankut YALÇINÖZ Doç. Dr. İlyas EKER Doç. Dr. Ulus ÇEVİK Doç. Dr. K. Çağatay BAYINDIR Çok konvertörlü FACTS cihazları, güç sistemlerinin denetim esnekliğini, çoklu güç sistemi parametrelerinin bağımsız ve eşzamanlı denetimlerini sağlayarak artırabilirler. Bu tezde, iletim seviyesinde modellenen ve analiz edilen çok konvertörlü FACTS cihazları şunlardır: Genelleştirilmiş Bütünleşik Güç Akış Denetleyicisi (GUPFC), Hatlarası Güç Akış Denetleyicisi (IPFC) ve Durgun Senkron Kompanzatör (STATCOM). Bu cihazların durgun-hal PSCAD modelleri programlama kodlamasına ihtiyaç duyulmadan güç akış çalışmaları için önerilmiştir. Düşük harmonik içerikli çok darbeli benzeri bir gerilim kaynaklı konvertör sözü geçen cihazların konvertör seviyesi modellemeleri için tasarlanmıştır. Tasarlanan konvertörün geriliminin büyüklüğü ve faz açısı, güç yarıiletkenlerinin temel şebeke frekansında tetiklenmelerine karşın etkin bir şekilde denetlenmektedir. GUPFC, IPFC ve BtB-STATCOM’un dinamik denetim nitelikleri, geliştirilen PSCAD tabanlı konvertör seviyesi modellerin çeşitli örnek güç sistemleri üzerinde kullanılmasıyla kapsamlı olarak çalışılmış ve analiz edilmiştir. IPFC için aktif ve reaktif güç akış denetim döngülerini ayrıştırmak amacıyla özgün bulanık-kural tabanlı bir denetim şeması tasarlanmış, çok yönlü ve karşılaştırmalı benzetim çalışmaları ile test edilmiştir. Bu cihazların konvertör seviyesi modelleri kullanılarak güç sistemlerinin geçici kararlılık çalışmaları da bu tezde ele alınmıştır. GUPFC için, senkron jeneratör salınımlarını söndürmek ve bir rüzgar çiftliğine yerleştirilmiş endüksiyon jeneratörlerinin hız kararlılıklarını artırmak için özgün kendi kendine ayarlamalı bir bulanık sönümleme denetleyicisi tasarlanmıştır. Aynı denetleyici alanlar arası salınım modlarının bastırılması amacıyla IPFC için uyarlanmıştır. Anahtar Kelimeler: FACTS Cihazları, Modelleme, Simülasyon. II ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my co-supervisor Prof. Dr. Mehmet Tümay for his guidance, advice, and encouragement throughout my studies, who is also a role model in my career. I always appreciate his ideas to build my own academic interests. I would like to express my sincere gratitude to my supervisor Assoc. Prof. Dr. Kamil Çağatay Bayındır for his remarkable advice, guidance, criticism, and encouragement throughout my studies. He has been great sources of inspiration to me. I wish to express my special thanks to the rector of Hasan Kalyoncu University, Prof. Dr. İbrahim Özdemir and engineering faculty staff for their good wishes and maintaining an excellent academic environment which had a positive impact on this work. I would like to thank deeply Electrical and Electronics Engineering Department staff for their insights and motivation during the time I worked in Atılım University. I gratefully thank Prof. Dr. Tankut Yalçınöz, Assoc. Prof. Dr. Ulus Çevik, and Assoc. Prof. Dr. İlyas Eker for participating in my thesis defense committee. I would like to express my deepest gratitude to my mother, father and my brother for their patience, sacrifice, encouragement, and continuous morale support. They rendered me enormous support during the whole study period. I would like to express my deepest gratitude to my wife Selma for her patience, sacrifice, encouragement, and continuous morale support. Specially, I would like to dedicate this work to my mother with thanks and appreciations for her great patience and encouragement. Her trust and morale support inspired me in the most moments of the study period. III CONTENTS PAGE ABSTRACT ............................................................................................................. I ÖZ ........................................................................................................................... II ACKNOWLEDGEMENTS .................................................................................... III CONTENTS ...........................................................................................................IV LIST OF TABLES..................................................................................................XI LIST OF FIGURES ............................................................................................. XIII LIST OF SYMBOLS ......................................................................................... XVII LIST OF ABBREVIATIONS .............................................................................. XXI 1. INTRODUCTION ............................................................................................... 1 1.1. Motivation for the Thesis .............................................................................. 3 1.2. Objectives of the Thesis ................................................................................ 4 1.3. Contributions of the Thesis ............................................................................ 5 1.4. General Outline ............................................................................................. 5 2. OVERVIEW OF FACTS DEVICES .................................................................... 7 2.1. Background on Alternating Current Power Transmission .............................. 7 2.1.1. Thermal Limit .................................................................................... 7 2.1.2. Maximum Power Transfer.................................................................. 7 2.1.3. Angle Stability ................................................................................... 8 2.1.4. Voltage Stability ................................................................................ 9 2.1.5. Transmission Line Loadability Characteristics ................................. 10 2.2. Classification of FACTS Devices ................................................................ 11 2.2.1. Static VAR Compensator (SVC) ...................................................... 13 2.2.2. Thyristor Controlled Series Capacitor/Compensator (TCSC)............ 15 2.2.3. Thyristor Controlled Phase Angle Regulator (TCPAR) .................... 16 2.2.4. Static Synchronous Compensator (STATCOM) ............................... 17 2.2.5. Static Series Synchronous Compensator (SSSC) .............................. 18 2.2.6. Unified Power Flow Controller (UPFC) ........................................... 19 2.2.7. Interline Power Flow Controller (IPFC) ........................................... 20 2.2.8. Generalized Unified Power Flow Controller (GUPFC) ..................... 21 IV 2.2.9. Back-to-Back STATCOM (BtB-STATCOM) ................................ 22 2.3. More Control Degrees of Freedom .............................................................. 23 2.4. Recent Advances in Power Semiconductors ................................................ 25 2.5. Field Applications of FACTS Devices at Transmission Level ..................... 25 2.6. Summary..................................................................................................... 27 3. STEADY-STATE MODELING......................................................................... 29 3.1. Introduction................................................................................................. 29 3.2. Proposed Steady-state Modeling Approach.................................................. 30 3.2.1. Configurable Multi-Converter FACTS Device................................... 31 3.2.2. Operating Constraints ........................................................................ 33 3.2.3. Control Constraints............................................................................ 35 3.2.3.1. Direct Control Mode .............................................................. 35 3.2.3.2. Indirect Control Mode............................................................ 36 3.3. Modeling in PSCAD ................................................................................... 37 3.3.1. Power Circuit .................................................................................... 37 3.3.2. Control Circuit .................................................................................. 37 3.4. Power Flow Studies ..................................................................................... 39 3.4.1. Test Systems ..................................................................................... 39 3.4.2. WSCC 3-Machine 9-Bus System ....................................................... 42 3.4.2.1. Case 1: STATCOM and SSSC Operations ............................. 42 3.4.2.2. Case 2: UPFC Operation ........................................................ 45 3.4.2.3. Case 3: IPFC Operation ......................................................... 45 3.4.2.4. Case 4: GUPFC Operation ..................................................... 47 3.4.2.5. Discussion of Simulation Results ........................................... 48 3.4.3. IEEE 14-Bus System ......................................................................... 49 3.4.3.1. Case 1: UPFC Operation ........................................................ 49 3.4.3.2. Case 2: IPFC Operation ......................................................... 51 3.4.3.3. Case 3: GUPFC Operation ..................................................... 51 3.4.3.4. Discussion of Simulation Results ........................................... 51 3.4.4. 3-Machine 7-Bus System ................................................................... 52 3.4.4.1. Case 1: Reactive Power-Voltage (Q-V) Characteristics .......... 52 V 3.4.4.2. Case 2: Real Power-Voltage (P-V) Characteristics ................. 54 3.4.4.3. Discussion of Simulation Results ........................................... 56 3.5. Summary..................................................................................................... 57 4. VOLTAGE SOURCE CONVERTER DESIGN ................................................. 59 4.1. Introduction................................................................................................. 59 4.2. Six-pulse VSC ............................................................................................. 60 4.2.1. Circuit Configuration......................................................................... 60 4.2.2. Working Principle ............................................................................. 61 4.2.3. Analysis of Six-pulse VSC ................................................................ 63 4.3. Twelve-pulse VSC ...................................................................................... 65 4.3.1. Circuit Configuration......................................................................... 65 4.3.2. Analysis of Twelve-pulse VSC .......................................................... 67 4.4. Quasi Multi-pulse VSC ............................................................................... 68 4.4.1. Circuit Configuration......................................................................... 68 4.4.2. Series Coupling Magnetic Interface ................................................... 72 4.4.3. Control Scheme for Quasi Multi-pulse VSC ...................................... 73 4.4.3.1. 2-angle Control Method ......................................................... 74 4.4.3.2. Pulse-generating Circuit......................................................... 76 4.4.4. Analysis of Quasi Multi-pulse VSC ................................................... 77 4.4.4.1. Quasi 48-pulse Operation....................................................... 77 4.4.4.2. Verification of 2-angle Control Method ................................. 79 4.5. Summary..................................................................................................... 83 5. DYNAMIC MODELING STUDIES .................................................................. 85 5.1. Introduction................................................................................................. 85 5.2. Simplex Optimization Method..................................................................... 87 5.3. Converter-Level Modeling of GUPFC ......................................................... 88 5.3.1. GUPFC Interacting with Power System ............................................. 88 5.3.2. GUPFC Controller Design ................................................................. 89 5.3.3. Finding Optimum Controller Parameters ........................................... 91 5.3.4. Simulation Studies ............................................................................. 93 5.3.4.1. Case 1: Start-up Transients .................................................... 94 VI 5.3.4.2. Case 2: Response to Real Power Flow Step Changes ............. 97 5.3.4.3. Case 3: Response to Reactive Power Flow Step Changes ..... 100 5.3.4.4. Case 4: Single-phase to Ground Fault .................................. 102 5.3.4.5. Case 5: Three-phase to Ground Fault ................................... 106 5.3.4.6. THD Content ....................................................................... 108 5.3.5. Discussion ....................................................................................... 108 5.4. Converter-Level Modeling of IPFC ........................................................... 109 5.4.1. IPFC Interacting with Power System ............................................... 109 5.4.2. IPFC Controller Design ................................................................... 110 5.4.2.1. Decoupled Controller Design ............................................... 111 5.4.2.2. Proposed Hybrid Fuzzy PI (HFPI) Controller ...................... 114 5.4.2.3. FUDE Design ...................................................................... 116 5.4.3. Finding Optimum Controller Parameters ......................................... 119 5.4.4. Simulation Studies ........................................................................... 121 5.4.4.1. Case 1 .................................................................................. 122 5.4.4.2. Case 2 .................................................................................. 124 5.4.4.3. THD Content ....................................................................... 128 5.4.5. Discussion ....................................................................................... 130 5.5. Converter-Level Modeling of BtB-STATCOM ......................................... 130 5.5.1. BtB-STATCOM Interacting with Power System.............................. 130 5.5.2. BtB-STATCOM Controller Design ................................................. 132 5.5.3. Simulation Studies ........................................................................... 133 5.5.3.1. Case1: Start-up Transients ................................................... 133 5.5.3.2. Case 2: Response to Real Power Transfer Step Changes ...... 136 5.5.3.3. Case 3: Single-phase to Ground Fault .................................. 138 5.5.3.4. Case 4: Three-phase to Ground Fault ................................... 141 5.5.3.5. THD Content ....................................................................... 143 5.5.4. Discussion ....................................................................................... 144 5.6. Summary................................................................................................... 144 6. TRANSIENT STABILITY STUDIES ............................................................. 147 6.1. Introduction............................................................................................... 147 VII 6.2. Literature Survey on Transient Stability Studies ........................................ 148 6.3. Transient Stability Improvement Using GUPFC ........................................ 149 6.3.1. Dynamic Equations for Power Generation ....................................... 149 6.3.1.1. Wind Model ........................................................................ 149 6.3.1.2. Blade Dynamics................................................................... 150 6.3.1.3. Self-excited Double Cage Induction Generator .................... 151 6.3.1.4. Salient-Pole Synchronous Generator .................................... 151 6.3.2. Power System Configuration ........................................................... 152 6.3.3. Damping Control Scheme of GUPFC .............................................. 155 6.3.3.1. Fuzzy Damping Controller (FDC)........................................ 156 6.3.3.2. Fuzzified Gain Tuner (FGT) ................................................ 157 6.3.3.3. Tuning of Scaling Factors .................................................... 158 6.3.4. Simulation Studies ........................................................................... 160 6.3.4.1. Case 1: Three-phase to Ground Fault ................................... 160 6.3.4.2. Case 2: Three-phase Fault with Longer Duration ................. 165 6.3.4.3. Case 3: Single-phase to Ground Fault .................................. 171 6.3.4.4. THD Content ....................................................................... 174 6.3.5. Discussion ....................................................................................... 174 6.4. Transient Stability Improvement Using IPFC ............................................ 175 6.4.1. Power System Configuration ........................................................... 175 6.4.2. Tuning of Scaling Factors ................................................................ 178 6.4.3. Simulation Studies ........................................................................... 178 6.4.3.1. Case 1: Three-phase to Ground Fault ................................... 180 6.4.3.2. Case 2: Two-phase to Ground Fault ..................................... 180 6.4.3.3. Case 3: Single-phase to Ground Fault .................................. 187 6.4.3.4. THD Content ....................................................................... 191 6.4.4. Discussion ....................................................................................... 192 6.5. Transient Stability Improvement using BtB-STATCOM ........................... 192 6.5.1. Power System Configuration ........................................................... 192 6.5.2. Simulation Studies ........................................................................... 194 6.5.2.1. Case 1: Three-phase to Ground Fault at Generator Bus ........ 195 VIII 6.5.2.2. Case 2: Three-phase to Ground Fault at Infinite Bus ............ 198 6.5.2.3. THD Content ....................................................................... 201 6.5.3. Discussion ....................................................................................... 202 6.6. Summary................................................................................................... 202 7. CONCLUSIONS AND FUTURE WORK........................................................ 205 REFERENCES ..................................................................................................... 211 CIRRICULUM VITAE ........................................................................................ 227 APPENDIX A: Converter Design Data for Power Flow Studies ..... Hata! Yer işareti tanımlanmamış. APPENDIX B: Test Systems Data ...................... Hata! Yer işareti tanımlanmamış. APPENDIX C: PI Controller Parameters ............ Hata! Yer işareti tanımlanmamış. APPENDIX D: Derivation of Maximum Power Injections for BtB-STATCOM Hata! Yer işareti tanımlanmamış. APPENDIX E: Programming Scripts .................. Hata! Yer işareti tanımlanmamış. IX X LIST OF TABLES PAGE Table 2.1. Overview of major FACTS devices with their attributes ......................... 14 Table 3.1. Flexible configuration of the multi-converter FACTS device .................. 32 Table 3.2. Operating constraints of the multi-converter FACTS device ................... 34 Table 3.3. Power flow results for voltage magnitude regulation @ 1.0 pu ............... 44 Table 3.4. Power flow results for real power regulation of Line 4-5 ........................ 44 Table 3.5. Power flow results for reactive power flow regulation of Line 4-6 .......... 45 Table 3.6. Parameters of the UPFC under different power flow control strategies ... 49 Table 3.7. Parameters of the IPFC under different power flow control strategies ..... 51 Table 3.8. Parameters of the GUPFC under different power flow control strategies 52 Table 3.9. Q-V characteristics of the two converters ............................................... 54 Table 4.1. Number of pulse-generating circuits per multi-converter FACTS device 77 Table 5.1. Simplex optimized controller parameters of GUPFC .............................. 93 Table 5.2. THD values .......................................................................................... 108 Table 5.3. Rule base for ΔVQ................................................................................. 117 Table 5.4. Simplex optimized controller parameters of IPFC ................................ 121 Table 5.5. Quantitative performance analysis of different controllers .................... 129 Table 5.6. THD values in case of three control schemes ........................................ 130 Table 5.7. THD values .......................................................................................... 143 Table 6.1. Optimization results of scaling factors .................................................. 160 Table 6.2. THD values of power system bus voltages ........................................... 174 Table 6.3. Optimization results of scaling factors .................................................. 179 Table 6.4. THD values of power system bus voltages ........................................... 191 Table 6.5. THD values of power system bus voltages ........................................... 202 XI XII LIST OF FIGURES PAGE Figure 2.1. Real power transfer between two buses ................................................... 7 Figure 2.2. Power-angle curve of a transmission line ................................................ 8 Figure 2.3. Voltage-power characteristics of Figure 2.1 (Kundur, 1994) ................... 9 Figure 2.4. Reactive power-voltage curves of Figure 2.1 (Kundur, 1994) ................ 10 Figure 2.5. Loadability characteristics of transmission lines (Zhang et al., 2006) .... 11 Figure 2.6. SVC configuration: (a) typical arrangement (b) VI characteristics ......... 15 Figure 2.7. TCSC configuration: (a) typical arrangement (b) z-α characteristics ...... 16 Figure 2.8. TCPAR configuration: (a) thyrsitor arrangement (b) vector diagrams .... 17 Figure 2.9. STATCOM configuration:(a) arrangement (b) operating modes ............ 18 Figure 2.10. SSSC configuration: (a) typical arrangement (b) operating modes ....... 19 Figure 2.11. UPFC configuration: (a) typical arrangement (b) operating modes ...... 20 Figure 2.12. IPFC configuration: (a) typical arrangement (b) operating mode ......... 21 Figure 2.13. GUPFC configuration: (a) typical arrangement (b) operating modes ... 22 Figure 2.14. BtB-STATCOM configuration with typical arrangement .................... 23 Figure 3.1. Generic multi-converter FACTS device ................................................ 31 Figure 3.2. Voltage source equivalent model of the generic FACTS device ............ 32 Figure 3.3. PSCAD models of shunt and series converters ...................................... 38 Figure 3.4. Control constraint implementation in PSCAD ....................................... 40 Figure 3.5. PSCAD model of the P-Q load connected at high voltage bus ............... 41 Figure 3.6. PSCAD model of WSCC 3-Machine 9-Bus System .............................. 43 Figure 3.7. P-Q Control planes of Line 4-6 obtained with UPFC ............................. 46 Figure 3.8. P-Q Control planes of Line 4-6 obtained with IPFC .............................. 46 Figure 3.9. P-Q control planes of Line 4-5 obtained with GUPFC ........................... 47 Figure 3.10. P-Q control planes of Line 4-6 obtained with GUPFC ......................... 48 Figure 3.11. PSCAD model of IEEE 14-Bus System............................................... 50 Figure 3.12. PSCAD model of 3-Machine 7-Bus System ........................................ 53 Figure 3.13. Comparative P-V curves of Bus 1 ....................................................... 55 Figure 3.14. Comparative P-V curves of Bus 3 ....................................................... 56 XIII Figure 4.1. Power circuit of three-phase six-pulse VSC......................................... 61 Figure 4.2. Four quadrant VSC operation .............................................................. 62 Figure 4.3. Simulated phase-to-neutral voltage waveforms of six-pulse VSC ........ 63 Figure 4.4. Simulated phase-to-phase voltage waveforms of six-pulse VSC .......... 64 Figure 4.5. Gating signals of GTOs for 180-degrees conduction ........................... 65 Figure 4.6. Harmonic spectrum of VAB for six-pulse VSC ..................................... 65 Figure 4.7. Power circuit of three-phase twelve-pulse VSC ................................... 66 Figure 4.8. Simulated phase-to-phase voltage waveforms of twelve-pulse VSC .... 67 Figure 4.9. Harmonic spectrum of VAB for twelve-pulse VSC ............................... 68 Figure 4.10. Power circuit configuration of three-phase quasi multi-pulse VSC ...... 70 Figure 4.11. PSCAD implementation of ¼ of quasi multi-pulse VSC ...................... 71 Figure 4.12. PSCAD implementation of magnetic interfaces ................................... 72 Figure 4.13. PSCAD implementation of series coupling magnetic interface ............ 73 Figure 4.14. Voltage vectors of converters M and N in rotating reference frame ..... 74 Figure 4.15. PSCAD implementation of equations (4.5) and (4.6) ........................... 75 Figure 4.16. PSCAD implementation of switching logic for six-pulse VSC ............ 76 Figure 4.17. Simulated voltage waveforms of quasi 48-pulse VSC.......................... 78 Figure 4.18. Harmonic spectrum of VAB for quasi 48-pulse operation ..................... 78 Figure 4.19. Four quadrant operation of the proposed quasi multi-pulse VSC ......... 81 Figure 4.20. Flexible magnitude/phase angle controlled quasi multi-pulse VSC ...... 82 Figure 5.1. Flow chart of the simplex optimization method in PSCAD .................. 88 Figure 5.2. WSCC 3-Machine 9-Bus System embedded with GUPFC................... 89 Figure 5.3. Control loops of GUPFC ..................................................................... 90 Figure 5.4. PSCAD implementation of simplex method ........................................ 92 Figure 5.5. Convergence performance of cost function in simplex method ............ 93 Figure 5.6. Simulated waveforms of case 1 ........................................................... 97 Figure 5.7. Simulated waveforms of case 2 ........................................................... 99 Figure 5.8. Simulated waveforms of case 3 ......................................................... 102 Figure 5.9. Simulated waveforms of case 4 ......................................................... 105 Figure 5.10. Simulated waveforms of case 5 ......................................................... 108 Figure 5.11. 4-Machine 4-Bus System embedded with IPFC ................................. 110 XIV Figure 5.12. PSCAD implementation of PI+DG controllers ................................... 113 Figure 5.13. PSCAD implementation of HFPI controller ........................................ 114 Figure 5.14. PSCAD-MATLAB interface ............................................................. 115 Figure 5.15. PSCAD implementation of SEPOCHDET ......................................... 115 Figure 5.16. Universe of Discourse ....................................................................... 116 Figure 5.17. MFs for FUDE output set .................................................................. 117 Figure 5.18. Control surfaces of the proposed FUDE ............................................ 118 Figure 5.19. Conceptual control configurations for the master VSC ........................ 119 Figure 5.20. Control scheme for the slave VSC ...................................................... 119 Figure 5.21. PSCAD implementation of simplex method ...................................... 120 Figure 5.22. Cost function minimization in simplex method ................................... 120 Figure 5.23. Dynamic performances of real power flow controllers ...................... 123 Figure 5.24. Dynamic performances of reactive power flow controllers ................ 125 Figure 5.25. Dynamic performance of real power flow controller for slave VSC ... 125 Figure 5.26. Dynamic performance of DC voltage controller for slave VSC ......... 126 Figure 5.27. d-q components of master VSC injected current ................................ 126 Figure 5.28. d-q components of master VSC voltage by HFPI controller............... 126 Figure 5.29. Anode-to-cathode voltage of a selected GTO in converter M ............ 127 Figure 5.30. Dynamic performances of real power flow controllers ...................... 127 Figure 5.31. Dynamic performances of reactive power flow controllers ................ 129 Figure 5.32. 3-Machine 7-Bus System embedded with BtB-STATCOM ............... 131 Figure 5.33. Control loops of BtB-STATCOM ..................................................... 132 Figure 5.34. Simulated waveforms of case 1 ......................................................... 135 Figure 5.35. Simulated waveforms of case 2 ......................................................... 138 Figure 5.36. Simulated waveforms of case 3 ......................................................... 140 Figure 5.37. Simulated waveforms of case 4 ......................................................... 143 Figure 6.1. Power system configuration embedded with GUPFC ........................ 153 Figure 6.2. PSCAD-MATLAB interface ............................................................. 154 Figure 6.3. Membership functions and fuzzy rules for STFDC ............................ 157 Figure 6.4. Control surfaces of the proposed STFDC .......................................... 158 Figure 6.5. PSCAD implementation of simplex method ...................................... 159 XV Figure 6.6. Convergence performance of cost function in simplex method .......... 159 Figure 6.7. Simulated STFDC performance against three-phase fault .................. 164 Figure 6.8. Simulated voltage and current waveforms of GUPFC converters....... 165 Figure 6.9. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 165 Figure 6.10. Simulated STFDC performance against longer three-phase fault ....... 169 Figure 6.11. Power fluctuations following three-phase fault .................................. 170 Figure 6.12. Simulated STFDC performance against single-phase to ground fault . 174 Figure 6.13. Two-Area System embedded with IPFC and its control scheme ........ 176 Figure 6.14. PSCAD-MATLAB interface ............................................................. 177 Figure 6.15. Cost function minimization for both FACTS devices ........................ 179 Figure 6.16. Simulated STFDC performance following three-phase fault .............. 184 Figure 6.17. Simulated voltage and current waveforms of IPFC converters ........... 184 Figure 6.18. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 184 Figure 6.19. Simulated STFDC performance against two-phase fault .................... 187 Figure 6.20. Simulated STFDC performance against single-phase fault ................ 191 Figure 6.21. Power system configuration embedded with BtB-STATCOM ........... 193 Figure 6.22. Simulated BtB-STATCOM performance in case 1 ............................ 197 Figure 6.23. Simulated voltage and current waveforms of the converters .............. 198 Figure 6.24. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 198 Figure 6.25. Simulated BtB-STATCOM performance in case 2 ............................ 201 XVI LIST OF SYMBOLS * : Complex conjugate ° : Degrees µ(i) : Membership function of the consequent of rule i A : Blade impact area a1-3 : Scaling factors of STFDC bi : Center of membership function of the consequent of rule i C : DC link capacitance Cp : Dimensionless power coefficient D : Damping coefficient of the SG dX/dt : First order time derivative of the variable X e : Internal generated voltage of the SG e(k) : Error at sample instant k ES : Line-to-line rms voltage of the sending-end side bus eX : X-axis of the internal generated voltage of the SG eXN : Line-to-neutral voltage of phase X H : Henry iD : D-component of the current IL : Transmission line current Iph : Phase current flowing into the converter iQ : Q-component of the current J : Inertia of the SEDCIG j : Square root of -1 k : Number of sampling instant Kp : Proportional gain of the PI controller Kw : Damping gain L : Inductance Lm : Mutual leakage inductance of the SEDCIG M : inertia constant of the SG n : Harmonic order XVII P : Number of pole pairs Pe : Real power flow error Pinj,m : Injected real power of converter m Pinj,mref : Injected real power of converter m Pline : Real power flow of the transmission line Plineref : Reference value of the real power flow of the transmission line Ploss,m : Real power loss of converter m PR : Receiving-end real power PRMAX : Maximum power transfer of receiving-end side at unity power factor Ptransfer,m : Transmitted real power of converter m from other converter(s) PW : Mechanical power extracted from the wind Qe : Reactive power flow error Qinj,m : Injected reactive power of converter m Qinj,mref : Reference value of injected reactive power of converter m Qline : Reactive power flow of the transmission line Qlineref : Reference value of the reactive power flow of the transmission line QR : Receiving-end reactive power Ra : Armature resistance RC : Common end-ring resistance of the SEDCIG RL : Transmission line resistance RLD : Per-phase resistance of the three-phase load Rs : Internal resistance of the DC voltage source s : Laplace operator Sline : Complex power flow of the transmission line t : Time T : Total simulation time TE : Electrical torque of the SG or SEDCIG TL : Load torque of the SEDCIG TM : Mechanical torque of the SG TX : X-axis time constant of the SG Vbus : Line-to-line rms voltage of local bus XVIII Vbusref : Reference value of line-to-line rms voltage of local bus Vconv : Line-to-neutral rms voltage of converter Vconv(max) : Maximum value of line-to-neutral rms voltage of converter VD : D-component of the voltage Vdc : DC link voltage VDref : Reference value of the D-component voltage VF : Average converter voltage Vf : Excitation winding voltage of the SG VM : Voltage phasor of converter M vn : Peak value of nth voltage harmonic component VN : Voltage phasor of converter N VQ : Q-component of the voltage VQref : Reference value of the Q-component voltage VR : Line-to-line rms voltage of the receiving-end side bus VS : Voltage phasor of the selected bus Vse : Line-to-neutral rms voltage of series converter Vsh : Line-to-neutral rms voltage of shunt converter VW : Wind speed VWB : Base or mean wind speed VWG : Gust wind component VWN : Noise wind component VWR : Ramp wind component VX : Voltage phasor of the quasi multi-pulse VSC VXn : Phase X-to-neutral voltage of the converter VXY : Phase X-to-Phase Y voltage of the converter w : angular frequency W : Watt wa : Speed of the rotating arbitrary reference frame wB : Blade angular velocity wi : Speed of generator-i wiref : Reference value of the speed of generator-i XIX XC : Capacitive reactance XL : Transmission line reactance XTCR : Impedance of TCR XTCSC : Impedance of TCSC XX : X-component of the reactance of the SG α : Phase angle between VM and VX β : Gain factor of the FGT βp : Blade pitch angle γ : Tip speed ratio δ : Phase angle between VD and VX δ : Rotor angle of the SG ΔX : Rate of change of variable X ζ : Thyristor firing angle (zeta) θconv : Phase angle of line-to-neutral rms voltage of converter θR : Phase angle of receiving-end side bus θS : Phase angle of sending-end side bus θse : Phase-angle of line-to-neutral rms voltage of series converter θsh : Phase-angle of line-to-neutral rms voltage of shunt converter μ : Micro ρ : Air density ΣX : Integral of variable X at sample instant k τi : Integral time constant of the PI controller φ : Flux linkage ΦM : Phase angle of voltage phasor of converter M ΦN : Phase angle of voltage phasor of converter N Ω : Ohm XX LIST OF ABBREVIATIONS AC : Alternating Current BtB-STATCOM : Back-to-Back Static Synchronous Compensator CPU : Central Processing Unit DC : Direct Current DFIG : Doubly Fed Induction Generator EMTDC : Electromagnetic Transients including Direct Current FACTS : Flexible Alternating Current Transmission Systems FDC : Fuzzy Damping Controller FGT : Fuzzified Gain Tuner FUDE : Fuzzy Decoupler GCT : Gate Commutated Thyristor GTO : Gate Turn-off Thyristor GUPFC : Generalized Unified Power Flow Controller HFPI : Hybrid Fuzzy Proportional Integral HVDC : High Voltage Direct Current IAE : Integral Absolute Error IEEE : Institute of Electrical and Electronics Engineers IGCT : Integrated Gate Commutated Thyristor IPFC : Interline Power Flow Controller ISE : Integral Square Error ITAE : Integral Time Absolute Error MF : Membership Function MSC : Mechanically Switched Capacitor MSR : Mechanically Switched Reactor MVA : Mega Volt-Ampere NR : Newton-Raphson PI : Proportional Integral PI+DG : Proportional Integral Control with Decoupled Gains PLL : Phase Lock Loop XXI P-Q : Real Power-Reactive Power PSCAD : Power System Computer Aided Design PU : Per unit P-V : Real Power-Voltage PWM : Pulse Width Modulation Q-V : Reactive Power-Voltage SEDCIG : Self-excited Double Cage Induction Generator SEPOCHDET : Set-Point Change Detector SG : Salient-Pole Synchronous Generator SSR : Subsynchronous Resonance SSSC : Static Series Synchronous Compensator STATCOM : Static Synchronous Compensator STFDC : Self-Tuning Fuzzy Damping Controller SVC : Static Var Compensator TCPAR : Thyristor Controlled Phase Angle Regulator TCR : Thyristor Controlled Reactor TCSC : Thyristor Controlled Series Capacitor/Compensator THD : Total Harmonic Distortion TSC : Thyristor Switched Capacitor TSR : Thyristor Switched Reactor UPFC : Unified Power Flow Controller VAR : Volt Ampere Reactive VI : Voltage-Current VSC : Voltage Source Converter WSCC : Western System Coordinated Council XXII XXIII 1. INTRODUCTION 1. A. Mete VURAL INTRODUCTION With fast technological advances and rapid population growth, electrical power demand has increased substantially over the last decades. This situation has led to heavily stressed traditional power systems which require either network expansion or network operation closer to its technical limits. Cost efficient solutions are usually preferred over network expansion which is very limited due to environmental reasons and high expenses. In many countries, authorization is hardly given to build new transmission lines so that existing transmission equipment has to be enforced to fulfill changing requirements. On the other hand, deregulation brings the evolution towards a competitive electricity market in which congestion occurs due to a violation of system operating limits when the transmission network is unable to put up all of the desired transactions. Efficient operation and planning of transmission grid are highly required in case of congestion management which is considerably complex in such competitive electricity market and necessitates better utilization of available power system capacities and increasing available transfer capability. Alternative generation facilities such as wind/solar energy based generation systems which lead up distributed generation, have become an inevitable trend due to the critical factors such as limited available primary energy resources used in conventional power plants, fast increase in fuel prices, and increasing awareness of environmental problems, such as global warming and pollution. Distributed electrical systems, on the contrary of traditional power systems where generation side is physically located apart from consumer side, bring complexity to achieve a larger stability margin and greater operating flexibility of existing power systems. Power system operation was not only affected in the past by stability related problems, leading to unpredictable system behavior, but also in today stability concerns are getting worse due to the changing operation requirements and increasing system complexity. Cost constraints have also become much tighter than in the past, increasing the operational complexity considerably. 1 1. INTRODUCTION A. Mete VURAL For the factors described above, it becomes evident that the operation of power system structure under great changes is a complex and challenging engineering task which requires efficient use of all power system elements without disturbing technical operational limits and power systems with increasing complexity are highly expected to be fast and real-time controlled to fulfill the requirements for providing uninterrupted and reliable electrical energy to customers in the event of generation and transmission outages. Flexible Alternating Current Transmission Systems (FACTS) emerge as “power electronic based solution” using solid-state switching devices and modern control algorithms to increase controllability and enhance power transfer capacity of existing transmission network. FACTS have gained greater interest during the last decades due to the deregulation and restructuring strategies of power systems. FACTS concept was originally proposed and conceptualized by Narain G. Hingorani (Hingorani, 1988) and later defined formally as “alternating current transmission systems incorporating power electronic-based and other static controllers to enhance controllability and increase power transfer capability” by the FACTS Terms & Definitions Task Force FACTS Working Group of the direct current (DC) and FACTS subcommittee of Institute of Electrical and Electronics Engineers (IEEE) (IEEE, 1997). With the increase of voltage and current ratings of solid-state power semiconductor devices, power electronics technology has penetrated into the area of high voltage transmission in terms of FACTS devices (controllers) receiving great attention to enhance power system operation by controlling one or more power system parameters simultaneously and independently (Hingorani, 2000). During the last two decades, FACTS devices have been proposed to enhance steady-state (static) performance of power systems, such as increase of transmission line capacity, real and reactive power flow control, loop-flow control, load sharing among parallel corridors, voltage regulation, congestion management, and optimal power flow for economic power system operation. The examples of dynamic performance improvement include; enhancement of small signal stability and transient stability of 2 1. INTRODUCTION A. Mete VURAL power systems by damping out oscillations, fast reactive power support for dynamic voltage control, maintaining voltage stability, and power quality improvement. 1.1. Motivation for the Thesis Since the time when FACTS devices were first proposed, modeling and control of different FACTS devices have been broadly studied. In particular, there are extensively research results covering a wide range of applications of singleconverter FACTS devices, such as Static Synchronous Compensator (STATCOM) and Static Series Synchronous Compensator (SSSC) in literature. Multi-converter FACTS devices, on the other hand, has emerged as a new opportunity to cope with the aforementioned power system problems by controlling multiple power system variables simultaneously and independently. However, the research for multiconverter FACTS devices is relatively narrow and limited. There exists a lack in realistic converter models for high power high voltage applications which takes switching of semiconductor devices into account. Generally the studies rely on two approaches. In the first approach, a set of linearized equations are derived using fundamental frequency model of each converter of the FACTS device. Here the converter is modeled as controllable voltage or current source operating with fundamental system frequency (50 or 60 Hz), under the assumption that the harmonics are neglected. This approach may be useful for steady-state or power flow studies. In the second approach, six-pulse elementary converters switched at frequencies relatively higher than the system frequency are used to approximate harmonic content and converter modulation techniques. This approach can suffer from high switching frequencies and relatively simple converter structure which are not suitable for high power applications. This situation has motivated to take a deep glance into the analysis of multi-converter FACTS devices including more realistic converter models and their advanced controls. Multi-converter FACTS devices are multi-input multi-output non-linear systems with operational constraints which require advanced control algorithms. On the other hand, fuzzy set theory presents good characteristics to address complex 3 1. INTRODUCTION A. Mete VURAL control problems and has already proven to be efficient in several planning, control, and operation problems in power systems. The fact that the need for computational intelligence based control techniques including optimization methods is indispensable for high performance control of the multi-converter FACTS devices has also motivated this work. The need for efficient utilization of power systems is increasing day by day in the world and in Turkey. Besides these global conditions, there is not a well-shaped research background on multi-converter FACTS devices in Turkey. This study will provide a strong background on this subject. 1.2. Objectives of the Thesis The objectives of the thesis are as follows: • To provide appropriate models for both single- and multi-converter FACTS devices for steady-state or power flow studies, • To design high power quasi multi-pulse voltage source converter for the simulation and analysis of both single- and multi-converter FACTS devices, • To provide converter-level models of the following multi-converter FACTS devices: Generalized Unified Power Flow Controller (GUPFC), Interline Power Flow Controller (IPFC), and Back-to-Back STATCOM (BtB-STATCOM) using high power quasi multi-pulse voltage source converters with switching and control schemes for dynamic and stability studies, • To design real and reactive power flow controllers for IPFC with improved decoupling function and enhanced dynamic performance, • To design damping controller for GUPFC to improve the transient stability of the wind farm integrated power system, • To design damping controller for IPFC to improve the transient stability of the power system by damping out inter-area mode of oscillations. 4 1. INTRODUCTION 1.3. A. Mete VURAL Contributions of the Thesis The contributions of this work are as follows: • A new method of representing single- and multi-converter FACTS devices in simulation program for studying steady-state behavior of power systems embedded with FACTS devices is proposed, designed, and tested. • A quasi multi-pulse voltage source converter with two control degrees of freedom and switching at fundamental system frequency is designed for converter-level modeling studies of the multi-converter FACTS devices. • A novel decoupled control scheme for real and reactive power flow control loops based on a hybrid fuzzy PI controller for IPFC is proposed, designed and tested. • A novel simplex optimized self-tuning fuzzy damping controller for GUPFC for transient stability enhancement of the wind farm integrated power system by damping synchronous generator oscillations and increasing speed stability of the induction generators, is proposed, designed and tested. • The proposed self-tuning fuzzy damping controller for GUPFC is adapted for IPFC for transient stability enhancement of the power systems by suppressing inter-area mode of oscillations. 1.4. General Outline This thesis is structured in seven chapters. After this introductory chapter, Chapter 2 provides a summarized review of power system problems, FACTS devices and their classification, recent advances in power electronics for FACTS concept, and some FACTS application examples. Chapter 3 addresses steady-state modeling of converter based FACTS devices for power flow studies in Power System Computer Aided Design (PSCAD) simulation program with version 4.2.1 (PSCAD, 2010). The modeling approach is verified with simulated cases on WSCC 3-Machine 9-Bus System, 3-Machine 7-Bus System, and IEEE 14-Bus System. Particular 5 1. INTRODUCTION A. Mete VURAL steady-state performance comparison is also made between the mentioned FACTS devices in Chapter 3. The design details of quasi multi-pulse converter including power circuit, magnetic interface, and pulse generating circuit for the power semiconductor devices are given in Chapter 4. Chapter 5 presents the dynamic models of GUPFC, IPFC, and BtB-STATCOM. The dynamic control characteristics of these devices are investigated using the developed PSCAD based converter-level models. The simulation studies are carried out and extensively analyzed in various test power systems. A hybrid fuzzy PI controller is proposed to get high decoupling performance between real and reactive power flow controllers of the IPFC. The proposed controller is compared with the parameter optimized PI controllers and the parameter optimized PI controllers having analytically calculated feed-forward decoupling gains. The comparative simulation studies are carried out on 4-Machine 4-Bus power system through a number of case studies. Chapter 6 deals with the transient stability studies of GUPFC, IPFC, and BtB-STATCOM. Different disturbance scenarios are studied to compare the performance of the proposed damping scheme of GUPFC with that of conventional approach. The proposed damping scheme is also adapted for IPFC to damp inter-area mode of oscillations. The transient stability enhancement of BtB-STATCOM is also investigated in Chapter 6. In Chapter 7, important conclusions of this work are presented and future work options on multi-converter FACTS devices are offered. References, curriculum vitae of the author, and the appendices are given at the end. 6 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL 2. OVERVIEW OF FACTS DEVICES 2.1. Background on Alternating Current Power Transmission 2.1.1. Thermal Limit Thermal limit of a transmission line is defined in terms of the maximum current carrying capacity (ampacity). The excess amount of current flowing on the line produces heat leading to undesirable results, such as annealing and gradual loss of mechanical strength of the conductor caused by temperature extremes and increase sag and decreased clearance to ground due to conductor expansion at higher temperatures (Kundur, 1994). So the transmission line can be utilized best only if it is loaded up to its thermal limit which cannot be done normally without line compensation. 2.1.2. Maximum Power Transfer Electrical power transfer from generation side to consumer side is preferred in alternating current (AC) form through overhead transmission lines due to flexibility and cost. By referring to Figure 2.1, the real (active) power flow between two arbitrary buses in a power system can be expressed in equation (2.1) (Kundur, 1994). Figure 2.1. Real power transfer between two buses PR = E S VR sin(θ S − θ R ) XL (2.1) 7 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL where PR and QR are the real and reactive power flow into Bus 2, respectively. ES and VR are the voltage magnitudes of Buses 1 and 2, respectively. θS and θR denote phase angles of Buses 1 and 2, respectively. XL is the reactance of the transmission line having negligible resistance and capacitance. From equation (2.1) a non-linear power-angle relationship can be obtained as in Figure 2.2 assuming fixed XL and fixed bus voltage magnitudes. There is a maximum limit of transmitted power when phase shift is 90°. Under fixed bus voltages, a suitable FACTS device can increase maximum limit of the transmitted power further by line compensation, i.e., reducing XL effectively. Figure 2.2. Power-angle curve of a transmission line 2.1.3. Angle Stability Power-angle curve in Figure 2.2 can be used to describe roughly the angle stability of the generators in a power system without making classification. Under steady-state conditions, there is equilibrium between input mechanical power and output electrical power of each synchronous generator in an interconnected system which leads to constant speed operation. When the system is perturbed for instance a fault occurs, this equilibrium is upset, resulting in accelerating or decelerating of the 8 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL rotors of the machines. If the machine connected at Bus 1 runs faster transiently than the other one connected at Bus 2, phase shift in equation (2.1) increases which result in an increase of real power transfer from Bus 1 to Bus 2 acting to reduce speed error between the machines. When phase shift increases further beyond a certain limit, real power transfer decreases which can lead to unstable operation. Fast and robust control algorithms for FACTS devices can solve the stability problem by real-time control of XL and/or phase shift. 2.1.4. Voltage Stability Voltage stability is defined as “the ability of a power system to maintain steady acceptable voltages at all buses in the system under normal operating conditions and after being subjected to a disturbance” (Kundur, 1994). In another words, voltage stability is the ability of a power system to meet its reactive power demand. The simple system in Figure 2.1 can be used to describe voltage stability problem in its simplest form assuming Bus 1 represents a large system that transfers real and reactive power through a transmission line to a load area, represented by Bus 2. The curves of the relationship between PR and VR for various load power factors are shown in Figure 2.3. Figure 2.3. Voltage-power characteristics of Figure 2.1 (Kundur, 1994) 9 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Due to the fact that voltage drop in the transmission line is a function of real as well as reactive power flow, load power factor is prominent on the power-voltage curves of the system. For a given power factor, real power can be transferred at two different voltage levels. The voltage stable operation is above the dashed line denoting locus of critical points. In another words, the system is voltage stable only if the load bus voltage VR is near to 1.0 per-unit (pu). Figure 2.4 shows QR-VR curves at Bus 2 for a fixed value of PR. Voltage stability limit is reached at the critical point where dQR/dVR reaches zero. The system is voltage stable at the right side of the locus of critical points where dQR/dVR is positive. Stable operation at the left side of the locus of critical points can be achieved effectively using reactive power compensation with a FACTS device having sufficiently control range. Figure 2.4. Reactive power-voltage curves of Figure 2.1 (Kundur, 1994) 2.1.5. Transmission Line Loadability Characteristics Reliable and efficient power transfer capability of a transmission line is directly influenced by ampacity, voltage and angle stability which define loadability characteristics of the line. Figure 2.5 shows operational characteristics of the 10 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL transmission lines for different voltage levels. In ideal, the usage of the transmission line for real power transmission is up to its thermal limit. As line length increases, voltage and angle stability limits determine line loading. These limits can be shifted upward, up to the thermal limit by means of utilizing appropriate FACTS devices. It is clear that the more line length, the more opportunity for the utilization of FACTS devices. Needs, benefits, and the practical requirements should be examined together to justify the investment into the appropriate FACTS device. Figure 2.5. Loadability characteristics of transmission lines (Zhang et al., 2006) 2.2. Classification of FACTS Devices Inherent limitations on AC power transmission mentioned in the previous sections point to the problems of maintaining economic and secure operation of large interconnected systems. These problems can be overcome with sufficient operation margins in the power transfer that can be maintained by the introduction of fast dynamic control of both real and reactive power using different types of FACTS devices. 11 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Depending on the connection type to the power network, FACTS devices can be divided into five categories: • Shunt FACTS devices • Series FACTS devices • Combined Shunt-Shunt FACTS devices • Combined Shunt-Series FACTS devices • Combined Series-Series FACTS devices Depending on the switching properties of the power semiconductor devices, FACTS devices can be categorized into two generations: • First generation or conventional FACTS devices with response times of about 2-3 cycles using thyristor with only ignition controlled by a gate • Second generation or converter based FACTS devices with faster response times of about 1-2 cycles using power semiconductor with both ignition and extinction controlled by a gate Second generation FACTS devices usually employ voltage source converter (VSC) based configurations which form the basis of converter based FACTS devices due to economy and performance (Gyugyi, 2000). Moreover, second generation FACTS devices have two fundamental advantages over first generation FACTS devices: • They employ self-commutated inverters (converters) as synchronous voltage sources which can internally generate or absorb reactive power without requiring bulky AC capacitors or reactors. • They can manage both real and reactive power independently. Second generation FACTS devices can be further classified according to the number of converters being utilized: 12 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL • Single-converter FACTS devices • Multi-converter FACTS devices Combining the above mentioned classification configurations, major FACTS devices applied at the transmission level and their main attributes are listed in Table 2.1 ignoring relative performance comparison and applications for power quality improvement and those for the distribution level. With the installation of energy storage units (super capacitor, battery, fuel cell, superconducting magnetic energy storage, etc.) in parallel to the DC link capacitors, depending on the storage size, converter based FACTS devices gain real power generation/absorption abilities which can further perform frequency regulation (Divya et al., 2009). 2.2.1. Static VAR Compensator (SVC) SVC is a static VAR generator or absorber by injecting capacitive or inductive current to maintain or control bus voltage or other power system variables (IEEE, 1994). Although SVC has different configurations in detail, Figure 2.6 shows a typical SVC configuration along with VI characteristics with thyristor controlled/switched reactor (TCR/TSR), thyristor switched capacitor (TCS), mechanically switched reactor (MSR), and mechanically switched capacitor (MSC) (Hingorani et al., 2000). TCR/TSR is utilized for absorbing reactive power and TSC is utilized for generating reactive power. The required reactive power is varied by the coordinated control of the combination of these branches. SVC gives a smoother and more precise response when compared compensation. 13 with the mechanically switched 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Table 2.1. Overview of major FACTS devices with their attributes FACTS device Connection First generation Static VAR compensator (SVC) Shunt Thyristor controlled series capacitor/compensator (TCSC) Series Thyristor controlled phase angle regulator (TCPAR) Combined Shunt-Series Attributes Voltage control, VAR compensation, voltage stability, power oscillation damping Power flow control, voltage control, voltage stability, series impedance control, power oscillation damping, subsynchronous resonance (SSR) mitigation Power flow control, phase angle control, voltage control, power oscillation damping, mitigation of (SSR) Multi-converter Single-converter Second generation Static synchronous compensator (STATCOM) Shunt Static series synchronous compensator (SSSC) Series Unified power flow controller (UPFC) Combined Shunt-Series Interline power flow controller (IPFC) Combined Series-Series Generalized unified power flow controller (GUPFC) Combined Shunt-Series Back-to-Back STATCOM (BtB-STATCOM) Combined Shunt-Shunt 14 Voltage control, VAR compensation, voltage stability, power oscillation damping Power flow control, voltage control, voltage stability, VAR compensation, power oscillation damping, SSR mitigation Power flow control, voltage control, voltage stability, VAR compensation, power oscillation damping, SSR mitigation Multi-line power flow control, voltage control, voltage stability, VAR compensation, power oscillation damping, SSR mitigation Multi-line power flow control, voltage control, voltage stability, VAR compensation, power oscillation damping, SSR mitigation Real power transfer, voltage control, VAR compensation, voltage stability, power oscillation damping 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Figure 2.6. SVC configuration: (a) typical arrangement (b) VI characteristics The required rating and the specification of the SVC are determined according to the VI characteristics of the SVC shown in Figure 2.6b. Since the reactive power of the capacitor is directly proportional to the system voltage, a sharp reduction of reactive power support at large voltage drops is observed during some severe contingencies (Hingorani et al., 2000). This situation is the major drawback of SVC applications for voltage support in power systems. 2.2.2. Thyristor Controlled Series Capacitor/Compensator (TCSC) TCSC typically consists of a TCR in parallel with a capacitor to vary effectively transmission line reactance XL in equation (2.1) mainly for power flow control and power oscillation damping. TCSC configuration is shown in Figure 2.7 where it is located in series with the transmission line (Hingorani et al., 2000). Operation principle of TCSC is to provide a variable capacitor in a continuous manner by means of controlling the effective reactance of the TCR with the thyristor firing angle ζ (zeta) which is measured from the zero crossing of the line current. At fundamental system frequency TCR becomes variable reactive impedance whose equivalent is given in equation (2.2) (Hingorani et al., 2000). 15 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Figure 2.7. TCSC configuration: (a) typical arrangement (b) z-α characteristics X TCR (ς ) = X TCR π π − 2ς − sin ς (2.2) where XTCR=wL, and XTCR≤ XTCR(ζ)≤∞. The controllable steady-state impedance of the TCSC at system fundamental frequency is obtained as X TCSC (ς ) = X C X TCR (ς ) X TCR (ς ) − X C (2.3) where XC=1/wC. From Figure 2.7b, the resonance region is inhibited for ζ1≤ ζ≤ ζ2 where XTCR(ζ) = XC. XTCSC is generally kept below XL to avoid over-compensation of the transmission line. 2.2.3. Thyristor Controlled Phase Angle Regulator (TCPAR) TCPAR, also known either as thyristor controlled phase shifting transformer or static phase shifting transformer is a replacement of phase shifting transformer for power flow control in a transmission line in steady-state conditions (Padiyar, 2007). The use of thyristors enables fast action to obtain a rapidly varying phase angle for dynamic regulation of power flow and stability improvement. TCPAR configuration is shown in Figure 2.8 (Hingorani et al., 2000). Phase shifting is attained by adding relatively small voltage vector Δv having ±90° phase shift relative to the system 16 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL voltage v as illustrated in Figure 2.8b. This small voltage vector resulted from the other two phases via shunt transformers is inserted in series with the transmission line. With this addition phase angle of the system voltage is varied. Thyristor switching enables relatively small angular adjustments making resultant angular change approximately proportional to the injected voltage, while the magnitude of system voltage remains almost constant (Hingorani et al., 2000). Figure 2.8. TCPAR configuration: (a) thyrsitor arrangement (b) vector diagrams 2.2.4. Static Synchronous Compensator (STATCOM) STATCOM is an advanced SVC with a VSC instead of controllable reactors and switched capacitors. STATCOM has many advantages over SVC that STATCOM has faster response, requires less space, being modular, and it can be interfaced with energy storage units. STATCOM configuration is shown in Figure 2.9 (Singh et al., 2009). During low voltage conditions STATCOM shows its superiority as the magnitude of the supplied reactive current is independent of the system voltage. However in SVC, the capacitive current drops linearly as system voltage reduces when high capacitive current is highly required. AC output of the converter, VSTATCOM is proportional to the DC link voltage Vdc. By varying VSTATCOM the reactive current is can be varied. Phase angle between VSTATCOM and VB is zero when neglecting losses (Padiyar, 2007). 17 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Figure 2.9. STATCOM configuration:(a) arrangement (b) operating modes 2.2.5. Static Series Synchronous Compensator (SSSC) SSSC is a series VSC based FACTS device to produce a controllable voltage in quadrature with the line current for power flow or bus voltage control (Gyugyi, 1997). SSSC has many advantages over TCSC that bulky passive components such as capacitors and reactors are eliminated. SSSC improves technical characteristics including symmetric capability in both inductive and capacitive operating modes. Moreover connecting an energy storage unit on the DC link is possible to exchange real power with the power system. Series injected voltage is controlled independent of the line current to effectively change the overall reactive voltage drop across the transmission line. Figure 2.10a depicts a typical SSSC arrangement (Sen, 1998). If VSSSC lags line current by 90°, VSSSC becomes a capacitive voltage, and if VSSSC leads line current by 90°, VSSSC becomes an inductive voltage. These two possible 18 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL operating modes emulate equivalent inductive or capacitive reactance in series with the line as denoted in Figure 2.10b while ignoring losses (Sen, 1998). By controlling the magnitude of VSSSC up to its maximum allowable limit, the amount of series compensation can be fully adjusted. Figure 2.10. SSSC configuration: (a) typical arrangement (b) operating modes 2.2.6. Unified Power Flow Controller (UPFC) UPFC is a versatile multi-converter FACTS device which can be regarded as the first example to this class. UPFC has been the most researched subject of all multi-converter FACTS devices to meet various control objectives of the electric power industry. UPFC configuration is shown in Figure 2.11 which was proposed by Gyugyi as the combination of STATCOM and SSSC (Gyugyi, 1992). In UPFC, the two VSCs are coupled through a common DC link to allow bi-directional real power transfer between the VSCs. The capability of real power exchange enables multifunctional flexibility so that the series voltage generated by the series VSC can be injected into the transmission line with controllable magnitude (0≤Vpq≤Vpqmax) and desired phase angle (0°≤θ≤360°) without requiring any external power source. This feature provides simultaneous or selective control of terminal voltage regulation, series compensation, and phase shifting for independent real and reactive power flow control. For instance, terminal voltage regulation can be attained if Vpq is inserted 19 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL having phase angle equal to that of VS. Series compensation can be applied if Vpq is inserted having phase angle that leads or lags 90° by IL. Transmission angle can be shifted if Vpq is inserted such that desired phase shift is obtained without any change in magnitude. Flexible operation mode shown in Figure 2.11b yields independent and simultaneous control of real and reactive power flow on the line which cannot be attained by single-converter FACTS devices. UPFC can also control bus voltage where its shunt VSC is connected by reactive power injection (Gyugyi, 1995). Figure 2.11. UPFC configuration: (a) typical arrangement (b) operating modes 2.2.7. Interline Power Flow Controller (IPFC) IPFC employs a number of series VSCs with a common DC link, each of which is connected to the transmission line via series coupling transformer to provide series compensation for a selected line of a multi-line substation (Gyugyi et al., 1999). The simplest IPFC configuration having two VSCs is shown in Figure 2.12a. Generally one VSC, for example lower VSC is assigned for flexible compensation, as shown in Figure 2.12b, by injecting full controllable voltage into the line for independent real and reactive power flow control. 20 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL Figure 2.12. IPFC configuration: (a) typical arrangement (b) operating mode This feature is not possible either in TCSC or SSSC in which only real power flow can be controlled. Upper VSC regulates DC link voltage by balancing real power between VSCs and at the same time it can regulate real or reactive power flow on the line where it is being coupled. Moreover IPFC can serve like a virtual transmission line so that an overloaded line can be relieved by forwarding real power flow to the underloaded line. Although IPFC and UPFC have the same number of control degrees of freedom, IPFC has received less attention generally in literature when compared with the UPFC based studies. 2.2.8. Generalized Unified Power Flow Controller (GUPFC) GUPFC is the extended version of UPFC with the addition of one or more series VSC to increase power system controllability (Fardanesh et al., 2000). GUPFC extends the concept of power flow and voltage control beyond that is achievable with either UPFC or IPFC. GUPFC having the simplest structure consists of one shunt VSC and two series VSCs as shown in Figure 2.13. Series VSCs can exchange real 21 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL power with two transmission lines to inject controllable voltages Vpq1 and Vpq2 with full angle control (0°≤θ1≤360°, 0°≤θ2≤360°) that cannot be attained either UPFC or IPFC. Shunt VSC both supports real power requirements of the series VCSs via common DC link and provide voltage support at the bus where it is being connected. GUPFC can control real and reactive power flows of the two parallel transmission lines as well as bus voltage simultaneously and independently, hence it has stronger control capabilities than UPFC. To add extra control degrees of freedom, the number of series VSCs can be increased to control more power flows at the same time. To relieve congestions, GUPFC may be installed in a substation to manage power flows of multi-lines or a group of lines and provide voltage support as well. Although the concept is not new, GUPFC has not gained much interest in literature. Figure 2.13. GUPFC configuration: (a) typical arrangement (b) operating modes 2.2.9. Back-to-Back STATCOM (BtB-STATCOM) BtB-STATCOM is a multi-converter FACTS device constructed by joining two separate STATCOMs at their DC link (Larsson et al., 2001), (Reed et al., 2003). 22 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL In literature, instead of “BtB-STATCOM” as the compensator name, “BtB DC link” or “VSC based BtB high voltage DC (HVDC) transmission link” are the alternative definitions (Tyagi et al., 2006), (Parkhidehet al., 2009), (Xinghao et al., 2009), (Liu et al., 2010). The concept can also be described as VSC based HVDC without long transmission network. As shown in Figure 2.14, each STATCOM is connected in parallel to the system bus via shunt coupling transformer. Common DC link provides bi-directional real power transfer between two AC grids (synchronous or asynchronous or even with different frequencies). In addition each STATCOM can provide independent reactive power support for dynamic voltage control. It is observed that there are few papers regarding BtB-STATCOM in literature. In this research, the capabilities of BtB-STATCOM is investigated for dynamic bus voltage control, real power transfer capability, and damping out oscillations caused by severe disturbances. Figure 2.14. BtB-STATCOM configuration with typical arrangement 2.3. More Control Degrees of Freedom The reactive power flow on the line in Figure 2.1 can be written in equation (2.4). The effective change in either or the combination of the line impedance and 23 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL phase angles by the applied compensation does not only change real power flow (equation (2.1)) but also reactive power flow is varied as well (Kundur, 1994). Operational characteristics of UPFC, IPFC, and GUPFC can overcome this natural real power-reactive power (P-Q) coupling phenomenon so that independent real and reactive power flow control can be provided simultaneously. This feature cannot be attained either by a conventional or a single-converter FACTS device. QR = E S VR (1 − cos(θ S − θ R )) XL (2.4) Independent P-Q control feature also regulates X/R ratio of the transmission line indirectly in which conventional series compensators such as fixed capacitor, TCSC, or SSSC only controls real power flow by varying line reactance. Conventional series compensation which are unable to control reactive power flow reduces only X, thus, X/R ratio is distorted significantly in which excessive amounts of reactive power flows are observed on the compensated lines which increase line losses significantly. Multi-converter FACTS devices, on the other hand, compensate against resistive line voltage drop so that effective value of R is also controlled to get a balanced X/R ratio (Hingorani et al., 2000). Control degrees of freedom of the FACTS devices can be defined as 2n-1 where n represents number of converters being utilized. For instance, the simplest IPFC and the simplest GUPFC can control three and five power system parameters in a simultaneous manner, respectively. Total MVA rating, roughly the sum of individual ratings of hardware elements such as high power converters and coupling magnetic interface, is effectively used in a multi-converter FACTS device. For instance, when the operation of individual STATCOM plus SSSC is compared with that of UPFC with the same MVA rating, the latter FACTS device provides an additional control capability, that is the capability to control the reactive flow on the transmission line. The independent operation of STATCOM and SSSC cannot provide this flexibility 24 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL even the sum of MVA ratings of STATCOM and SSSC is equal to that of UPFC. In this regard, UPFC provides more control capabilities to the power system. 2.4. Recent Advances in Power Semiconductors The development of FACTS devices has continued to grow with the growing capabilities of power semiconductors. Silicon based thyristors is widely used in first generation FACTS devices which have been present for several decades with voltage rating up to 11.0 kV (Chakraborty, 2011). The applications of second generation FACTS devices have been implemented using high power converters ranging from 10 MVA to 250 MVA. Gate turn-off thyristor (GTO), gate commutated thyristor (GCT), and integrated gate commutated thyristor (IGCT) are the common options with switching frequencies up to a few kHz. Silicon based GTOs have current rating up to 10 kA with voltage rating up to 9.0 kV (Chakraborty, 2011). GCT with ratings 6 kV and 6 kA has proven itself for high power converter applications for STATCOM (Reed et al., 2001). The performance and electrical rating of IGCT has increased dramatically in recent years. IGCTs with ratings 4.5-10 kV and 4.0 kA-6.5 kA are available in the market (Yongsug et al., 2009). IGCT does not require snubber circuits and has better turn-off characteristics, lower conducting and switching loss, and simpler gate control compared with GTO. It finds an application area of high power converters for wind power now, and seems to be a future option for extensive application prospect, including FACTS devices (Chengsheng et al., 2009). Ongoing semiconductor research for the next decade seems to cover mainly silicon carbide and gallium nitride materials to increase suitability and broadened applications of semiconductor devices in mega-watt range systems (Vobecky, 2011). 2.5. Field Applications of FACTS Devices at Transmission Level Although there are numerous successful FACTS installation examples including first generation, some application examples of the second generation 25 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL FACTS devices applied at the transmission level are listed below for the sake of highlight: • ± 50 MVAR STATCOM has been put in service for a couple of years at 154 kV Sincan transformer substation in Ankara, Turkey for reactive power compensation, terminal voltage regulation, and stability enhancement (Gultekin et al., 2012). • World’s first UPFC application is comprised of two ± 160 MVA converters at Inez Substation in Kentucky, USA and has been in service since 1998 for voltage support and power flow control (Renz et al., 1999). • ± 100 MVAR STATCOM at Sullivan substation in North-Eastern Tennessee, USA has been in service since 1995 (Schauder et al., 1997). • 80 MVA-154 kV UPFC comprised of two ± 40 MVA converters at Gangjin substation in Korea, has contributed to voltage stability enhancement and power flow control since 2003 (Im et al., 2005). • ± 200 MVA convertible static compensator, which can be configured as either STATCOM, SSSC, UPFC, or IPFC, has been installed in 2001 at 345 kV Marcy substation in New York, USA for maximizing the use of existing transmission network and improving voltage and power flow control capabilities (Zelingher et al., 2000). • +133/-41 MVA STATCOM has been in service at 115 kV Essex substation near Burlington, USA since 2001 for dynamic reactive power compensation for smooth voltage control over a wide range of operating conditions (Reed et al., 2001. • World’s largest STATCOM which has been planned at Toshin substation in Japan in 2010 rated at 450MVA for stability improvement and dynamic voltage control (Fujii et al., 2010). • ±100 MVA STATCOM has been commissioned at Talega 138 kV substation in California, USA since 2003 for dynamic reactive power support during peak load conditions (Reed et al., 2002). 26 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL • ±72 MVA BtB-STATCOM consisting of two ± 36 MVA STATCOMs have been installed for the first time in Eagle Pass substation and in Piedras Negras substation to enable bi-directional real power transfer between USA and Mexico as well as reactive power support for dynamic voltage control at two distinct buses (Larsson et al., 2001). 2.6. Summary This chapter has surveyed main technical limitations of AC power transmission and the FACTS devices with their operational characteristics as a solution option. In addition, recent advances in semiconductor technology development and some real-world FACTS installation examples are reviewed and summarized. It is emphasized that the multi-converter FACTS devices have more control capabilities than single-converter FACTS devices. With more control degrees of freedom by employing more converters, more control objectives can be achieved. Reactive power flow control is only attainable with more converters coupled through a common DC link. However GUPFC, IPFC, and BtB-STATCOM have received less attention in literature when compared with STATCOM, SSSC, and UPFC. The following next chapters will focus on modeling of these multi-converter FACTS devices in both steady and dynamic states. It is evident that these FACTS devices due to their special characteristics will play an essential role in the design and the operation of the future electric power systems. 27 2. OVERVIEW OF FACTS DEVICES A. Mete VURAL 28 3. STEADY-STATE MODELING A. Mete VURAL 3. STEADY-STATE MODELING 3.1. Introduction Power flow (load flow) studies which require steady-state modeling are crucial for the design and performance analysis phases of the FACTS devices embedded in power systems. The decisions and the future expansion options are specified based on the results obtained from power flow studies. In this chapter, an approach for the steady-state modeling of GUPFC, IPFC, and BtB-STATCOM for power flow studies is presented. In power flow studies of the IPFC, each VSC is generally modeled as pure sinusoidal three-phase balanced voltage source whose magnitude and phase angle are controlled. This voltage source is assumed to operate at fundamental system frequency of 50 Hz or 60 Hz and connected to the transmission line in series with a series reactance/impedance, which represents coupling transformer. Each coupling transformer is modeled as pure inductive reactance if converter losses are neglected (Xuan et al., 2004), (Xia et al., 2008), (Vasquez-Arnez et al., 2008). When the losses of the converters are taken into account, each coupling transformer is modeled as impedance having both resistive and reactive components (Zhang, 2003), (Bhowmick et al., 2009), (Yankui et al., 2006), (Vinkovic et al., 2011), (Natália et al., 2012). Alternatively, series voltage source is decomposed into direct and quadrature components which facilitates the control of the source (Vasquez-Arnez et al., 2008). Each series converter of the IPFC is modeled as controllable impedance inserted into the compensated line in series (Fardanesh et al., 2004). Power flow studies of the GUPFC assumes that the shunt and the series converters can be represented as ideal voltage sources with series reactances/impedances when losses are ignored (Padhy et al., 2005), (Vasquez-Arnez et al., 2008). When losses are taken into account, each series transformer is modeled as impedance having resistive and reactive components (Zhang et al., 2001), (Zhang et al., 2004). Discrepantly, the shunt converter of the GUPFC is modeled as current source with series connected reactance (Vasquez-Arnez et al., 2008). 29 3. STEADY-STATE MODELING A. Mete VURAL Power flow studies of the BtB-STATCOM is limited and have been studied under the concept of VSC based HVDC in which shunt converters are modeled as voltage sources with series impedances including converter losses into account (Zhang et al., 2004), (Pizano-Martinez et al., 2007). The inclusion of voltage/current sources provides real and reactive power exchange between the FACTS device and the power grid at newly added ghost buses which forms the basis of power injection models of the FACTS devices. Conventional Newton-Raphson (NR) power flow algorithm is then modified by the user using the set of real and reactive power injections at the buses where the FACTS devices are located. Generally the structure of the Jacobian matrix is preserved but Jacobian matrix formation for IPFC and GUPFC is different by taking derivatives with respect to real and imaginary parts of the line current as opposed to conventional approach (Vinkovic et al., 2011). Alternatively, NR solution algorithm is accomplished by a power system analysis software package instead of writing the codes by the user. The power injection model of the FACTS device is then defined in a user-defined model for power flow studies of the power systems embedded with the FACTS devices (Tümay et al., 2004), (Vural et al., 2007). In this chapter a different steady-state modeling approach for power flow studies of GUPFC, IPFC, and BtB-STATCOM is proposed in PSCAD neither requires a power injection based user-defined model nor modification of NR codes by the user is required due to real and reactive power injections caused by the FACTS device. 3.2. Proposed Steady-state Modeling Approach The aforementioned modeling approaches in literature are powerful even for relatively large power systems having many buses but suffer from the complexities of the programming codes in NR power flow algorithm. However, the proposed modeling approach is graphically implemented in PSCAD without editing NR codes by the user. Instead, Electromagnetic Transients including Direct Current (EMTDC), the simulation engine of PSCAD, handles the interaction of the FACTS device and 30 3. STEADY-STATE MODELING A. Mete VURAL the power system and solves both operating and control constraint equations required for the power flow study. 3.2.1. Configurable Multi-Converter FACTS Device For the purpose of the study a generic configurable multi-converter FACTS device having four converters with a common DC link is presented in Figure 3.1. By turning on/off appropriate switches (S1-4) six types of FACTS devices in nine different configurations can be obtained as listed in Table 3.1. VSC1 and VSC4 are connected at Buses i and j via shunt coupling transformers Tr1 and Tr4, respectively. Series converters VSC2 and VSC3 are connected to the transmission lines Lines m and n, via series coupling transformers Tr2 and Tr3, respectively. Each VSC can synthesize three-phase controllable AC voltage so that each VSC is modeled as a sinusoidal voltage source with controllable magnitude (Vsh1-2,Vse1-2) and phase angle (θsh1-2,θse1-2) as shown in Figure 3.2. Figure 3.1. Generic multi-converter FACTS device 31 3. STEADY-STATE MODELING A. Mete VURAL Table 3.1. Flexible configuration of the multi-converter FACTS device Mode Switch positions S2 S3 ON ON ON OFF OFF ON ON OFF S4 OFF ON OFF OFF FACTS device STATCOM-1 STATCOM-2 SSSC-1 SSSC-2 1 2 3 4 S1 ON ON OFF OFF 5 ON ON ON ON BtB-STATCOM 6 ON OFF ON OFF UPFC-1 7 ON ON OFF OFF UPFC-2 8 OFF OFF OFF OFF IPFC 9 ON OFF OFF OFF GUPFC Control attribute Bus i voltage Bus j voltage Line m real or reactive power flow Line n real or reactive power flow Buses i and j voltage + real power transfer Bus i voltage + Line m real and reactive power flows Bus i voltage + Line n real and reactive power flows Line m real power flow + Line n real and reactive power flows Bus i voltage + Line m/n real and reactive power flows Each voltage source is assumed to have the capabilities of independent reactive power injection (Qinj1-4) and dependent real power injection (Pinj1-4) through the transformers to the power system. DC link enables real power exchange between converters (Ptransfer1-4) so that the sum of real power injections into the power system is zero. Ploss1-4 is the sum of switching loss plus coupling transformer loss of each related VSC, respectively. Figure 3.2. Voltage source equivalent model of the generic FACTS device 32 3. STEADY-STATE MODELING A. Mete VURAL 3.2.2. Operating Constraints Operating constraint of the FACTS device is mainly related with the maximum voltage injection capability and the MVA rating of each commissioned converter. A set of equations for voltage constraint in polar form of each converter can be written in equation (3.1). Vconv is the generic symbol representing line-toneutral rms voltage of shunt/series converter (Vsh1-2, Vse1-2). θconv is the respective phase angle of Vconv (θsh1-2, θse1-2). 0 ≤ Vconv ≤ Vconv(max)     0 ≤ θ conv ≤ 2π  (3.1) Each converter should be fed from a constant DC link voltage for “voltage source” based operation. DC link voltage Vdc is defined in equation (3.2) for singleconverter operation (Mode 1-4) and should be kept constant in steady-state. This constraint is established by regulating Vdc to its reference that can be succeeded by a closed-loop control scheme. In steady-state, time derivative of Vdc becomes zero and equation (3.2) reduces to equation (3.3) for converter m. Pinj ,m + Ploss ,m = CV dc dVdc dt (3.2) Pinj ,m + Ploss ,m = 0 (3.3) In multi-converter operation (Mode 5-9), equation (3.3) should be modified since real power transfer occurs between converters. For converter m the constraint is updated as given in equation (3.4). Pinj , m − Ptransfer, m + Ploss,m = 0 (3.4) 33 3. STEADY-STATE MODELING A. Mete VURAL Steady-state operating requirements of each configuration are listed in Table 3.2 based on real and reactive power interactions given in Figure 3.2 and equations (3.3) and (3.4). Maximum amount of real and reactive power related with each converter is a constraint and defined in terms of MVA converter rating in pu. Real power constraint is derived on the fact that conservation of power. Loss meeting function of the FACTS device can be theoretically assigned to any converter in a number of ways. In single-VSC operation, each converter should meet losses itself from the power system. In multi-VSC operation, overall losses can be met by only single converter or any converter combination. For the sake of simplicity, only one converter is assigned to meet overall losses of the multi-converter FACTS device. Table 3.2. Operating constraints of the multi-converter FACTS device 1 2 3 4 Loss meeting VSC1 VSC4 VSC2 VSC3 5 VSC1 6 VSC1 7 VSC1 8 VSC2 9 VSC1 Mode Constraint equations in pu Real power Reactive power Apparent power Pinj1 + Ploss1 = 0 -1.0 ≤ Qinj1 ≤ 1.0 (Pinj12 + Qinj12) ≤ 1.0 Pinj4+ Ploss4 = 0 -1.0 ≤ Qinj4 ≤ 1.0 (Pinj42 + Qinj42) ≤ 1.0 Pinj2 + Ploss2 = 0 -1.0 ≤ Qinj2 ≤ 1.0 (Pinj22 + Qinj22) ≤ 1.0 Pinj3 + Ploss3 = 0 -1.0 ≤ Qinj3 ≤ 1.0 (Pinj32 + Qinj32) ≤ 1.0 Pinj1 – Ptransfer1 + ... ... + Ploss1 + Ploss4 = 0 -1.0 ≤ Qinj1 ≤ 1.0 (Pinj12 + Qinj12) ≤ 1.0 Pinj4 – Ptransfer4 = 0 -1.0 ≤ Qinj4 ≤ 1.0 (Pinj42 + Qinj42) ≤ 1.0 Ptransfer1 + Ptransfer4 = 0 Pinj1 - Ptransfer1 + ... ... + Ploss1 + Ploss2 = 0 -1.0 ≤ Qinj1 ≤ 1.0 (Pinj12 + Qinj12) ≤ 1.0 Pinj2 - Ptransfer2 = 0 -1.0 ≤ Qinj2 ≤ 1.0 (Pinj22 + Qinj22) ≤ 1.0 Ptransfer1 + Ptransfer2 = 0 Pinj1 – Ptransfer1 + ... ... + Ploss1 + Ploss3 = 0 -1.0 ≤ Qinj1 ≤ 1.0 (Pinj12 + Qinj12) ≤ 1.0 Pinj3 – Ptransfer3 = 0 -1.0 ≤ Qinj3 ≤ 1.0 (Pinj32 + Qinj32) ≤ 1.0 Ptransfer1 + Ptransfer3 = 0 Pinj2 – Ptransfer2 + ... ... + Ploss2 + Ploss3 = 0 -1.0 ≤ Qinj2 ≤ 1.0 (Pinj22 + Qinj22) ≤ 1.0 Pinj3 – Ptransfer3 = 0 -1.0 ≤ Qinj3 ≤ 1.0 (Pinj32 + Qinj32) ≤ 1.0 Ptransfer2 + Ptransfer3 = 0 Pinj1 – Ptransfer1 + ... ... + Ploss1 + Ploss2 + ... ... + Ploss3= 0 -1.0 ≤ Qinj1 ≤ 1.0 (Pinj12 + Qinj12) ≤ 1.0 Pinj2 – Ptransfer2 = 0 -1.0 ≤ Qinj2 ≤ 1.0 (Pinj22 + Qinj22) ≤ 1.0 Pinj3 – Ptransfer3 = 0 -1.0 ≤ Qinj3 ≤ 1.0 (Pinj32 + Qinj32) ≤ 1.0 Ptransfer1 + Ptransfer2 +... ... + Ptransfer3 = 0 34 3. STEADY-STATE MODELING A. Mete VURAL 3.2.3. Control Constraints 3.2.3.1. Direct Control Mode In direct control mode, the user sets the reference values of the real and reactive power injections for each VSC directly in any operating mode of the FACTS device. In steady-state, equation (3.5) can be written as a control constraint for reactive power injection for converter m. This case is valid for all modes (Mode 1-9). Qinj ,m − Qinj ,m ref = 0 (3.5) When revealing real power injection constraint, reference value of the real power injection by converter m should be equal to the power loss of the converter in steadystate, as written in equation (3.6). This case is valid for single-converter operation (Mode 1-4). In multi-converter operation (Mode 5-9), reference values of the desired real power injections become dependent upon each other. For example for UPFC-1, equation (3.7) is derived and written as real power injection constraints for the two converters. Equation (3.7) can be modified as equations (3.8) and (3.9) for IPFC and GUPFC, respectively. In direct control mode, the effects of real and reactive power injections on power system variables, such as, real and reactive power flows, real and reactive transmission losses, bus voltage profile, can be investigated based on power injection concept. Ploss ,m + Pinj ,m ref = 0 (3.6) Ploss1 + Ploss 2 + Pinj ,1ref + P inj , 2 ref = 0 (3.7) Ploss 2 + Ploss 3 + Pinj , 2 ref + P inj ,3 ref = 0 (3.8) Ploss1 + Ploss 2 + Ploss 3 + Pinj ,1 ref + Pinj , 2 ref + P inj ,3 ref = 0 (3.9) 35 3. STEADY-STATE MODELING 3.2.3.2. A. Mete VURAL Indirect Control Mode In indirect control mode, the user sets reference values of the power system parameters such as, bus voltage and real and reactive power flows instead of direct real and reactive power injections by VSCs. The bus voltage control constraint is given in equation (3.10) and can be solved generally by the FACTS device having a shunt VSC (Mode 1,2,5,6,7,9). Vbus is the voltage magnitude of the local bus, to which shunt VSC is connected. Vbusref is the reference value of the voltage magnitude of the local bus. In a similar manner, power flow control constraint pair given in equation (3.11) is solved by the FACTS device having multi-converters (Mode 5-9). Alternatively, only real or only reactive power flow constraint is required to be solved merely, this can be established by the FACTS device having series converters (Mode 3,4,6-9). Vbus − Vbus ref = 0 (3.10)  Pline − Pline ref = 0    Qline − Qline ref = 0 (3.11) Apparent power constraint of any mode, given in the last column of Table 3.2, is not supposed to be a control constraint either in direct/indirect control mode. It is not come up to a reference value, instead it is observed explicitly and expected to be in the limits of FACTS device rating. It can be observed that under which operating conditions, violation of apparent power rating occurs. Real power constraints, given in equations (3.6) and (3.9), should also be provided in indirect control mode. Either in direct or indirect control mode, for a given control objective, required voltage magnitude and phase angle of each converter are iteratively found in PSCAD by updating the solution at each solution time step. Depending on the control requirements these two control modes can be operated simultaneously. 36 3. STEADY-STATE MODELING 3.3. A. Mete VURAL Modeling in PSCAD 3.3.1. Power Circuit PSCAD is well-accepted graphical based electromagnetic time domain transient simulation environment and principally suited for simulating time domain instantaneous responses of electrical systems. Power circuit of the FACTS device, consisted of shunt/series converters and the coupling transformers is modeled using standard available components of the PSCAD master library which is shown in Figure 3.3. Each shunt/series converter is constructed using three-phase voltage source model-2, whose AC voltage magnitude and phase angle are controlled through external signals. Three-phase two-winding transformer is connected as delta/wye which couples AC output of shunt converter with the high voltage of system bus. Three identical single-phase two-winding transformers are used to inject AC voltage of the series converter into the transmission line. The shunt and the series converters are combined together to realize the respective FACTS device together with its control circuit mentioned in the next section. Design data of the shunt and series converters are given in Appendix A. The switches presented in Figure 3.1 are implemented using three-phase breakers with single line view, shown in Figure 3.3. 3.3.2. Control Circuit Each control constraint, defined either in direct/indirect control mode, is treated as a closed-loop control problem and solved via a simple PI controller. So it is guaranteed that each controlled variable is equal to its reference value in steadystate by choosing appropriate controller parameters. Control circuits for both direct/indirect control modes are implemented in PSCAD and depicted in Figure 3.4. The error signal obtained by differencing the actual and the reference value of the controlled variable drives the controller to produce suitable adjustments of control inputs of the converter. In order to bring clarity and to make the solution 37 3. STEADY-STATE MODELING A. Mete VURAL appropriate for power flow studies, the voltage and the phase angle of the respective converter are used as control inputs in steady-state conditions. Figure 3.3. PSCAD models of shunt and series converters 38 3. STEADY-STATE MODELING A. Mete VURAL In direct control mode, reactive and real power injections by the converter m of the FACTS device are controlled by the voltage magnitude, Vcontrolm and the phase angle, ph_vscm, respectively as shown in Figure 3.4. After the power flow problem has reached to a solution, PSCAD variable Vcontrolm (m=1,2,3,4) reaches to its steady-state values of Vsh1-2, Vse1-2 and PSCAD variable ph_vscm (m=1,2,3,4) becomes equal to the steady-state values of θsh1-2, θse1-2, respectively. In indirect control mode, external power system parameters such as line real and reactive power flows and/or bus voltage magnitudes are regulated at their desired values by the control inputs of the converters. In both modes, PI controller is also used as constraint provider, so it holds voltage magnitude and phase angle of the converter within allowed limits. Operating constraints given in equation (3.1) are satisfied by this means. All controlled variables are graphically displayed using multimeter blocks in PSCAD master library. 3.4. Power Flow Studies 3.4.1. Test Systems The proposed steady-state modeling approach for multi-converter FACTS devices is tested and verified through case studies in different test systems whose branch and line data are given in Appendix B. These systems are Western System Coordinated Council (WSCC) 3-Machine 9-Bus System (Sauer et al., 1997), IEEE 14-Bus System (Washington, 2012), and 3-Machine 7-Bus System (Fardanesh, 2004) with 100 MVA base each. The components of the test systems are modeled using standard components of the PSCAD master library. All generators and the condenser are modeled using three-phase voltage source model-2, (for condenser, voltage source is phase angle controlled), transmission line is modeled using coupled pi section transmission line, and the transformer is modeled using three-phase twowinding transformer. P-Q load which is connected at high voltage bus is modeled as a custom module using PSCAD master library components in PSCAD, as shown in Figure 3.5. 39 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.4. Control constraint implementation in PSCAD 40 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.5. PSCAD model of the P-Q load connected at high voltage bus 41 3. STEADY-STATE MODELING A. Mete VURAL Duration of the simulation run is always set to a relatively long time to observe and ensure that all the variables approach to their steady-state values after the simulation is completed. The key to the simulation cases is to guarantee that operating limits are not violated and stable solutions of the control constraints are always held. Regulator parameters of each mode in each case study are listed in Appendix C. Total loss of the single-converter FACTS device is assumed to be 0.015 pu on a 100 MVA base (Lee et al., 2003) so that the multi-converter operation yields an operational loss that is integer multiples of this value. With this respect, UPFC or IPFC has a total loss of 0.030 pu, and GUPFC has a total loss of 0.045 pu. Solution speed is kept as fast as possible by setting solution time step relatively long (100 µs) while keeping the stability of PSCAD. 3.4.2. WSCC 3-Machine 9-Bus System 3.4.2.1. Case 1: STATCOM and SSSC Operations PSCAD model of WSCC 3-Machine 9-Bus System is shown in Figure 3.6. Without any compensation, power flow solution of the system is found as: Receiving-end Line 4-5 flow = 0.7983+j0.1528 pu, receiving-end Line 4-6 flow = 0.5349+j0.0573. At first, non-real power-voltage (P-V) remote/local bus voltages are regulated to 1.0 pu by Modes 1,3,4 (indirect control mode). STATCOM-1 (Mode 1) is positioned at Bus 4 (VSC1) and SSSC1-2 (Mode 3,4) are positioned on Lines 4-5 and 4-6, respectively. Simulation results listed in Table 3.3 have proven that STATCOM-1 and SSSC1-2 are able to regulate bus voltages effectively although the primary function of SSSC is known as power flow regulation. Bus 9 is regulated by SSSC-1 at the expense of device rating constraint violation. 42 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.6. PSCAD model of WSCC 3-Machine 9-Bus System 43 3. STEADY-STATE MODELING A. Mete VURAL Table 3.3. Power flow results for voltage magnitude regulation @ 1.0 pu Bus No, i 4 5 6 7 8 9 Uncompensated Vi (pu) 0.9930 0.9665 0.9830 1.0010 0.9911 1.0010 STATCOM-1 Qinj1 (pu) + 0.1272 + 0.6423 + 0.3359 + 0.0050 + 0.3893 - 0.3434 SSSC-1 Qinj2 (pu) + 0.1654 + 0.0168 + 0.4907 - 0.0002 + 0.0230 + 2.2900 SSSC-2 Qinj3 (pu) + 0.0762 + 0.7550 + 0.0014 + 0.2782 + 0.0118 + 0.1584 Secondly, real power flow on Line 4-5 is regulated by STATCOM-1 and SSSC-1 at a sequence of set points, defined in terms of arbitrary chosen positive/negative percentage changes of the uncompensated real power flow (indirect control mode). Results are listed in Table 3.4 including resultant VSC output voltage and injected reactive power to the system. Without device rating constraint violation, SSSC-1 is able to regulate real power flow at its desired values. However, Line 4-5 is regulated by STATCOM-1 at the expense of device rating violation. Specifically, real power flow that cannot be forced to zero by STATCOM-1 is easily regulated to zero by SSSC-1 which completes the regulation task better than STATCOM-1 with a slightly smaller device rating. Table 3.4. Power flow results for real power regulation of Line 4-5 P4-5ref - 25% - 50% - 75% - 100% + 2% + 5% + 7% + 10% STATCOM-1 P4-5+jQ4-5 (pu) 0.5987-j0.2546 0.3991-j0.3794 0.1995-j0.3955 0.0320-j0.1642 0.8142+j0.2382 0.8382+j0.3775 0.8541+j0.4773 0.8781+j0.6384 SSSC-1 P4-5+jQ4-5 (pu) 0.5987+j0.1795 0.3991+j0.1720 0.1995+j0.1182 0.0000-j0.0050 0.8142+j0.1453 0.8382+j0.1390 0.8541+j0.1345 0.8781+j0.1274 STATCOM-1 Qinj1, Vsh1 (pu, kV) -3.1370, 0.10 -3.1720, 8.17 -2.4140, 4.66 -0.0030, 0.05 0.6433, 21.6 1.6410, 22.93 2.3520, 23.80 3.4920, 25.07 SSSC-1 Qinj3, Vse1 (pu, kV) -0.0510, 1.84 -0.0734, 3.81 -0.0621, 6.07 0.0013, 9.05 0.0050, 0.14 0.0133, 0.35 0.0189, 0.49 0.0278, 0.70 Thirdly, reactive power flow on Line 4-6 is regulated by STATCOM-1 and SSSC-2 according to an arbitrary sequence of set points for reactive power flow, similarly in the above task (indirect control mode). Results are listed in Table 3.5 including resultant VSC output voltage and injected reactive power to the system. STATCOM-1 and SSSC-2 are able to regulate reactive power flow at zero. Without device rating constraint violation SSSC-2 is able to regulate reactive power flow at 44 3. STEADY-STATE MODELING A. Mete VURAL its desired values. However, Line 4-6 is regulated by STATCOM-1 at the expense of device rating violation. Table 3.5. Power flow results for reactive power flow regulation of Line 4-6 Q4-6ref STATCOM-1 P4-6+jQ4-6 (pu) - 25% - 50% -75% - 100% + 25% + 50% +75% + 100% 0.5556+j0.0429 0.5527+j0.0286 0.5498+j0.0143 0.5468+j0.0000 0.5613+j0.0716 0.5641+j0.0859 0.5669+j0.1002 0.5696+j0.1146 3.4.2.2. SSSC-2 P4-6+jQ4-6 (pu) 0.5458+j0.0429 0.5441+j0.0286 0.2640+j0.0143 0.3487+j0.0000 0.5493+j0.0716 0.5510+j0.0859 0.5528+j0.1002 0.5547+j0.1146 STATCOM-1 Qinj1, Vsh1 (pu, kV) 0.8256, 21.87 0.7109, 21.71 0.5961, 21.55 0.4810, 21.38 1.0560, 22.18 1.1700, 22.33 1.2850, 22.48 1.4000, 22.63 SSSC-2 Qinj3, Vse2 (pu, kV) 0.0058, 1.20 0.0043, 1.03 0.0305, 2.59 0.0276, 1.78 0.0095, 1.55 0.0117, 1.72 0.0142, 1.89 0.0168, 2.07 Case 2: UPFC Operation UPFC-2 (Mode 7) is positioned at Bus 4 (VSC1) and on Line 4-6 (VSC3). Bus 4 voltage, V4 is regulated at 1.0 pu by VSC1 while Pinj1 is regulated at -0.030 pu to meet the losses of the converters and ensuring real power balance between them (indirect control mode). At the same time Qinj3 is regulated at values of 0.1 pu, 0.2 pu, and 0.3 pu, respectively by VSC3 (direct control mode). Since UPFC has two converters, control degree of freedom is three, so that Vsh1, Vse3, and θse3 are the independent control parameters. However, θsh1 should be regulated to ensure real power balance among the converters. For each regulated value of Qinj3, θse3 is altered from 0º to 360º in small degrees to obtain P-Q control planes of Line 4-6 as shown in Figure 3.7. 3.4.2.3. Case 3: IPFC Operation IPFC (Mode 8) is positioned on Line 4-5 (VSC2) and on Line 4-6 (VSC3). Bus 4 voltage, V4 is regulated at 1.0 pu by VSC2 while Pinj2 is regulated at -0.030 pu to meet the losses of the converters and ensuring real power balance between them (indirect control mode). At the same time Qinj3 is regulated at values of 0.1 pu, 0.2 pu, and 0.3 pu, respectively by VSC3 (direct control mode). Since IPFC is a two- 45 3. STEADY-STATE MODELING A. Mete VURAL VSC FACTS device, control degree of freedom is three, so that Vse2, Vse3, and θse3 are independent control parameters. However, θse2 should be regulated to ensure real power balance among the converters. For each regulated value of Qinj3, θse3 is altered from 0º to 360º in small degrees to obtain P-Q control planes of Line 4-6 as shown in Figure 3.8. Figure 3.7. P-Q Control planes of Line 4-6 obtained with UPFC Figure 3.8. P-Q Control planes of Line 4-6 obtained with IPFC 46 3. STEADY-STATE MODELING 3.4.2.4. A. Mete VURAL Case 4: GUPFC Operation GUPFC (Mode 9) is positioned at Bus 4 (VSC1), on Line 4-5 (VSC2), and on Line 4-6 (VSC3). Bus 4 voltage, V4 is regulated at 1.0 pu by VSC1 while Pinj1 is regulated at -0.045 pu to meet the losses of the converters and ensuring real power balance between the three converters (indirect control mode). At the same time Qinj2 and Qinj3 are regulated concurrently at values of 0.05 pu, 0.1 pu, and 0.12 pu, respectively (direct control mode). Since GUPFC is a three-VSC FACTS device, control degree of freedom is five, so that Vsh1, Vse2, Vse3, θse2, and θse3 are independent control parameters. However, θsh1 should be regulated to ensure real power balance among the converters. For each set of regulated reactive power injections, θse3 is altered from 0º to 360º in small degrees while keeping θse2 lags θse3 by 30º arbitrarily for the sake of simplicity, although VSC2 and VSC3 can operate independently. Obtained P-Q control planes of Lines 4-5 and 4-6 are presented in Figures 3.9 and 3.10, respectively. Figure 3.9. P-Q control planes of Line 4-5 obtained with GUPFC 47 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.10. P-Q control planes of Line 4-6 obtained with GUPFC 3.4.2.5. Discussion of Simulation Results By examining Tables 3.4 and 3.5, undeterministic real and reactive power flows are observed in both of the above tasks. This is due to the utilization of singleconverter FACTS devices which are mentioned in Section 2.3. This might necessitate using multi-converter topologies providing multiple control degrees of freedom, if independent real and reactive power flow regulation is required on a specific line. It is generally concluded that STATCOM is practical for voltage regulation and SSSC exhibits superior real and reactive power flow regulation performance than STATCOM with smaller device rating of SSSC. It is also concluded from the obtained P-Q circles that UPFC, IPFC, or GUPFC is able to increase/decrease real and reactive power flows as well as reverse the direction of flow. Zero reactive power flow can also be achieved to decrease transmission losses. The higher reactive compensation level which means higher reactive power injection, the larger P-Q control area is attained by the FACTS device. These results have been verified from literature (Gyugyi et al., 1995), (Gyugyi et al., 1999). Maximum attainable reactive compensation level for each converter is always observed under 1.0 pu because of non-zero Ptransfer and converter losses. 48 3. STEADY-STATE MODELING A. Mete VURAL 3.4.3. IEEE 14-Bus System 3.4.3.1. Case 1: UPFC Operation PSCAD model of IEEE 14-Bus System is shown in Figure 3.11. Power flow control capabilities of UPFC-1 and UPFC-2 are investigated in this case study. Uncompensated parameters of the test system are as follows: V5 = 1.020 pu, P52 +jQ52 = - 0.4074 + j0.1667 pu, and P54 + jQ54 = 0.6293 + j0.0276 pu. First, UPFC-1 (Mode 6) is positioned at Bus 5 (VSC1) and on Line 5-2 (VSC2) in indirect control mode. Bus 5 voltage, V5 is regulated at different set points by VSC1 while Pinj1 is regulated at -0.030 pu to meet the losses of the converters and ensuring real power balance between them. For the given set of reference values, power flow solution is obtained with the internal parameters of UPFC-1. The results are listed in Table 3.6. Secondly, UPFC-2 (Mode 7) is positioned at Bus 5 (VSC1) and on Line 5-4 (VSC3) in indirect control mode. Similarly V5 is regulated at different set points by VSC1 while Pinj1 is regulated at -0.030 pu. For the given set of reference values, power flow solution is obtained with the internal parameters of UPFC-2. The results are listed in Table 3.6. Table 3.6. Parameters of the UPFC under different power flow control strategies scheduled system variables P52ref + jQ52ref V5ref 0.15+j0.40 1.00 -0.20+j0.05 1.01 -0.35+j0.15 1.01 -0.50-j0.15 0.95 scheduled system variables P54ref + jQ54ref V5ref 0.50+j0.02 1.00 0.80+j0.05 1.05 -0.20+j0.01 1.00 0.15-j0.025 1.015 UPFC-1 VSC1 output voltage VSC2 output voltage magnitude (kV) phase angle (º) magnitude (kV) phase angle (º) 12.21 -41.46 2.35 4.05 12.13 -39.78 0.81 17.62 12.16 -38.80 0.57 -35.74 10.39 -37.16 0.79 -82.73 UPFC-2 VSC1 output voltage VSC3 output voltage magnitude (kV) phase angle (º) magnitude (kV) phase angle (º) 12.01 -38.34 0.73 -71.10 12.10 -39.89 0.99 -8.09 11.87 -35.07 2.50 -122.74 12.25 -36.75 1.42 -122.49 49 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.11. PSCAD model of IEEE 14-Bus System 50 3. STEADY-STATE MODELING 3.4.3.2. A. Mete VURAL Case 2: IPFC Operation IPFC (Mode 8) is positioned on Line 5-2 (VSC2) and on Line 5-4 (VSC3) to control reactive power flow of Line 5-2 and real and reactive power flows of Line 54 at their desired values in indirect control mode. Pinj2 is regulated at -0.030 pu to meet the losses of the converters and ensuring real power balance between them. For the given reference values of the real and reactive power flows, power flow solutions including internal parameters of IPFC are listed in Table 3.7. Table 3.7. Parameters of the IPFC under different power flow control strategies scheduled system variables P54ref + jQ54ref Q52ref 0.50+j0.10 j0.01 0.65+j0.008 j0.08 -0.20+j0.005 -j0.08 -0.40-j0.10 j0.015 3.4.3.3. IPFC VSC2 output voltage VSC3 output voltage magnitude (kV) phase angle (º) magnitude (kV) phase angle (º) 3.66 -141.41 1.16 29.68 0.68 -109.69 0.35 68.06 1.83 -112.24 0.48 100.03 2.12 -127.56 2.31 199.48 Case 3: GUPFC Operation GUPFC (Mode 9) is positioned at Bus 5 (VSC1), on Line 5-2 (VSC2) and on Line 5-4 (VSC3) to control real and reactive power flows of Line 5-2 and real and reactive power flows of Line 5-4 simultaneously in indirect control mode. At the same time V5 is regulated at various set points independently from the controlled flows and Pinj1 is regulated at -0.045 pu to meet the losses of the three converters and ensuring real power balance between them. Table 3.8 indicates the results of power flow with the internal parameters of the GUPFC for the given set of reference values. 3.4.3.4. Discussion of Simulation Results The simulation results prove that the proposed FACTS device model in various operating modes is capable of handling the scheduled real and reactive power flows and bus voltage in indirect control mode. Operational and control constraints are satisfied with a stable solution and an acceptable simulation time. It is shown that 51 3. STEADY-STATE MODELING A. Mete VURAL well-known control functions, such as real and reactive power flow increase/decrease as well as reversing real power flow are all implemented in this case study. Multicontrol objectives are met with the multi-converter FACTS devices in steady-state. Table 3.8. Parameters of the GUPFC under different power flow control strategies GUPFC scheduled system variables P52ref + jQ52ref P54ref + jQ54ref V5ref -0.20+j0.10 0.50+j0.01 1.04 0.40+j0.01 0.40-j0.01 1.03 0.30-j0.01 0.65-j0.01 1.03 -0.035-j0.20 0.08+j0.025 1.065 VSC1 output voltage VSC2 output voltage VSC3 output voltage magnitude (kV) phase angle (º) magnitude (kV) phase angle (º) magnitude (kV) phase angle (º) 13.08 -40.10 0.74 42.53 0.59 67.02 12.80 -45.72 3.59 38.70 0.93 37.71 12.80 -47.02 3.67 40.23 1.71 35.26 13.20 -38.63 1.22 89.46 1.29 207.44 3.4.4. 3-Machine 7-Bus System Power flow studies of BtB-STATCOM in 3-Machine 7-Bus System (including generator buses), shown in Figure 3.12, are conducted. BtB-STATCOM installation is implemented at two neighboring buses, namely, Bus 1 (VSC1) and Bus 3 (VSC4) which is different from a BtB DC link that connects two remote-end buses via long HVDC transmission. 3.4.4.1. Case 1: Reactive Power-Voltage (Q-V) Characteristics Q-V characteristics of the two converters of BtB-STATCOM as two independent STATCOMs are investigated by decoupling the DC links of the converters. Qinjref is changed in steps for each VSC independently. θsh1 and θsh2 are regulated individually to meet losses (0.015 pu) of STATCOM-1 and STATCOM-2, 52 3. STEADY-STATE MODELING A. Mete VURAL Figure 3.12. PSCAD model of 3-Machine 7-Bus System 53 3. STEADY-STATE MODELING A. Mete VURAL respectively with zero real power transfer between them. Qinjref max is calculated according to operating constraints in Table 3.2 for Modes 1 and 2. Numerical results are illustrated in Table 3.9. Table 3.9. Q-V characteristics of the two converters Capacitive Compensation No FACTS Inductive Compensation 3.4.4.2. VSC1 (kV, deg) 14.06, -12.41° 13.94, -12.49° 13.82, -12.56° 13.70, -12.64° 13.58, -12.73° 0.0, 0.0° 13.33, -12.90° 13.20, -12.99° 13.07, -13.09° 12.94, -13.19° 12.80, -13.30° Qinj1 (pu) 0.999 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -0.999 V1 (pu) 0.9955 0.9896 0.9836 0.9774 0.9712 0.9652 0.9584 0.9517 0.9450 0.9380 0.9309 VSC4 (kV, deg) 14.10, -25.71° 13.99, -25.89° 13.87, -26.07° 13.75, -26.25° 13.63, -26.45° 0.0, 0.0° 13.38, -26.86° 13.25, -27.08° 13.12, -27.31° 12.99, -27.55° 12.85, -27.80° Qinj4 (pu) 0.999 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -0.999 V3 (pu) 0.9990 0.9931 0.9871 0.9810 0.9748 0.9688 0.9620 0.9554 0.9487 0.9419 0.9349 Case 2: Real Power-Voltage (P-V) Characteristics BtB-STATCOM and STATCOM are compared when improving P-V curves of Buses 1 and 3 under steady-state conditions when demanded real power (load) at these buses is increased in steps. At first, STATCOM-1 and STATCOM-2 are commanded simultaneously to inject pre-defined Qinjref at Buses 1 and 3, respectively. Next, BtB-STATCOM is operated to hold voltage levels against to increasing demanded power when max. possible real power transfer occurs between the two VSCs. The derivation of Pinjref max and Qinjref max for these operations are derived in Appendix D. Comparative P-V curves of Buses 1 and 3 for two different directions of real power transfer are shown in Figures 3.13 and 3.14, respectively. 54 3. STEADY-STATE MODELING A. Mete VURAL (a) Bus 1 voltage profile when real power transfer is from VSC1 to VSC4 (b) Bus 1 voltage profile when real power transfer is from VSC4 to VSC1 Figure 3.13. Comparative P-V curves of Bus 1 55 3. STEADY-STATE MODELING A. Mete VURAL (a) Bus 3 voltage profile when real power transfer is from VSC1 to VSC4 (b) Bus 3 voltage profile when real power transfer is from VSC4 to VSC1 Figure 3.14. Comparative P-V curves of Bus 3 3.4.4.3. Discussion of Simulation Results Results show that either STATCOM or BtB-STATCOM can control bus voltages in steady-state and improve voltage stability of the power system by improving P-V curves of the local buses. Coupling the DC links of the two STATCOMs yields real power transfer from one neighboring bus into another in BtB-STATCOM operation. Real power transfer, which brings an extra control 56 3. STEADY-STATE MODELING A. Mete VURAL degree of freedom in power flow studies, changes real and reactive power flow distributions on transmission lines, hence changes voltage profiles indirectly. This situation should be considered for BtB-STATCOM design in practical applications. 3.5. Summary A new modeling approach for power flow studies of the power systems embedded with single- and multi-converter FACTS devices is presented in PSCAD which is based on the regulation of magnitude and phase angle of the converters in steady-state conditions. Operational and control constraints defined for each FACTS device are solved in PSCAD using simple PI regulators. Direct and indirect control modes for each FACTS device are tested and verified with various case studies in different test systems. Graphical interface of PSCAD removes programming burden such as coding or Jacobian matrix modification of NR method due to contributions of shunt/series converters in terms of power injections. Also it contributes to a clear, flexible, and understandable modeling approach but at the expense of PI regulator tuning for each mode. The model is expandable so that the number of converters can be increased with simple modifications to the constraints. Converter losses can be explicitly defined and modeled. The proposed approach is also beneficial for large scale systems if sufficient computing power and large memory are available. 57 3. STEADY-STATE MODELING A. Mete VURAL 58 4. VOLTAGE SOURCE CONVERTER DESIGN 4. VOLTAGE SOURCE CONVERTER DESIGN 4.1. Introduction A. Mete VURAL High power voltage source converter (VSC), developed from the applications of low and medium power levels in industrial applications, is the building block of the second generation FACTS devices having single or multiple converter arrangements (Kazerani et al., 2002), (Tan et al., 2006). VSC can also be regarded as a self-commutating converter, built from power semiconductors having turn-off capabilities, such as GTO, GCT, or IGCT, and has the capability of both consuming and generating reactive power which provides independent and simultaneous control of real and reactive power flows. This property makes VSC superior when compared with the line commutating converter which is only able to consume reactive power from the power system and suffers from commutation failures of conventional thyristors having only turn-on capabilities. VSC based topologies are generally preferred over current source converters for FACTS applications at transmission level due to higher losses and more complicated control (Hingorani et al., 2000), (Kazerani et al., 2002), (Bahrman et al., 2003). Converter-level modeling of the multi-converter FACTS devices requires realistic high power VSC design for dynamic performance analysis and transient stability studies if realistic time domain simulated responses are required to be observed. In converter design, the objective is to minimize switching frequency of the power semiconductors hence minimize losses and to produce high quality quasisinusoidal voltage waveform at transmission level with minimum or no filtering requirements. Multi-pulse converter topology can be preferred over multi-level one when back-to-back operation of two or more VSCs fed from a common DC link is considered. Since DC link voltage control is easy due to a single DC voltage level as opposed to multi-level structures for back-to-back VSCs in multi-converter FACTS device applications (Soto et al., 2002), (Lee et al., 2003). On the other hand, quasi multi-pulse topology can be preferred over true multi-pulse one due to: i) simple 59 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL design with ordinary transformers without employing phase-shifting zig-zag transformers which can bring extra cost when practical aspects are considered (Lee et al., 2003), ii) total harmonic distortion (THD) similar to that of true multi-pulse one (Cavaliere et al., 2002), (Lee et al., 2003). The objective of this chapter is to give design details of high power quasi multi-pulse VSC design for converter-level models of GUPFC, IPFC, and BtBSTATCOM suitable for dynamic performance analysis and transient stability studies. First, basic circuits and operating principles of six-pulse and twelve-pulse converters, which are the basic building blocks of the proposed quasi multi-pulse VSC are discussed and summarized. Next, power circuit design and control scheme of the quasi multi-pulse VSC are given with the details including pulse-generating circuit for the power semiconductors. PSCAD is used to simulate the output voltage waveforms of the converters for evaluation together with their harmonic content. 4.2. Six-pulse VSC 4.2.1. Circuit Configuration Three-phase two-level six-pulse VSC consists of six valves as shown in Figure 4.1. There are three arms having two valves each. Each valve is comprised of turn-off capable power semiconductor, such as GTO, and a reverse-parallel diode. For self-commutating converter operation, each GTO should be turn on and off at controlled time instants to shape AC output voltage from a fixed DC voltage, maintained by a capacitor which is large enough to retain changes in DC current without changes in DC voltage. Diode is used to provide a path for inductive current whenever the GTO in the same valve is turned off. In VSC, DC voltage always has one polarity while the power reversal is achieved by reversal of DC current. Therefore, power semiconductor only requires unidirectional voltage blocking capability. Under constant DC voltage, three-phase output of the six-pulse VSC can be controlled both in magnitude and phase angle, normally accomplished by pulse width 60 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL modulation (PWM) control. There are different PWM methods in literature to reduce harmonic content as much as possible to make AC output voltage resembling a pure sinusoid. Unfortunately high frequency PWM control is considered uneconomical for high power applications due to high switching losses, thus resulting both in decreased conversion efficiency and in bulk cooling equipment. Figure 4.1. Power circuit of three-phase six-pulse VSC 4.2.2. Working Principle To investigate the interaction of six-pulse VSC with the power system, switches S1 and S3 are turned off while S2 is turned on in Figure 4.1. In this case, VSC is able to exchange real and/or reactive power with the three-phase system through interface reactor L according to the four quadrant operation which is presented in Figure 4.2 (Sood, 2004). Often, leakage impedance of the coupling magnetic interface (shunt for STATCOM, series for SSSC) can serve as the inductive impedance with or without L, which electrically separates sinusoidal three-phase system voltages and three-phase voltages of the six-pulse VSC containing harmonics. DC side voltage is kept constant by rectifier and inverter operations which are 61 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL illustrated in Figures 4.2a and 4.2b, respectively. In rectifier operation capacitor is charged by taking real power from the three-phase system. In inverter operation capacitor is discharged by injecting real power into the three-phase system. Reactive power compensation is accomplished by making converter current Iph purely reactive. If Iph leads three-phase system voltage, eAN by 90°, as shown in Figure 4.2c, reactive power is injected into the three-phase system. Alternatively, if Iph lags eAN by 90°, as shown in Figure 4.2d, reactive power is taken from the three-phase system. Vector control of the VSC provides required magnitude and the phase angle of the VSC output voltage in either one of or the combinations of the operations available in four quadrant operation. VSC output voltage is synchronized with the voltage of the three-phase system by a phase lock loop (PLL) to match required phase angle shift. The operation principle and the interaction with the power system is the same for more complicated VSC configurations regardless of the converter topology to meet high voltage/current ratings and to reduce harmonic content which is acceptable for FACTS applications at transmission level. Figure 4.2. Four quadrant VSC operation 62 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL 4.2.3. Analysis of Six-pulse VSC For the sake of clarity and to highlight basic operation, six-pulse VSC is isolated from the three-phase system by turning on switches S1 and S3, and turning off switch S2, shown in Figure 4.1. An external DC voltage source is connected at the DC terminals and a three-phase resistive load RLD is connected at the AC terminals. The circuit is simulated in PSCAD for 4 cycles with Vdc is set to 3.0 kV, C=2000 µF, RLD and Rs is set to 1.0 MΩ and 0.001 Ω, respectively. GTO and diode have turn on/off resistances of 0.005 Ω and 1.0E8 Ω, respectively. Snubber circuit elements are ignored. The simulated phase-to-neutral and phase-to-phase voltage waveforms of six-pulse VSC are shown in Figures 4.3 and 4.4, respectively. Each phase is shifted by ± 120° with respect to other phases for balanced three-phase operation. A simple square-wave switching scheme is applied with a switching frequency of 50 Hz so that each GTO conducts only for 180° or 10 ms duration, as shown in Figure 4.5. This type of switching is called 180-degree conduction in which only three GTOs remain on at any time instant. Figure 4.3. Simulated phase-to-neutral voltage waveforms of six-pulse VSC Fourier series expansion of the phase-to-phase voltage waveform, VAB is given by the equation (4.1) to have an idea about the harmonic content, generated by 63 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL the six- pulse operation in an analytical approach (Dávalos et al., 2005). The voltages VBC and VCA exhibit similar patterns except phase shifts of -120° and +120°, respectively. ∞ nπ   V AB (t ) = ∑ v n sin  nwt +  6  n =1  (4.1) The peak value of nth voltage harmonic component is given in equation (4.2). Noting that n=6r±1, (r=0,1,2,…). Even and triplen harmonics are zero. vn = 4 nπ Vdc cos nπ 6 (4.2) Figure 4.4. Simulated phase-to-phase voltage waveforms of six-pulse VSC Figure 4.6 illustrates dominant harmonics in the harmonic spectrum of phaseto-phase voltage VAB by applying fast Fourier transform in PSCAD where the voltage waveform is broken down into a spectrum of sinusoidal frequencies up to the 61st harmonic. The dominant harmonics have an index of m=6r±1 for six-pulse VSC where r is positive integer (m=5,7,11,13,17,19,…). These significant harmonic components are illustrated in percentage of the fundamental component. 64 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL Figure 4.5. Gating signals of GTOs for 180-degrees conduction Figure 4.6. Harmonic spectrum of VAB for six-pulse VSC 4.3. Twelve-pulse VSC 4.3.1. Circuit Configuration In six-pulse VSC operation, THD is relatively high as a consequence of availability of low order harmonic components (5,7,11,13,…), which are not suitable for high power FACTS applications. One way to decrease the level of harmonics is 65 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL to increase the number of six-pulse units. Twelve-pulse operation can be achieved by summing phase-to-phase voltage of one converter (upper one) with the phase-toneutral voltage of the other converter (lower one) by means of a magnetic interface as shown in Figure 4.7. Figure 4.7. Power circuit of three-phase twelve-pulse VSC To correct inherent phase shift between the phase-to-phase and phase-toneutral voltages, the gating patterns of wye-connected converter should require a phase shift of +30°, or the gating patterns of delta-connected converter should require a phase shift of -30°. Magnetic interface is generally designed either using two three-phase-two-winding transformer banks having a total of twelve windings or six single-phase transformers having a total of twelve windings. However in the proposed design which is shown in Figure 4.7, three single-phase-three-winding transformers are used, having a total of nine windings only. Since phase-to-phase 66 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL voltage is √3 times the phase-to-neutral voltage, turns ratio of delta and wye windings are selected such that the ratio of the secondary side of delta-winding to that of wye-winding becomes √3. 4.3.2. Analysis of Twelve-pulse VSC Phase-to-phase voltage waveforms in Figure 4.8 are obtained by simulating the circuit in Figure 4.1 by replacing six-pulse VSC with twelve-pulse one. Three 25/3 MVA rated (5.0kV/3.0kV/1.732kV) transformers with leakage reactance of j0.1 pu are used. The resultant voltage signal resembles more closely to a perfect sinusoidal waveform than the one obtained from six-pulse operation. Figure 4.8. Simulated phase-to-phase voltage waveforms of twelve-pulse VSC Fourier series expansion of the twelve-pulse waveform of phase-to-phase voltage VAB is given by the equation (4.3) (Dávalos et al., 2005). The voltages VBC and VCA exhibit similar patterns except phase shifts of -120° and +120°, respectively. ∞ nπ   V AB (t ) = ∑ v n sin  nwt +  6  n =1  (4.3) 67 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL The peak value of nth voltage harmonic component is given in equation (4.4). Noting that n=12r±1, (r=0,1,2,…). vn = 8 nπ Vdc cos nπ 6 (4.4) Figure 4.9 illustrates dominant harmonics in the harmonic spectrum of phaseto-phase voltage VAB. The dominant harmonics have an index of m=12r±1 for twelve-pulse VSC where r is positive integer (m=11,13,23,25,35,37…). Although THD is decreased and twelve-pulse arrangement effectively reduces 5th and 7th harmonics, 11th and 13th harmonics still exist which require further process. Figure 4.9. Harmonic spectrum of VAB for twelve-pulse VSC 4.4. Quasi Multi-pulse VSC 4.4.1. Circuit Configuration The proposed quasi multi-pulse VSC is designed using four phase-shifted twelve-pulse converter units (1,2,3,4) that are connected in series in line side and connected in parallel in the DC link side, as shown in Figure 4.10. Based on required 68 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL blocking voltage and peak current ratings, parallel and/or series combinations of GTOs can also be employed for reasons of economy and easy availability of switches with lower ratings (Sun et al., 2004). In this design, only one GTO with a reverseparallel diode per valve is utilized as the switching device to increase simulation speed. For the purpose of VSC control which will be discussed later, the overall circuit is decomposed into two main parts, namely converters M and N, respectively. Phase-A of twelve-pulse converter unit 1 is coupled to the phase-A of twelve-pulse converter unit 2 with a single-phase transformer A1. Similarly, phase-B and phase-C are coupled using transformers B1 and C1, respectively to make a quasi 24-pulse converter (converter M). The second quasi 24-pulse converter (Converter N) is built up using the other twelve-pulse converter units (3-4) and single-phase transformers A2, B2, and C2. Phase-A of converter M and that of converter N are electromagnetically added using transformers A1 and A2, since the primaries are connected in series. In a similar fashion, transformers B1 and B2 are used to sum phase-B of converter M with that of converter N. Transformers C1 and C2 are used to sum phase-C of converter M with that of converter N. Summing and interfacing magnetics also couples VSC output voltage with the transmission level with no requirement to an extra shunt coupling transformer by adjusting the voltage ratings of primaries of A1, A2, B1, B2, C1, C2. Phase shift angle between two adjacent twelve-pulse converters should be 7.5° (Singh et al., 2009). So, 7.5º, 0.0º, -7.5º, and -15º phase shifts are applied to the gating signals of each upper six-pulse converter of twelve-pulse unit 1,3,2,4, correspondingly. This arrangement also satisfies that twelve pulse units 1 and 3 and units 2 and 4 can operate as two independent quasi 24-pulse converters, respectively. On the other hand, gating signals of each lower six-pulse converter of four twelvepulse units are shifted by 30° one by one with respect to each upper side VSC for proper twelve-pulse operation. Figure 4.11 shows only ¼ of the PSCAD implementation of the quasi multi-pulse VSC, which is designed using PSCAD master library components. Figure 4.12 shows PSCAD implementation of two different magnetic interfaces required for quasi multi-pulse operation. 69 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL Figure 4.10. Power circuit configuration of three-phase quasi multi-pulse VSC 70 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL Figure 4.11. PSCAD implementation of ¼ of quasi multi-pulse VSC 71 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL More specifically, Figure 4.12a illustrates the details of the magnetic interface for twelve-pulse operation, which is modeled as a PSCAD default module. Summing and magnetic interface for quasi multi-pulse VSC is presented in Figure 4.12b, which is modeled directly on the main project page of PSCAD. Figure 4.12. PSCAD implementation of magnetic interfaces 4.4.2. Series Coupling Magnetic Interface Power circuit configuration in Figure 4.10 can be used as shunt connection by adjusting the parameters of the summing and magnetic interface, shown in Figure 4.12b. For GUPFC and IPFC, series connection is also required. In this context, a 72 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL series coupling magnetic interface shown in Figure 4.13 can be designed to directly inject three-phase AC voltages of the series VSCs to three-phase transmission line. Figure 4.13. PSCAD implementation of series coupling magnetic interface 4.4.3. Control Scheme for Quasi Multi-pulse VSC Each quasi multi-pulse VSC of the multi-converter FACTS device should be controlled both in magnitude and phase angle to meet the required control objectives. As mentioned before, high frequency PWM methods which can easily control both converter voltage and phase angle are not useful for high power applications due to high switching losses. This type of work is rich in literature in which approximated or simple converter models (six-pulse operation) are employed, not realistic for high power applications. Line frequency switching at 50 Hz or 60 Hz can be preferred alternatively, where each GTO is switched only once per cycle. This brings a difficulty due to the fact that the rms value of the fundamental component of the converter voltage becomes only a function of DC link voltage, which is strictly regulated to a constant value for proper VSC operation. So the only control 73 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL parameter for six-pulse operation and hence quasi multi-pulse VSC, regardless of the FACTS device and the multi-pulse configuration is the phase shift applied to the gate pulse pattern of the GTOs. In order to bring an extra control degree, the “2-angle control” method is adopted from literature (Hagiwara et al., 2003). In this approach, quasi multi-pulse VSC can be controlled both in magnitude and phase angle by appropriate two kinds of phase shifts even GTOs are switched at line frequency. The calculation procedure of these two shift angles are given in the next section. 4.4.3.1. 2-angle Control Method 2-angle control method can be described by the phasor diagram shown in Figure 4.14 (Hagiwara et al., 2003). VM and VN respectively denote output voltage vectors of quasi 24-pulse converters (converters M and N in Figure 4.10), described by the equation (4.5). VX is the resultant summation vector of the quasi multi-pulse VSC comprised of leading converter M and lagging converter N, respectively. Subscript X describes the relevant VSC in the multi-converter FACTS device (sh1,sh2,se1,se2 in Figure 3.2). VS is the reference voltage vector from a selected bus in the power system whose phase angle is measured by a PLL for axis synchronization. Since AC output voltage magnitude of each quasi 24-pulse VSC is equal and constant, the voltage vector VX can only be controlled both in magnitude and phase angle by choosing appropriate phase angles (ΦM, ΦN) using equation (4.6). Figure 4.14. Voltage vectors of converters M and N in rotating reference frame 74 4. VOLTAGE SOURCE CONVERTER DESIGN r  VM = VM ∠φ M = V M ∠(α − δ )°  r  V N = V N ∠φ N = V N ∠ − (α + δ )° (2VF )2 − (VD ref ) 2 α = tan −1 (V ) + (V ) ref 2 D δ = tan −1 ( − VQ ref ref 2 A. Mete VURAL (4.5) ) 2 , Q VQ ref (4.6) VD ref VF = 0.5(VM+VN) is the measured average converter voltage to minimize measurement variations, VDref and VQref are required d-axis (direct axis) and q-axis (quadrature axis) components of VX, computed from control loops of the multiconverter FACTS device, which will be discussed in Chapters 5 and 6. Synchronization with the d-axis is ensured with the following set of relations where θS is the phase angle of the selected bus, measured using PLL. Equations (4.6) and (4.7) are implemented to compute the required phase angles (ΦM, ΦN) for converters M and N in real-time using blocks of continuous system model functions in PSCAD master library, as represented in Figure 4.15. phM = θ S + (α − δ ) phN = θ S − (α + δ ) (4.7) Figure 4.15. PSCAD implementation of equations (4.5) and (4.6) 75 4. VOLTAGE SOURCE CONVERTER DESIGN 4.4.3.2. A. Mete VURAL Pulse-generating Circuit Pulse-generating circuit is used to generate square type waveforms for GTO switching. In PSCAD, logic level one is used to turn on GTO, while logic level zero is used to turn off GTO. PSCAD implementation of the pulse generating scheme for six-pulse VSC is shown in Figure 4.16. Figure 4.16. PSCAD implementation of switching logic for six-pulse VSC In the pulse-generating scheme, 50 Hz or 60 Hz sinusoidal signal with amplitude one is compared with zero. Hence, for the first half-cycle of fundamental frequency the comparator output becomes logic one, and for the second half-cycle the comparator output becomes logic zero. The produced square-wave is phase shift controlled since the phase shift of sinusoidal signal can be externally controlled. One comparator should produce two complementary pulses firing upper and lower GTO of a given arm to prevent short circuit of DC link. In total, three comparators that are ±120° out of phase with each other are needed to produce six pulses for the three-arm 76 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL for balanced three-phase operation. The required number of pulse-generating circuits for each multi-converter FACTS device aimed in this research is listed in Table 4.1. Table 4.1. Number of pulse-generating circuits per multi-converter FACTS device FACTS device Number of VSC Number of GTO IPFC BtB-STATCOM GUPFC 2 2 3 2x6x8=96 2x6x8=96 3x6x8=144 Number of pulse-generating circuit 2x8=16 2x8=16 3x8=24 4.4.4. Analysis of Quasi Multi-pulse VSC 4.4.4.1. Quasi 48-pulse Operation The circuit shown in Figure 4.1 is simulated for a fundamental frequency of 60 Hz by replacing six-pulse VSC with the proposed quasi multi-pulse VSC with the same simulation parameters for six-pulse and twelve-pulse topologies. Summing and magnetic interface in Figure 4.12b is designed using six 16.67 MVA (10.0kV/10.0kV) rated single-phase transformers with a leakage reactance of j0.1 pu each. The primary side is rated at 10 kV for convenience, although is set to higher values generally to couple with high voltage transmission level in FACTS applications. Quasi 48-pulse voltage waveforms are simulated by setting ΦM and ΦN both to zero. Phase-to-neutral and phase-to-phase voltages are presented in Figure 4.17. The resultant voltage signals resembles more closely to a perfect sinusoidal waveform than previously mentioned converter topologies. Figure 4.18 plots harmonic spectrum of phase-to-phase phase-A voltage, plotted in Figure 4.17. Although, 48-pulse operation does not cancel all the harmonics of orders 6n±1 (n=1,2,3,…), their amplitudes are strongly decreased. For example, 11th and 13th order harmonics are effectively reduced when compared with either six-pulse or twelve-pulse topology. As a result, THD is effectively reduced to 3.76 %. Except 11th and 13th order harmonics, dominant harmonics have an index of 77 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL 48r±1 (r=1,2,3,…) almost obtained by true 48-pulse configuration (Lee et al., 2003), (Geethalakshmi et al., 2007). Figure 4.17. Simulated voltage waveforms of quasi 48-pulse VSC Figure 4.18. Harmonic spectrum of VAB for quasi 48-pulse operation Fourier series expansion of true 48-pulse waveform of phase-to-phase voltage VAB can be given by the equation (4.8) for the sake of clarity (Geethalakshmi et al., 2007). The voltages VBC and VCA exhibit similar patterns except phase shifts of -120° and +120°, respectively. ∞ V AB (t ) = ∑ v n sin (nwt + 18.75°n + 11.25°i ) n =1 78 (4.8) 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL The peak value of nth voltage harmonic component is given in equation (4.9). Noting that n=48r±1, (r=0,1,2,…) and i= -1 for n=47,95,… and i=1 for n=49,97,…, respectively. vn = 32 nπ Vdc cos nπ 6 (4.9) Although theoretically possible, the converter topology can become more and more complicated if the pulse numbers above 48 are applied that can be rarely justified in practical applications. It is shown that a quasi 48-pulse VSC is sufficient for 100 MVA STATCOM application (Schauder et al., 1995) and a true 48-pulse topology is designed for 80 MVA SVC (Mori et al., 1993). The proposed quasi multi-pulse VSC is designed such that the AC outputs of two quasi 24-pulse converters are magnetically added, each of which is independently and externally phase shift controlled. On the other hand, four twelvepulse converter units are designed together with appropriate phase shifts to operate as quasi 48-pulse converter if external phase shifts are set to zero. In this sense, at the best case, the proposed VSC can show the harmonic performance of quasi 48-pulse topology and thereby named as “quasi multi-pulse”. In Chapters 5 and 6, the actual THD content of the proposed quasi multi-pulse VSC will be evaluated and compared with the IEEE standards when its shunt/series combinations are utilized in GUPFC, IPFC, and BtB-STATCOM configurations. 4.4.4.2. Verification of 2-angle Control Method 2-angle control method is verified by open-loop control of the quasi multipulse VSC when the phase shifts of quasi-24 pulse converters (ΦM, ΦN) are externally commanded to show how the magnitude and phase angle of VX in Figure 4.14 can be freely controlled. The converter is isolated from the power system as the previous analysis cases and it is connected with a wye-connected resistive load in its AC side and DC side is fed from a constant DC voltage source. The closed-loop 79 4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL control requires the calculation of VDref and VQref from external control loops for each VSC of the multi-converter FACTS device. This situation is thoroughly studied and discussed in detail in Chapters 5 and 6. In the verification procedure, at first the output of the quasi multi-pulse VSC is forced to align on four different quadrants on the graph of polar plot, as shown in Figure 4.19. This case study shows how the phase angle of VX can be controlled in the range between 0° and 360°. Secondly, it is demonstrated how both the magnitude and phase angle of the output of quasi multipulse VSC can be freely controlled using randomly selected simulation results under the condition that the output of each quasi 24-pulse converter is fixed and equal to 7.75 kV. The cases are shown in Figure 4.20. 80 4. VOLTAGE SOURCE CONVERTER DESIGN Voltage VM Voltage VN A. Mete VURAL Voltage VX ΦM (ref)=0.0° ΦN (ref)=0.0° D 7.75677 (kV) -0.1203 (°) D 7.75677 (kV) Voltage VM -0.1203 D 15.5135 (°) (kV) Voltage VN -0.1203 (°) Voltage VX VX in first quadrant ΦM (ref)=90.0° ΦN (ref)=0.0° D 7.74924 (kV) 90.04 (°) D 7.7533 (kV) Voltage VM 0.01782 D 10.9686 (°) (kV) Voltage VN 45.03 (°) Voltage VX VX in second quadrant ΦM (ref)=180.0° ΦN (ref)=90.0° D 7.75677 (kV) 179.9 (°) D 7.74439 (kV) Voltage VM 90.18 D 10.9589 (°) (kV) Voltage VN 135.1 (°) Voltage VX VX in third quadrant ΦM (ref)=270.0° ΦN (ref)=180.0° D 7.74925 (kV) -89.97 (°) D 7.7533 (kV) Voltage VM -180 D 10.9686 (°) (kV) Voltage VN -135.2 (°) Voltage VX VX in fourth quadrant ΦM (ref)=0.0° ΦN (ref)=270.0° D 7.7533 0.0736 (kV) (°) D 7.74925 (kV) -90.12 D 10.9553 (°) (kV) -44.95 (°) Figure 4.19. Four quadrant operation of the proposed quasi multi-pulse VSC 81 4. VOLTAGE SOURCE CONVERTER DESIGN Voltage VM Voltage VN A. Mete VURAL Voltage VX ΦM (ref)=30.0° ΦN (ref)=60.0° D 7.75497 (kV) 30.02 (°) D 7.74879 (kV) Voltage VM 59.89 D 14.9759 (°) (kV) Voltage VN 44.94 (°) Voltage VX ΦM (ref)=174.0° ΦN (ref)=320.0° D 7.74935 (kV) 174 (°) D 7.75164 (kV) Voltage VM -40.17 D 4.61606 (°) (kV) Voltage VN -113.9 (°) Voltage VX ΦM (ref)=190.0° ΦN (ref)=350.0° D 7.75272 (kV) -169.9 (°) D 7.75164 (kV) Voltage VM -10.12 D 2.86963 (°) (kV) Voltage VN -91.23 (°) Voltage VX ΦM (ref)=250.0° ΦN (ref)=12.0° D 7.75174 (kV) -110 (°) D 7.75243 (kV) Voltage VM 12.02 D 7.54778 (°) (kV) Voltage VN -49.05 (°) Voltage VX ΦM (ref)=180.0° ΦN (ref)=0.0° D 7.75331 (kV) -180 (°) D 7.75331 (kV) D 0.01782 8.75729e-... (°) (kV) 0 (°) Figure 4.20. Flexible magnitude/phase angle controlled quasi multi-pulse VSC 82 4. VOLTAGE SOURCE CONVERTER DESIGN 4.5. A. Mete VURAL Summary A realistic and high power quasi multi-pulse VSC for multi-converter FACTS devices is proposed and designed with given all details down to the GTO level, including magnetic interface and control scheme. First, working principles of elementary two-level six-pulse and twelve-pulse converter topologies are discussed. Later on, quasi multi-pulse VSC is designed using four twelve-pulse converter units which is more accurate than existing low-order or average models. Line frequency switching scheme is applied to minimize converter losses and voltage/current stresses on each GTO valve are fairly decreased using multi-converter structure. 2angle control method is adapted from literature to gain an extra control degree to the proposed VSC without changing the magnitude of the DC link voltage. Harmonic content is quantitatively evaluated in terms of individual harmonic voltages and THD. Power and voltage rating are flexible so that quasi multi-pulse VSC can be simulated with regard to different operating requirements. For the next two chapters, the designed quasi multi-pulse converter topology will be used as the building element for GUPFC, IPFC, and BtB-STATCOM where the test and the verification of the model will be done digitally in PSCAD in one sense. 83 4. VOLTAGE SOURCE CONVERTER DESIGN 84 A. Mete VURAL 5. DYNAMIC MODELING STUDIES A. Mete VURAL 5. DYNAMIC MODELING STUDIES 5.1. Introduction Dynamic modeling of the multi-converter FACTS devices aims to investigate the instantaneous time-domain responses of these devices when controlling one or more power system parameters. Generally, regardless of the FACTS device type and application, dynamic modeling is divided into two main categories: “average model” and “converter-level model”. In average modeling approach, the converter dynamics are represented using linear time-domain differential equations in dq synchronous rotating frame. In this modeling approach, discrete-time nature of converter switching and the effects of harmonics are neglected. Converter output voltage is usually described by the expression which is the function of a constant multiplication factor (usually modulation index of PWM method), an angle (required phase shift of converter voltage), and a conceptual DC link voltage. Modulation index and phase shift of each converter are the two control inputs of each VSC of the FACTS device to perform the given control task where the DC link dynamics are generally modeled as a power balance equation in terms of dq components of voltage and current. In this regard, IPFC is modeled using a set of linearized differential equations in rotating dq frame (Menniti et al., 2002), (Moghadam et al., 2010), (Moghadam et al., 2011), (Ajami et al., 2009). Voltage source representing each VSC of IPFC is controlled by a duty-cycle vector which is applied to conceptual DC link voltage to approximate converter switching (Strzelecki, et al., 2005). In converter-level modeling approach, the studies are varied according to converter structures. For example, each VSC of IPFC is modeled as PWM triggered two-level six-pulse converter with a DC voltage source which approximates DC link (Ye et al., 2006), with a DC link capacitor (Muruganandham, et al., 2012). Each VSC of IPFC is modeled using three-level twelve-valve neutral-point-clamped converter having two DC capacitors (Karthik, 2007). Switching frequencies are in the range between 1-2 kHz. 48-pulse VSC consisting of four three-level converters is used in IPFC configuration, with line real and reactive power flow control (Aali, et al., 85 5. DYNAMIC MODELING STUDIES A. Mete VURAL 2010), with only bus voltage control (Bharathi et al., 2011). IPFC based on multioutput sparse matrix converter switching at relatively high frequency of 10 kHz is modeled (Hosseini et al., 2011). Dynamic modeling studies of GUPFC are rather limited in literature when compared with IPFC based studies although there are plenty of UPFC based dynamic studies. For instance, average converter models are used for each VSC of GUPFC (Lubis 2011a). Alternatively in average modeling approach, the controlled voltage source representing each VSC of GUPFC is embedded into the power system model directly and the simulation engine iteratively solves the system equations (Fardanesh et al., 2000), (Sun et al., 2003). Converter-level modeling studies of GUPFC have recently been published. Elementary two-level six-pulse converter topology is the most common power circuit scheme (Prakash et al., 2007), (Sujin et al., 2012), (Abdul et al., 2012). Sixty-pulse converter model of GUPFC comprised of five three-phase three-level converters and five phase-shifting transformers are presented (Lubis 2011b). Dynamic modeling of BtB-STATCOM is approximated using average modeling approach where each output of VSC is modeled as controllable ideal voltage source (Tyagi et al., 2006), (Xinghao et al., 2009), (Lee et al., 2011), (Parkhideh et al., 2009). On the other hand, converter-level models of BtBSTATCOM are more detailed. For instance, two elementary two-level six-pulse converters are used in BtB-STATCOM configuration (Ruihua et al., 2005), (Jovcic et al., 2007), (Liu et al., 2010). Converter structure is pretty simple that does not reflect realistic BtB-STATCOM operation completely. More detailed converter topologies are alternatively considered. For instance quasi multi-pulse converter topology consisting of sixteen six-pulse units are combined to build each VSC of BtBSTATCOM (Hagiwara et al., 2003). The BtB system consists of two sets of four three-phase neutral-point-clamped converter units each having twelve GTOs driven by PWM (Hagiwara et al., 2005), (Hagiwara et al., 2008). 24-pulse three-level voltage source converters with fundamental frequency switching for HVDC system is proposed (Madhan Mohan, et al., 2009). 86 5. DYNAMIC MODELING STUDIES 5.2. A. Mete VURAL Simplex Optimization Method Due to nonlinear nature of converter switching and the interactions among the controllers of the multi-converter FACTS device, finding optimum parameters of the control scheme while satisfying stable operation of the multi-converter FACTS device is not an easy task. It is presented that the inherent dynamic interactions between individual controllers of the UPFC can lead to unstable operation even though each controller of UPFC itself is designed satisfactorily (Wang et al., 2000). For a GUPFC, the situation can become desperately as more control functions are attributed to GUPFC. One solution depends on analytical approaches such as zieglernichols oscillation method, smith predictor, and pole assignment methods, which require exact mathematical model of the system which is difficult to obtain without simplification or averaging (Goodwin et al., 2000). Another solution may suffer from the long computing time to find the optimum parameters where several simulation runs exist to select the best parameters (PSCAD, 2005). Alternatively, a direct search algorithm, which is called “simplex method”, is used in this research (Neider et al., 1965) that is integrated into the PSCAD (Gole et al., 2005). This method does not rely on gradient information and applicable for highly-nonlinear multi-input multioutput systems without obtaining mathematical models and hence suitable for finding the minimum of an objective or a cost function defined by several variables. In this research, simplex method is executed not only to find the optimum multicontroller parameters but also to find the best parameters for a specific designed component in PSCAD. Simplex is the name of a geometric figure whose vertices are defined by variable numbers. For example, for two-variable optimization, simplex is a triangle, for three-variable optimization, simplex is a tetrahedron. The problem becomes a pattern search that compares function values at all vertices. The worst vertex, where the cost function is the largest, is rejected and replaced by a new vertex. A new simplex is formed until the function values at the vertices are the smallest. Simplex size is then reduced iteratively and the coordinates of the minimum point are found. The flow chart of the simplex optimization method is shown in Figure 5.1. 87 5. DYNAMIC MODELING STUDIES Set initial parameter set Start Update parameter set A. Mete VURAL No Convergence ? Evaluate objective function by simulating power system embedded with FACTS device Execute simplex algorithm Yes Output parameter set in a file End Figure 5.1. Flow chart of the simplex optimization method in PSCAD 5.3. Converter-Level Modeling of GUPFC 5.3.1. GUPFC Interacting with Power System Three quasi multi-pulse VSCs based GUPFC is positioned on WSCC 3Machine 9-Bus System as shown in Figure 5.2. It is aimed to control five power system parameters simultaneously. These are real and reactive power flows of lines L-45 and those of L-46, and Bus 4 voltage. GUPFC is in operation while switch, sw1 is closed, and switches, sw2-3 are opened. The AC terminal of shunt VSC (VSC1) is connected to the Bus 4 through a magnetic interface which is conceptually drawn and named as “tr1”. Similarly, the AC terminals of series VSCs (VSC2-3) are connected to the neighboring transmission lines, namely, L-45 and L-46 through magnetic interfaces, named as “tr2-3”. The DC terminals of each VSC are joined in a DC link, which is represented by a capacitor C (0.2 F), provides real power exchange between the three VSCs. Each VSC of GUPFC is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 60 Hz, 8.33 MVA, 20/2/1.154 kV with a leakage reactance of j0.025 pu. Each single-phase transformer of summing and magnetic interface is rated at 60 Hz, 16.67 MVA, 137.92/38 kV, j0.1 pu for 88 5. DYNAMIC MODELING STUDIES A. Mete VURAL shunt VSC. For series VSC, the rating is modified as 36/36 kV, j0.025 pu. Each single-phase transformer of series coupling magnetic interface is rated at 60 Hz, 33.33 MVA, 104.13/40 kV, j0.01 pu. Figure 5.2. WSCC 3-Machine 9-Bus System embedded with GUPFC 5.3.2. GUPFC Controller Design The control of the quasi multi-pulse VSC depends on the decomposition of the converter voltage into its d- and q-axis components as mentioned in Chapter 4. In this regard, control loops of GUPFC are designed as in Figure 5.3. Once the reference value of each controlled power system parameter is decided, an error signal is generated by comparing the reference value with the actual or measured value of the controlled variable. The error signal is then used as an input to the PI controller to 89 5. DYNAMIC MODELING STUDIES A. Mete VURAL determine the required axis components of shunt and series converter voltages. The control loops are designed according to the fact that the quadrature component (qaxis) of the series injected voltage mainly controls real power flow, while the direct component (d-axis) of the series injected voltage controls reactive power flow (Ye et al., 2006), (Mishra, 2006), (Liming et al., 2007), (Xia et al., 2010). Since GUPFC’s losses are met by VSC1, the shunt converter control is the DC link voltage control, E and the voltage magnitude control of Bus 4, V4, achieved by VshD (Figure 5.3a) and VshQ (Figure 5.3b), respectively. On the other hand, series VSC2 controls real and reactive power flows of Line L-45, achieved by Vse2Q (Figure 5.3c) and Vse2D (Figure 5.3d), respectively. Series VSC3 controls real and reactive power flows of Line L-46, achieved by Vse3Q (Figure 5.3e) and Vse3D (Figure 5.3f), respectively. A total of twelve parameters of GUPFC’s control scheme (6xproportional gain, Kp and 6xintegration time constant τi) is optimized using simplex method to alleviate controller interaction. Figure 5.3. Control loops of GUPFC 90 5. DYNAMIC MODELING STUDIES A. Mete VURAL 5.3.3. Finding Optimum Controller Parameters Optimal parameter set of GUPFC’s controllers given in equation (5.1) is investigated iteratively by minimizing the cost function described in equation (5.2). The derived cost function is based on the sum of integral square error (ISE) of individual controllers. The PSCAD configuration for this task is shown in Figure 5.4. { p = K p1 , τ i1 , K p 2 , τ i 2 , K p 3 , τ i 3, K p 4 , τ i 4 , K p 5 , τ i 5 , K p 6 , τ i 6 T ( F ( p ) = ∫ (V 4 ref − V 4 ) 2 + ( E ref − E ) 2 + (Q 45 t =0 ref } (5.1) − Q45 ) 2 + ... ) ... + ( P45 ref − P45 ) 2 + (Q46 ref − Q46 ) 2 + ( P46 ref − P46 ) 2 dt (5.2) The total simulation time T in equation (5.2) is chosen much longer than the settling time of the whole control system. Reference values of real and reactive power flows are chosen same as in case 1 in the next section. F(p) is plotted against iteration number in Figure 5.5 and the optimum parameters are listed in Table 5.1. The algorithm is converged in 504 iterations for a tolerance of 1.0E-6. Due to interaction between converters, the individual converter design is not preferred and only one cost function is identified to obtain stable and reasonably dynamic performance. 91 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.4. PSCAD implementation of simplex method 92 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.5. Convergence performance of cost function in simplex method Table 5.1. Simplex optimized controller parameters of GUPFC DC voltage controller initial parameters optimized parameters Kp1 Ti1 0.800000 0.010000 39.159948 Reactive power Kp3 flow controller initial parameters optimized parameters 0.100000 15.227331 Reactive power Kp5 flow controller initial parameters optimized parameters Shunt VSC1 AC voltage controller Kp2 initial 0.800000 parameters optimized 0.007580 15.240716 parameters Series VSC2 Real power Ti3 Kp4 flow controller initial 0.100000 parameters optimized 0.001005 0.795768 parameters Series VSC3 Real power Ti5 Kp6 flow controller 0.001000 0.100000 0.001000 14.966115 0.001010 initial parameters optimized parameters Ti2 0.010000 0.000988 Ti4 0.001000 0.001003 Ti6 0.200000 0.001000 29.389397 0.001006 5.3.4. Simulation Studies PSCAD environment is used to simulate the multi-machine power system embedded with GUPFC as shown in Figure 5.2. The following case studies are undertaken for evaluating the dynamic performance of the proposed GUPFC in controlling real and reactive power flows of the lines along with bus voltage control 93 5. DYNAMIC MODELING STUDIES A. Mete VURAL and under two types of faults. The simplex optimized controller parameters listed in Table 5.1 are used in the simulations and the nominal DC link voltage of the GUPFC is controlled at 2.0 kV throughout all simulation cases. Solution time-step is set to 100 µs in PSCAD. 5.3.4.1. Case 1: Start-up Transients The start-up transients of the GUPFC are investigated when it is commanded to increase L-45 real power flow from 0.7983 pu (uncompensated flow) to 1.0 pu (20% increase) and L-46 real power flow from 0.5349 pu (uncompensated flow) to 0.74 pu (28% increase) at t=0+. At the same time, GUPFC holds both of the reactive power flows of L-45 and L-46 at zero. Note that the uncompensated reactive power flows of the lines are j0.1548 pu and j0.0573 pu, respectively. The simulation results for this case study are shown in Figures 5.6a-l. No overshoot is observed in the tracking signals of the real power flows in Figures 5.6a and 5.6c. P45 and P46 come to their desired values with no steady-state error within around 1.0 s, respectively. The maximum overshot/undershoot with the PI controllers for Q45 and Q46 is about 30% (Figures 5.6b and 5.6d). The DC link voltage is a very important factor for successful operation of shunt and series converters of GUPFC. On account of this, E is tightly regulated at 2.0 kV (Figure 5.6e). Actual DC link voltage settles on the 2.0 kV line within 1.0 s. Figure 5.6f shows the response of the power system to a step change in V4 reference at 1.0 pu based on 230 kV transmission level. Note that the uncompensated magnitude of V4 is 0.9828 pu and it is regulated by the shunt converter of the GUPFC with no overshoot and with a reasonable transient performance. The tracking performances of all individual power system parameters are stable in this case study. The settling times of the control loops are generally in the order of 1.0 s due to the fact that the time constant of the power system with the GUPFC is relatively large. 94 5. DYNAMIC MODELING STUDIES A. Mete VURAL (a) Real power flow control of Line L-45 at start-up (b) Reactive power flow control of Line L-45 at start-up (c) Real power flow control of Line L-46 at start-up (d) Reactive power flow control of Line L-46 at start-up 95 5. DYNAMIC MODELING STUDIES A. Mete VURAL (e) DC link voltage control of GUPFC at start-up (f) Bus 4 voltage control at start-up (g) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) during start-up (h) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) during start-up 96 5. DYNAMIC MODELING STUDIES A. Mete VURAL (i) Phase shifts for converters M and N of VSC3 (ΦM and ΦN) during start-up (j) Series inserted voltage by VSC2 during start-up (k) Series inserted voltage by VSC3 during start-up (l) GTO anode to cathode voltage of VSC1 during start-up Figure 5.6. Simulated waveforms of case 1 5.3.4.2. Case 2: Response to Real Power Flow Step Changes Real power flow references for both lines (L-45, L-46) are decreased from 1.0 pu to 0.85 pu and from 0.74 pu to 0.60 pu at 10.5 s, simultaneously. The other references of GUPFC control loops are kept unchanged as in case 1. Figures 5.7a-f 97 5. DYNAMIC MODELING STUDIES A. Mete VURAL show the traces of real and reactive power flows of Line L-45 and L-46, GUPFC DC link voltage, and V4, respectively. Real power traces reach to their reference values within about 0.5 s after the step change command is applied with no steady-state error. The transmission line reactive power flows stay constant as zero after following a 6 % undershoot and 10 % overshoot in Q45 and Q46, respectively. PI controller could keep GUPFC DC link voltage in its reference so that the trace has almost no change towards step change command to real power flows. The response of V4 after the step change command in real power flow references is almost constant on 1.0 pu line. PI control scheme for each control loop in this case study exhibits stable performance. (a) Real power flow of Line L-45 for a step-change at 10.5 s (b) Reactive power flow of Line L-45 in response to step-changes 98 5. DYNAMIC MODELING STUDIES A. Mete VURAL (c) Real power flow of Line L-46 for a step-change at 10.5 s (d) Reactive power flow of Line L-46 in response to step-changes (e) Bus 4 line-to-line rms voltage voltage in response to step-changes (f) DC link voltage of GUPFC in response to step-changes Figure 5.7. Simulated waveforms of case 2 99 5. DYNAMIC MODELING STUDIES 5.3.4.3. A. Mete VURAL Case 3: Response to Reactive Power Flow Step Changes In this case, at 10.5 s, reactive power flow references for Line L-45 and L-46 are changed from 0.0 pu to -0.15 pu and from 0.0 pu to -0.10 pu, simultaneously. The other references in GUPFC control loops are kept constant as in case 1. Figures 5.8af show the traces of real and reactive power flows of Line L-45 and L-46, GUPFC DC link voltage, and V4, respectively. When comparing cases 2 and 3 by examining Figures 5.7a and 5.8b, the settling time of the reactive power control loop is about 0.5 s longer than that of real power control loop. The same amount of delay in the response of reactive power control loop in Figure 5.7c is also observed when compared with the response of real power control loop in Figure 5.8d. The real power flow controllers response to the step change command of reactive power flows with a 7% and 2.6 % overshoot, respectively. After following these transients, GUPFC could bring real and reactive power flows to their desired values with no steady-state error. GUPFC DC link voltage is controlled tightly so that the trace has almost no change towards step change command to reactive power flows. When comparing Figures 5.7f and 5.8f, the response of V4 after the step change in reactive power flow reference is more ludic than the case after the step change in real power flow reference. The sluggish response of GUPFC is due to the fact that voltage magnitude is sensitive to reactive power. (a) Real power flow of Line L-45 in response to step-changes 100 5. DYNAMIC MODELING STUDIES A. Mete VURAL (b) Reactive power flow control of Line L-45 for a step-change at 10.5 s (c) Real power flow of Line L-46 in response to step-changes (d) Reactive power flow control of Line L-46 for a step-change at 10.5 s e) Bus 4 line-to-line rms voltage in response to step-changes of reactive power flows 101 5. DYNAMIC MODELING STUDIES A. Mete VURAL f) DC link voltage of GUPFC in response to step-changes of reactive power flows Figure 5.8. Simulated waveforms of case 3 5.3.4.4. Case 4: Single-phase to Ground Fault The dynamic performance of the GUPFC is evaluated by applying phase-A to ground fault at Bus 8 (Figure 5.2) at 10.5 s for 100 ms through an impedance of j0.285 pu and cleared without any change in the network configuration. Probability of realization of such a disturbance is high as the ratio of single-phase to ground faults is about 80-81 % of fault types (Heine et al., 2003), (Bordalo et al., 2006). The reference values of real and reactive power flows of Line L-45 and L-46 along with V4 are controlled by GUPFC as in case 1. Figures 5.9a-f show comparative simulated responses to the fault. In Figures 5.9a and 5.9b, the real and reactive power flows on Line L-45 return to their controlled values within 1.0 s after the fault is applied with and overshoot of about 10% and undershoot of about 5%. In Figure 5.9c, even real power flow response of Line L-46 is more ludic than that of Line L-45, it shows less oscillation and comes to its controlled value within 1.5 s. Reactive power flow on Line L-46 has similar overshoot transients compared with the one on Line L-45, but having smaller settling time. For fault condition, V4 drops to not greater than 2% of its nominal value and shows a transient increase, not greater than 1% of its nominal value. The disturbance lasts for 0.5 s. GUPFC DC link voltage oscillation is not sustained following after the fault and the test system with GUPFC survive through the fault and returns to stability smoothly in maximum 1.5 s in this case study. 102 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figures 5.9g-l also show the simulated voltage and current waveforms of the GUPFC converters under single-phase to ground fault condition. (a) Line L-45 real power flow response to phase-A to ground fault at 10.5 s (b) Line L-45 reactive power flow response to phase-A to ground fault at 10.5 s (c) Line L-46 real power flow response to phase-A to ground fault at 10.5 s 103 5. DYNAMIC MODELING STUDIES A. Mete VURAL (d) Line L-46 reactive power flow response to phase-A to ground fault at 10.5 s (e) Bus 4 line-to-line rms voltage response to phase-A to ground fault at 10.5 s (f) GUPFC DC link voltage response to phase-A to ground fault at 10.5 s (g) VSC1 injected voltage (shunt) 104 5. DYNAMIC MODELING STUDIES A. Mete VURAL (h) VSC1 injected current (shunt) (i) VSC2 injected voltage (primary side of series coupling transformer) (j) VSC2 injected current (primary side of series coupling transformer) (k) VSC3 injected voltage (primary side of series coupling transformer) (l) VSC3 injected current (primary side of series coupling transformer) Figure 5.9. Simulated waveforms of case 4 105 5. DYNAMIC MODELING STUDIES 5.3.4.5. A. Mete VURAL Case 5: Three-phase to Ground Fault A three-phase to ground fault with a duration of 100 ms is applied at Bus 9 (Figure 5.2) through an impedance of j0.285 pu at time 10.5 s. This disturbance is the most severe disturbance with an occurrence probability of 1.5-3.0 % (Heine et al., 2003), (Bordalo et al., 2006). The reference values of real and reactive power flows of Line L-45 and Line L-46 along with V4 are controlled by GUPFC as in case 1. Figures 5.10a-f show comparative simulated responses to the short circuit. Real power flows on Line L-45 and L-46 are severely disturbed since their overshoot magnitude is two times bigger than the cases in previous fault. But GUPFC retrieves the flows to their controlled values in around 1.0 s. The waveforms in Figures 5.10b and 5.10d indicate that for the same fault duration with the previous case, reactive power flows on Line L-45 and L-46 result in more oscillation within approximately same recovery time without losing stability. The transient in V4 during the disturbance occurs between around 0.95 pu and 1.025 pu which is few wider than in previous case due to influential fault. Combining cases 4 and 5, the voltage excursions in DC link are avoided which is essential for the successful GUPFC operation. Eventually it can be deduced that the GUPFC is able to mitigate the two fault types within 1.0-1.5 s without losing stability. (a) Line L-45 real power flow response to three-phase short circuit at 10.5 s 106 5. DYNAMIC MODELING STUDIES A. Mete VURAL (b) Line L-45 reactive power flow response to three-phase short circuit at 10.5 s (c) Line L-46 real power flow response to three-phase short circuit at 10.5 s (d) Line L-46 reactive power flow response to three-phase short circuit at 10.5 s (e) Bus 4 line-to-line rms voltage response to three-phase short circuit at 10.5 s 107 5. DYNAMIC MODELING STUDIES A. Mete VURAL (f) GUPFC DC link voltage response to three-phase short circuit at 10.5 s Figure 5.10. Simulated waveforms of case 5 5.3.4.6. THD Content Table 5.2 lists the average recorded THD values of the voltages measured from three common coupling points (Buses 4-5-6) between GUPFC and the power system when GUPFC is commanded to control real and reactive power flows of lines L-45 and L-46 with the reference values given in case 1. Records of the simulation run lasting for 12.5 s show that GUPFC switching at fundamental frequency of 60 Hz does not cause the violation of the THD upper limit for 230 kV transmission level (IEEE, 1993). It is seen that voltage distortions at common coupling points are within the acceptable limits. Consequently, filtering is not required even GTOs are switching at fundamental system frequency. Table 5.2. THD values Common coupling point Bus 4 Bus 5 Bus 6 THD (%) 1.50 0.52 0.43 5.3.5. Discussion GUPFC is built using two series and one shunt quasi multi-pulse VSC designed in Chapter 4. GUPFC dynamic performance on the control of real and reactive power flows of two neighboring transmission lines and bus voltage control is evaluated through different simulation scenarios including faults on WSCC 3- 108 5. DYNAMIC MODELING STUDIES A. Mete VURAL Machine 9-Bus System. The robustness of the GUPFC controllers is ensured by tuning of controller parameters using simplex method which does not rely on mathematical model of the system. It is concluded that conventional PI controllers are stable and yet practically applicable. This study verifies the control scheme of the quasi multi-pulse VSC mentioned in Chapter 4 in one respect. It is also noted that the quasi multi-pulse VSCs do not inject any harmonics with no more than THD=1.5%, which complies with the IEEE regulations. In this regard, high switching frequency or filter circuit is not required. 5.4. Converter-Level Modeling of IPFC 5.4.1. IPFC Interacting with Power System Two quasi multi-pulse VSCs based IPFC is located on 4-Machine 4-Bus System as shown in Figure 5.11 whose data are given in Appendix B. A total of three power system parameters are aimed to control simultaneously in this simulation configuration. These are real and reactive power flows of Line-2 and real power flow of Line-1. IPFC is activated while switches sw1 and sw2 are opened. The AC terminal of VSC1 and that of VSC2 are connected to two neighboring transmission lines (Lines 1 and 2) through magnetic interfaces, named as “tr1-2”, respectively. The DC terminals of each VSC are joined in a DC link, which is represented by capacitor C (0.2 F), provides real power exchange between the two VSCs. Each VSC of IPFC is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 50 Hz, 8.33 MVA, 10/1/0.5774 kV with a leakage reactance of j0.1 pu. Each single-phase transformer of summing and magnetic interface is rated at 50 Hz, 16.67 MVA, 23.42/23.42 kV, j0.1 pu. Each single-phase transformer of series coupling magnetic interface is rated at 50 Hz, 33.33 MVA, 23.42/9.0 kV, j0.01 pu. 109 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.11. 4-Machine 4-Bus System embedded with IPFC 5.4.2. IPFC Controller Design The dynamic performance of IPFC suffers from the strong dynamic interaction between real and reactive power flows due to inherent properties of AC power transmission. To reduce or eliminate this coupling effect, a number of studies on other members of FACTS devices are available in literature. It is realized that these studies rely on decoupling parameters of approximated FACTS device model or converterlevel model of elementary six-pulse VSCs driven by high frequency PWM methods, which is not realistic for high power applications. Firstly, a d-q current controller is proposed with no-cross coupling for a grid connected inverter (Schauder, 1991). Later on a new control scheme originated from this controller in which a decoupled controller with an internal predictive loop for UPFC is suggested (Papic et al., 1997). In the proposed control scheme, the parameters of reactance of series coupling transformer and system bandwidth are required for gain design. Other articles propose different types of decoupled controllers for non-converter-level model of UPFC where an equivalent ideal voltage source model of UPFC is considered with no harmonics (Yu et al., 1996), (Yam et al., 2002), (Papic et al., 2003), (Ye et al., 2006), (Farahani et al., 2006), (Ande et al., 2007), (Ma, 2007). A decoupling controller is designed, but 110 5. DYNAMIC MODELING STUDIES A. Mete VURAL control performance counts on exact system parameters and UPFC model (Yu et al., 1996). A dynamic decoupled compensator for UPFC is designed (Yam et al., 2002). The design relies on classical control design techniques which rely on exact mathematical model of the system, damping ratio and system bandwidth should also be exactly known. A decoupling matrix compensator consisting of four controllers is developed that relies on ABCD parameters of approximated UPFC model (Farahani et al., 2006). A decoupled UPFC controller for dynamic control of real and reactive power flows is considered (Ande et al., 2007). UPFC is experimentally validated by six-pulse VSCs where PWM control is used (Liming et al., 2005). To achieve decoupling, reactance values of shunt and series coupling transformers should be exactly known. In this research, the decoupling effect between real and reactive power flow control loops is reduced by a new hybrid fuzzy PI (HFPI) control scheme applied to IPFC. The proposed controller is based on conventional simplex optimized PI controller operating in conjunction with Mamdani-type fuzzy inference system with linearly distributed linguistic rules. With this way, a fast response is obtained with minimal interaction to track the changes in reference values of the real and reactive power flows. Design phase neither requires exact mathematical description nor system transfer function. The performance of the proposed HFPI controller is compared with both conventional PI control and PI control with analytically computed feed-forward decoupled gains. 5.4.2.1. Decoupled Controller Design Assuming series resistance and inductance of tr1 in Figure 5.11 are included into the transmission line parameters RL and XL, respectively. Then, the current on Line-1, IL can be derived as IL = VS − V R − V X R L + jX L (5.3) 111 5. DYNAMIC MODELING STUDIES A. Mete VURAL where VX is line-to-neutral rms voltage phasor of series injected voltage which is synthesizes by VSC1, VS and VR are the line-to-neutral rms voltage phasors of the sending-end and receiving-end sides, respectively. Complex power at the sending-end side is S s = Ps + jQs = 3VS I L * (5.4) where symbol (*) denotes complex conjugate and PS and QS denote sending-end real and reactive power flows on Line-1, respectively. Assuming VR leads VS by a small angle δ (cos δ≈1, sinδ≈0), PS and QS can be expressed as  Ps  RL 2 + X L 2  VQ  RL  Qs − Qs 0   Ps 0  A = Q   − V  + X − P + P  + Q  X L2  s s s0   D  s0  L  (5.5) where A=3VS/(RL+XL), VD and VQ are the d- and q-axis components of VX in rotating reference frame, respectively (VX=VD+jVQ). PS0 and QS0 are the uncompensated real and reactive power flows when there is no compensation (VD=VQ=0). In equation (5.5), real and reactive power flows are naturally coupled and needs to be decoupled for efficient dynamic power flow control. Taking first-derivative of equation (5.5) with respect to time yields equation (5.6). Assuming PS0 and QS0 are at certain values and VS is regulated at a constant value. d dt  PS  RL 2 + X L 2 d  VQ  RL d = A + Q  dt − VD  X L dt X L2  S  QS  − P   S (5.6) The derivative terms in equation (5.6) can be approximated using forward difference operator with a small time Δt as represented below: 1 ∆t  ∆PS  RL 2 + X L 2 = A ∆Q  ∆tX L 2  S  ∆VQ  RL  − ∆V  + ∆tX  D L 112  ∆QS  − ∆P   S (5.7) 5. DYNAMIC MODELING STUDIES A. Mete VURAL where df/dt≈Δf/Δt with Δf=f(t+Δt)˗f(t) (Levy et al., 2011). According to equation (5.7), the required changes in PS and QS are respectively related to VQ and VD. This result also confirms the GUPFC’s controllers design, given in Section 5.3.2. The last summing terms are the coupling terms and can vanish if the following feed-forward gains are added to the conventional PI control scheme once the reference of power flows (PSref and QSref) are externally defined by the user or supervisory control. VQ ref = K p1 ( PS ref − PS ) + R 1 ( PS ref − PS )dt − L Q S ∫ Ti1 XL − VD ref = K p 2 (QS ref − QS ) + 1 R (QS ref − QS )dt + L PS ∫ Ti 2 XL (5.8) where VQref and VDref denote desired d-q components of series converter voltage. PS and QS are respectively the current values of real and reactive power flows measured at time t. Kp1 and Kp2 are the proportional gains of real and reactive power flow controllers, respectively. Ti1 and Ti2 are the integration time constants of real and reactive power flow controllers, respectively. In this case, the control scheme mentioned so far is regarded as PI control with decoupled gains (PI+DG). PSCAD implementation of PI+DG control scheme is shown in Figure 5.12. Noting that if RL/XL ratios are set to zero or port A of sum blocks are disabled then the control scheme simply becomes PI control. Figure 5.12. PSCAD implementation of PI+DG controllers 113 5. DYNAMIC MODELING STUDIES 5.4.2.2. A. Mete VURAL Proposed Hybrid Fuzzy PI (HFPI) Controller In previous section, decoupling gain design is made analytically under some assumptions in system model. Moreover the dynamic performance of PI+DG relies on exact knowledge of RL and XL which can change due to environmental factors. In this regard, a HFPI controller is designed in support to PI controllers as shown in Figure 5.13. The supplementary signals (delVd and delVq) are generated by a Mamdani-type fuzzy inference system in MATLAB fuzzy logic toolbox and called “fuzzy decoupler” (FUDE), which is realized using heuristic information based on coupling characteristics. It is aimed that the power flow controller adapts itself based on instantaneous system states rather than off-line system parameters which are substantially liable to changes during real-life operation. FUDE which is designed in MATLAB communicates online with PSCAD in real-time. For this purpose, a module is prepared in PSCAD to link the MATLAB as shown in Figure 5.14. PSCAD communicates with a MATLAB m-file through FORTRAN scripts written in that module. All related codes are presented in Appendix E. PSCAD and MATLAB exchange information at every time step in a continuous manner. Figure 5.13. PSCAD implementation of HFPI controller 114 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.14. PSCAD-MATLAB interface FUDE is activated by a set-point change detector (SEPOCHDET) when the first set-point change either in PS or QS occurs. In this sense, SEPOCHDET shown in Figure 5.15 keeps the advantage of executing simple PI controllers during start-up. First derivatives of PSref and QSref are absolute valued and sent to a monostable multivibrator which is a binary-logic, edge-triggered PSCAD component. A positive edge on its input results in the output going high and remaining high for the rest of the simulation after being turned on. Consequently, SEPOCHDET produces the signal “defico” as logic one to connect the outputs of FUDE to the PI controllers to reduce interaction between real and reactive power flow controllers during set-point changes. Figure 5.15. PSCAD implementation of SEPOCHDET 115 5. DYNAMIC MODELING STUDIES 5.4.2.3. A. Mete VURAL FUDE Design The system response is examined for sequences of set-point changes when only PI controllers with optimum parameters are employed. For example, if QS hugely deviates from its set-point while PSref is decreased sharply, a large control signal ΔVD that pulls it toward to its set-point is expected. Similarly, when QSref is suddenly increased, PS tends to decrease and a large control signal ΔVQ is required. As a first step, x(k) is defined as the input set of crisp numerical signals of Pe, ΔPe, Qe, ΔQe at sampling instant k, limited to its universe of discourse. Pe and Qe are the real and reactive power flow errors, ΔPe and ΔQe are the real and reactive power flow error rates, respectively. x(k) is then fuzzified according to seven linguistic characteristics, defined for its each element. Abbreviations in Figure 5.16 for the membership functions (MFs) that quantify the meaning of linguistic characteristics are the following: N3: big negative, N2: medium negative, N1: small negative, Z: zero, P1: small positive, P2: medium positive, and P3: big positive. Intersection point M is specific for each member in x(k). Figure 5.16. Universe of Discourse Output set y(k) also needs fuzzification at the sampling instant k using membership function (MF) set for ΔVQ and ΔVD depicted in Figure 5.17. Intersection point N is specific for each member in y(k). 116 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.17. MFs for FUDE output set Rule base for output ΔVQ is listed in Table 5.3 which is identical to that of ΔVD, but designed for ΔQe/Qe. Every entity merges the error rate and the error fuzzy set values. For instance, first rule is R1: If ΔPe is P3 and Pe is P3 then ΔVQ is P3 Table 5.3. Rule base for ΔVQ ΔPe/Pe N3 N2 N1 Z P1 P2 P3 N3 N3 N3 N3 N2 N2 N1 Z N2 N3 N3 N2 N2 N1 Z P1 N1 N3 N2 N2 N1 Z P1 P2 Z N2 N2 N1 Z P1 P2 P2 P1 N2 N1 Z P1 P2 P2 P3 P2 N1 Z P1 P2 P2 P3 P3 P3 Z P1 P2 P2 P3 P3 P3 In the next step, the min fuzzy operator is applied as the antecedent of the rule, which has more than one part that should be ANDed with each other. The min fuzzy operator is also used in the implication step, implemented for each rule. Here, the output fuzzy set is truncated by a real number given by the antecedent of the rule. The result of implication is innately fuzzy, so to determine crisp outputs (ΔVQ, ΔVD), the popular centroid defuzzification scheme is utilized as the last step. Finally, the actual outputs of FUDE are obtained. For instance, ΔVQ at the sampling instant k can be written using equation (5.9). µ(i) and bi are the aforementioned MF and the center of MF of the consequent of rule i, respectively. The control surfaces of the proposed FUDE are shown in Figure 5.18. 117 5. DYNAMIC MODELING STUDIES ∆VQ (k ) = A. Mete VURAL ∑i49=1 bi ∫ µ (i ) (5.9) 49 ∑ ∫ µ (i ) i =1 Figure 5.18. Control surfaces of the proposed FUDE The conceptual controller configurations presented in terms of block diagrams are illustrated in Figure 5.19 for VSC2 or “the master VSC” of IPFC where real and reactive power flow control is made simultaneously. The configuration is implemented in two stages, outer control loop by i) HFPI controller, ii) PI+DG controller, iii) PI controller and inner control loop to implement 2-angle control method mentioned in previous chapter. Limiters can be either defined externally or internally as the PI controller parameters. They are used to limit the values of d-q voltage components by consideration of the maximum voltage generation capacity of each VSC of IPFC. VSC1 or “the slave VSC” of IPFC regulates DC link capacitor voltage and controls real power flow on Line-1, simultaneously. The control scheme based on parameter optimized PI controllers is shown in Figure 5.20. Error in DC link voltage drives PI controller to produce d-component of VSC1 output voltage to achieve DC link voltage control. Similarly, real power flow control on Line-1 is carried out by qcomponent of VSC1 output voltage. 118 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.19. Conceptual control configurations for the master VSC Figure 5.20. Control scheme for the slave VSC 5.4.3. Finding Optimum Controller Parameters Simplex method iteratively finds the optimal parameter set p={Kp1, Kp2, Ti1, Ti2} for PI controllers of the master VSC and the slave VSC by minimizing the cost functions given in equations (5.10) and (5.11) depending on sum of ISEs of the controlled variables. PSCAD implementation of simplex method is shown in Figure 5.21. 119 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.21. PSCAD implementation of simplex method ) (5.10) H ( p ) = 100 ∫ ( P1ref − P1 ) 2 + ( E ref − E ) 2 dt (5.11) T ( F ( p ) = 100 ∫ ( P2 ref − P2 )2 + (Q2 ref − Q2 )2 dt t =0 T ( ) t =0 T is total simulation time in equations (5.10) and (5.11). While FUDE is off, simplex method is executed for a sequence of unit step changes applied to P2ref and Q2ref for Line-2, which are same as in case 1 in the next section. During optimization routine, the variations of F(p) and H(p) against iteration number are plotted in Figures 5.22a and 5.22b, respectively. (a) Cost function for master controller (b) Cost function for slave controller Figure 5.22. Cost function minimization in simplex method 120 5. DYNAMIC MODELING STUDIES A. Mete VURAL Optimum parameter set is listed in Table 5.4. First, parameters of the master control scheme are optimized using equation (5.10) under the condition that slave controller is employed with pre-defined parameters providing a robust and stable IPFC performance. Here it is not ensured that these parameters are optimal, but they give satisfactory dynamic performance. Secondly, parameters of slave control scheme are optimized using equation (5.11) while the solution of the first case results is applied to master control scheme. The algorithm is executed for a tolerance of 1.0E-6. Table 5.4. Simplex optimized controller parameters of IPFC F(p) Method Nonoptimized Simplex Kp1 Ti1 Kp2 Ti2 9.1940 0.8 0.01 0.8 0.01 0.2930 192 0.00086 192 0.00124 Kp1 Ti1 Kp2 Ti2 266.886 0.01 0.001 0.01 0.001 43.7829 0.05154 0.00529 0.01489 0.00434 VSC2 H(p) Method Nonoptimized Simplex VSC1 5.4.4. Simulation Studies To test and evaluate the decoupling performances of different controllers, 4Machine 4-Bus System embedded with IPFC shown in Figure 5.11 is simulated in PSCAD. Solution time-step is set to 100 µs. While IPFC is de-activated when the switches (sw1, sw2) are closed, real and reactive power flows of Lines 1 and 2 are measured to design reasonable set-point changes. The following control tasks and the controllers are considered for the case studies: • Line-1 sending-end real and reactive power flow control by optimized PI controllers • IPFC DC link voltage control by optimized PI controller 121 5. DYNAMIC MODELING STUDIES A. Mete VURAL • Line-2 sending-end real and reactive power flow control by 5.4.4.1. - Optimized PI controllers (with zero-decoupled gains) - Optimized PI controllers with decoupled gains (PI+DG) - Optimized PI controllers with FUDE (HFPI controller) Case 1 In this case study, IPFC is activated by opening the switches (sw1, sw2) and the dynamic performances of aforementioned controllers are simulated and compared when the system is subjected to a sequence of unit-step changes in real and reactive power flow commands of Line-2. Reference for real power flow on Line-1 is set as 2.3 pu and IPFC DC link voltage is regulated at 1.0 kV throughout the case study. As observed in Figure 5.23, reactive power flow command is altered to force coupling during the instants when real power flow command is constant. Although PI controller is parameter optimized, relatively large fluctuations in real power flow are observed at times, t=1.0 s, 2.0 s, and 3.0 s, respectively (Figures 5.23a-c). PI controller with decoupled gains (PI+DG) gives better results when the dynamic performance is compared with that of PI controller only. Although PI controller or PI+DG gives satisfactory steady-state tracking performance, inherent coupling between power flow control loops are not avoided and IPFC dynamic performance is adversely affected. On the other hand, HFPI controller has the superior decoupling feature as evidence from the response curves since the variations in real power flow is effectively minimized when reactive power flow command is changed. Moreover, Figures 5.23d-f gives a comparison between the responses of different controllers to step-changes in real power flow command. HFPI controller responses with less oscillations and shows reduced overshoot characteristics. The dynamic performance of reactive power flow control loop with different control schemes are also evaluated in this case study. Figure 5.24 shows the traces of different reactive power flow controllers in response to unit-step change in real power flow command. As shown in Figures 5.24ac, HFPI controller performance is superior to either PI controller or PI+DG on tracking 122 5. DYNAMIC MODELING STUDIES A. Mete VURAL reference signal and HFPI controller effectively minimizes the coupling effect between two power flow control loops. Figure 5.23. Dynamic performances of real power flow controllers As the consequence of unit-step command, reactive power flow fluctuations are minimized better by HFPI controller with less oscillatory and reduced overshoot response when compared with the other control schemes. Two commonly used measures for control system performance, namely ISE and integral absolute error (IAE) are calculated for (0.9 s ≤ t ≤ 5.0 s) in Table 5.5 to have a quantitative and exact comparison between different control schemes. Figure 5.25 shows the dynamic performance of slave VSC real power flow controller and it is found that among the three controllers, the variations are the smallest in case of HFPI controller which gives a smoother response when compared 123 5. DYNAMIC MODELING STUDIES A. Mete VURAL with PI+DG. DC link voltage excursions of IPFC for different control schemes are depicted in Figure 5.26. DC voltage controller is almost robust and gives satisfactory response for all control modes. But when the comparisons are particularly made at instants (t=1.0 s, 1.5 s, 2.0 s, 2.5 s, 3.0 s, 3.5 s), relatively smaller spikes are observed at the simulated waveforms in case of HFPI controller. Figure 5.27 compares the d-q components of injected current of the master converter in case of three controllers. Prominent time instants are marked with red rectangles when real power flow reference is changed in case of iD and when reactive power flow reference is changed in case of iQ. These spikes in marked regions showing the interactions between the two power flow controllers are effectively reduced by the proposed HFPI controller. Although the spikes caused by HFPI controller are practically the same when compared with the ones caused by PI controller, HFPI controller weakens the spikes much better than PI+DG. Figure 5.28 shows control signals (VDref and VQref) for inner control loop and the measured voltages (VD and VQ) of the master converter at the primary windings of series coupling transformer Tr1. It is ensured that the “2-angle control” block operates stable and the orthogonal components of the master converter voltage perfectly trace their pertinent reference values in case of HFPI controller. Figure 5.29 depicts anode-to-cathode voltage of one selected GTO from Group M of the master converter in case HFPI controller is activated. As designed for quasi multipulse operation, GTO is triggered only once in one fundamental cycle of 50 Hz. 5.4.4.2. Case 2 In this case study, controller references are kept exactly the same as in case 1 and RL/XL ratio of the Line-2 is increased by three times to investigate and compare the parameter sensitivity of the three control schemes. Figures 5.30 and 5.31 show comparative tracking performances of the controllers for real and reactive power flows of the Line-2, respectively. ISE and IAE performance indices are listed in Table 5.5 for 0.9 s ≤ t ≤ 5.0 s. As shown in Figures 5.30a-c, real power flow control loop is interacted adversely with reactive power flow control loop when PI+DG is employed. 124 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.24. Dynamic performances of reactive power flow controllers Figure 5.25. Dynamic performance of real power flow controller for slave VSC 125 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.26. Dynamic performance of DC voltage controller for slave VSC Figure 5.27. d-q components of master VSC injected current Figure 5.28. d-q components of master VSC voltage by HFPI controller 126 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.29. Anode-to-cathode voltage of a selected GTO in converter M Figure 5.30. Dynamic performances of real power flow controllers PI+DG has the maximum overshoot of all controllers and gives relatively the slowest response when compared with the other control schemes. The same situation is also observed in Figures 5.31a-c when reactive power flow of Line-2 is controlled by PI+DG during set-point changes in real power flow. As expected, the performance of PI+DG for both real and reactive power flow control loops degrades 127 5. DYNAMIC MODELING STUDIES A. Mete VURAL significantly, since decoupled gains are designed offline using transmission line data. When comparing cases 1 and 2 quantitatively, an increase of 32.68% in ISE and an increase of 80% in IAE are observed for real power PI+DG controller. Similarly, an increase of 62.55% in ISE and an increase of 127.18% in IAE are observed for reactive power PI+DG controller. It is because of the PI gains are optimized for the operating conditions in case 1 that the dynamic performance of PI controller slightingly weakens when compared with that of case 1. Even though the system parameters are changed, HFPI controller successfully reduces the interactions between real and reactive power flows with the lowest ISE and IAE indices when compared with either PI controller or PI+DG. Furthermore, it is observed in Figure 5.30d-f and in Figure 5.31d-f that HFPI controller gives a smooth response and greatly improves rise time and settling time of the control loops when responding to set-point changes. 5.4.4.3. THD Content Table 5.6 lists the highest THD values computed using the first 63 harmonics at four common coupling points between IPFC and the power system. Records for 1.0 s≤t≤5.0 s confirm that IPFC does not cause the violation of the THD upper limit of 2.5 % for 154 kV transmission level (IEEE, 1993). Consequently, filtering is not required even GTOs are switched at fundamental frequency. 128 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.31. Dynamic performances of reactive power flow controllers Table 5.5. Quantitative performance analysis of different controllers Case 1 Control Action for Line-2 real power flow reactive power flow Case 2 Control Action for Line-2 Controller ISE IAE PI PI+DG HFPI PI PI+DG HFPI 5.8784 5.3502 4.5300 4.5269 3.6717 2.6631 136.2015 115.8114 88.8933 168.0034 116.8833 73.9114 real power flow 129 reactive Power flow Controller ISE IAE PI PI+DG HFPI PI PI+DG HFPI 5.8918 7.0987 5.5127 4.5761 5.9683 2.9794 140.4160 208.7502 112.5168 172.4952 265.5316 69.4454 5. DYNAMIC MODELING STUDIES A. Mete VURAL Table 5.6. THD values in case of three control schemes Controller PI PI+DG HFPI Controller PI PI+DG HFPI Case 1 THD@Bus1 0.48 % 0.48 % 0.46 % THD@Bus3 0.91 % 0.90 % 1.3 % THD@Bus2 0.75 % 0.74 % 0.71 % THD@Bus4 0.98 % 0.97 % 1.51 % Controller PI PI+DG HFPI Controller PI PI+DG HFPI Case 2 THD@Bus1 0.45 % 0.46 % 0.46 % THD@Bus3 0.80 % 0.82 % 1.21 % THD@Bus2 0.70 % 0.70 % 0.69 % THD@Bus4 0.89 % 0.89 % 1.47 % 5.4.5. Discussion The proposed HFPI controller minimizes the interactions between the control loops of real and reactive power flows and gives a smoother response when compared with either PI+DG or PI controller. Even system coefficients change, it is still able to alleviate these interactions and robust to uncertainty. On the other hand, the performance of PI+DG strongly relies on the knowledge of system parameters and only performs better than PI controller under the condition that the model parameters match with the parameters of decoupled gain design. HFPI controller does not disturb other IPFC control loops, such as power flow control on Line-1 and DC link voltage control although it introduces small voltage ripples in the DC interface. So the interactions between the controllers are obtained minimum for multi-functioning FACTS device which is highly desired. 5.5. Converter-Level Modeling of BtB-STATCOM 5.5.1. BtB-STATCOM Interacting with Power System BtB-STATCOM having two quasi multi-pulse VSCs is located between two neighboring buses, Buses 1 and 3 of 3-Machine 7-Bus System as shown in Figure 5.32. The same system is used for power flow studies of BtB-STATCOM in Chapter 3. 130 5. DYNAMIC MODELING STUDIES A. Mete VURAL Figure 5.32. 3-Machine 7-Bus System embedded with BtB-STATCOM Two-VSC configuration extends the capabilities of conventional STATCOM that the bi-directional real power transfer from one bus to another is possible. The AC terminal of VSC1 is connected at Bus 1 through a magnetic interface which is conceptually drawn and named as “tr1”. Similarly, the AC terminal of VSC2 is connected at Bus 3 through “tr2”. A total of three power system parameters are aimed to control simultaneously in this simulation configuration. These are voltage magnitudes of Buses 1 and 3 and DC power flow among Buses 1 and 3 in two directions. The DC terminals of each VSC are joined in a DC link, which is represented by capacitor C (0.2 F), provides real power exchange among the two converters. Each VSC of BtB-STATCOM is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 50 Hz, 8.33 MVA, 20/2/1.1548 kV with a leakage reactance of j0.025 pu. Each single-phase transformer of summing and magnetic interface is rated at 50 Hz, 16.67 MVA, 137.92/38 kV, j0.1 pu. 131 5. DYNAMIC MODELING STUDIES A. Mete VURAL 5.5.2. BtB-STATCOM Controller Design In BtB-STATCOM, two-degrees of freedom (voltage magnitude and phase angle) for each VSC is based on the decomposition of quasi multi-pulse VSC voltage into its d- and q-axis components as mentioned in Chapter 4. The inputs of 2-angle control method, VDref and VQref of each VSC can be calculated from the PI control blocks as shown in Figure 5.33. VSC1 control, the same as that of shunt VSC of GUPFC, is the DC link voltage control, E and the voltage magnitude control of Bus 1, V1, which are achieved by Vsh1D (Figure 5.32a and Vsh1Q (Figure 5.32b), respectively. Figure 5.33. Control loops of BtB-STATCOM VSC2 control is the real power transfer among the two VSCs through the DC link and voltage magnitude control of Bus 3, V3, achieved by Vsh2D (Figure 5.32c) Vsh2Q (Figure 5.32d), respectively. The chosen PI parameters for VSC1 and those of VSC2 of BtB-STATCOM are given in Appendix C. 132 5. DYNAMIC MODELING STUDIES A. Mete VURAL 5.5.3. Simulation Studies The power system embedded with BtB-STATCOM, shown in Figure 5.32, are simulated in PSCAD to test quasi multi-pulse VSCs and their control schemes for BtB-STATCOM operation through comprehensive simulation cases. Solution time step of PSCAD is set as 100 μs. DC link voltage is controlled at 2.0 kV throughout all cases. 5.5.3.1. Case1: Start-up Transients BtB-STATCOM is started up to control bus voltages (V1 and V3) at 1.0 pu and to enable real power transfer between Buses 1 and 3. Noting that uncontrolled bus voltages are 0.99 pu and 0.97 pu on 154 kV base, respectively. Real power transfer (Ptransfer2) is set at 0.5 pu on 100 MVA base. Since start-up transients are highly dependent upon voltage ramp up time of the generators in PSCAD, a ramp-up time of 0.05 s, divisible into the period of the fundamental frequency, is selected (PSCAD, 2005). The results are graphically presented in Figures 5.34a-j. No overshoot is observed in the tracking signals of bus voltages in Figures 5.34a and 5.34b. V1 and V3 come to their desired values with no steady-state error within 0.06 s and 0.8 s, respectively. This is due to different reactive power requirements of each bus. The steady-state magnitudes of injected reactive powers into Buses 1 and 3 are 13 MVAR and 65 MVAR, respectively. Figure 5.34c shows the response of the real power transfer from Bus 1 to Bus 3 to a step change of 0.5 pu at t=0+. After 1.4 s, real power flow comes to its desired value with no overshoot. The DC link voltage regulation is a key factor for the successful operation of voltage source based converters. On account of this, E is tightly regulated at 2.0 kV (Figure 5.34d). Actual DC link voltage settles on 2.0 kV line within 0.2 s. Figures 5.34e-j show some related signals taken from the simulation. 133 5. DYNAMIC MODELING STUDIES A. Mete VURAL (a) Bus 1 line-to-line rms voltage control at start-up (b) Bus 3 line-to-line rms voltage control at start-up (c) Real power transfer control from Bus1 to Bus3 at start-up (d) DC link voltage control at start-up (e) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) during start-up 134 5. DYNAMIC MODELING STUDIES A. Mete VURAL (f) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) during start-up (g) d-q components of VSC1 voltage during start-up (h) d-q components of VSC2 voltage during start-up (i) Injected three-phase currents by VSC1 during start-up (j) Injected three-phase currents by VSC2 during start-up Figure 5.34. Simulated waveforms of case 1 135 5. DYNAMIC MODELING STUDIES 5.5.3.2. A. Mete VURAL Case 2: Response to Real Power Transfer Step Changes BtB-STATCOM is commanded to reverse real power transfer between Buses 1 and 3 from 0.4 pu to -0.4 pu at 4.0 s and restore it back to its previous value at 6.0 s. The other reference points of BtB-STATCOM control loops are kept unchanged as in case 1. Figures 5.35a-h show the traces of this case study. Figure 5.35a shows that real power transfer reaches to its commanded values in around 1.0 s after the step change command is applied. The response is robust with no steady-state error. The DC link voltage stays constant after following a 20 % undershoot and 25 % overshoot. The response of V1 and V3 is constant on 1.0 pu line and not shown here. Although practical PI controllers are utilized, all responses regarding this case study exhibit satisfactory and stable performance. BtB-STATCOM is able to reverse the direction of real power transfer between neighboring buses without disturbing other control parameters. (a) Reversing real power transfer from Bus1 to Bus3 (b) DC link voltage transients 136 5. DYNAMIC MODELING STUDIES A. Mete VURAL (c) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) (d) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) (e) d-q components of VSC1 voltage (f) d-q components of VSC1 voltage (g) Injected three-phase currents by VSC1 137 5. DYNAMIC MODELING STUDIES A. Mete VURAL (h) Injected three-phase currents by VSC2 Figure 5.35. Simulated waveforms of case 2 5.5.3.3. Case 3: Single-phase to Ground Fault The dynamic performance of the BtB-STATCOM is evaluated by applying phase-A to ground fault at the middle of the Line 3-P at 10.5 s for 100 ms and cleared without any change in the network configuration. The reference values of all control loops of BtB-STATCOM are kept constant as in case 1. Figures 5.36a-j show simulated responses to the fault. The rms voltage magnitudes of compensated buses without/with BtB-STATCOM are compared and presented in Figures 5.36a and 5.36b. V1 and V3 returns to their controlled values within 1.0 s after the fault is cleared and an overshoot of less than 0.25 % and 2.5% is observed, respectively. Voltage sag does not go below more than 0.5 % of nominal value of V1 and 7.5 % of nominal value of V3, respectively. For both measurements, BtB-STATCOM could hold voltage levels higher than the uncompensated case during fault. Real power transfer drops around 17.0 % of its nominal value during fault but it restores within 1.65 s with an overshoot of 2.5 % after the fault is cleared (Figure 5.36c). PI control could hardly keep DC link voltage at its steady-state value against sustained oscillation, but DC link voltage returns to its controlled value within around 0.7 s following after the fault (Figure 5.36d). It is deduced that the magnitude of the real power transfer is inversely proportional to the DC link voltage controller performance. Tracking performances of all PI controllers show that the controlled parameters do not pass to unstable region even though the controllers have simple structure in nature. Figures 5.36e-j demonstrates some recorded signals of BtBSTATCOM related with this case study. 138 5. DYNAMIC MODELING STUDIES A. Mete VURAL (a) Bus 1 voltage response to phase-A to ground fault (b) Bus 3 voltage response to phase-A to ground fault at 10.5 s (c) Real power transfer response to phase-A to ground fault at 10.5 s (d) DC link voltage response to phase-A to ground fault at 10.5 s (e) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) 139 5. DYNAMIC MODELING STUDIES A. Mete VURAL (f) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) (g) VSC1 controller output signals in response to phase-A to ground fault at 10.5 s (h) VSC2 controller output signals in response to phase-A to ground fault at 10.5 s (i) Injected three-phase currents by VSC1 (j) Injected three-phase currents by VSC2 Figure 5.36. Simulated waveforms of case 3 140 5. DYNAMIC MODELING STUDIES 5.5.3.4. A. Mete VURAL Case 4: Three-phase to Ground Fault A three-phase to ground fault, which is the most severe disturbance is applied to the middle of Line 3-P at 10.5 s for 100 ms and cleared. The reference values of all control loops of BtB-STATCOM are kept constant as in case 1. Figures 5.37a-j show comparative simulated responses to the short circuit. Voltage sag less than 1.5 % and swell no more than 1.0 % are recorded for V1 in Figure 5.37a. BtBSTATCOM retrieves the voltage magnitude to its controlled value in less than 1.5 s. In Figure 5.37b, voltage sag for Bus 3 goes 40% of nominal value and recovers in around 1.5 s after the fault is cleared. Real power transfer is severely disturbed since Bus 3 is next to the fault location. It drops to a negative value that the direction of flow is temporary reversed from 0.4 pu to -0.04 pu due to fault. The disturbance lasts no more than 2.5 s. Combining Figures 5.37c and 5.37d, the excursions occurred in real power transfer for this case study is more than those of case 3. DC link voltage recorded in Figure 5.37d is more ludic than the trace observed during phase-A to ground fault condition (Figure 5.36d). The performances of PI controllers are relatively poor in case of three-phase fault but without losing stability. Figures 5.37ej also present some recorded signals of BtB-STATCOM related with this case study. (a) Bus 1 voltage response to three-phase fault (b) Bus 3 voltage response to three-phase fault at 10.5 s 141 5. DYNAMIC MODELING STUDIES A. Mete VURAL (c) Real power transfer response to three-phase fault at 10.5 s (d) DC link voltage response to three-phase fault at 10.5 s (e) Phase-shifts for converters M and N of VSC1 (ΦM and ΦN) (f) Phase-shifts for converters M and N of VSC2 (ΦM and ΦN) (g) VSC1 controller output signals in response to three-phase fault at 10.5 s 142 5. DYNAMIC MODELING STUDIES A. Mete VURAL (h) VSC2 controller output signals in response to three-phase fault at 10.5 s (i) Injected three-phase currents by VSC1 (j) Injected three-phase currents by VSC1 Figure 5.37. Simulated waveforms of case 4 5.5.3.5. THD Content Table 5.7 shows THD of voltage waveforms during BtB-STATCOM steadystate operation in case 1. The voltage harmonics are within acceptable limits of IEEE-519 standard (IEEE, 1993). Table 5.7. THD values Common coupling point Bus 1 Bus 3 THD (%) 0.33 0.30 143 5. DYNAMIC MODELING STUDIES A. Mete VURAL 5.5.4. Discussion Quasi multi-pulse VSC designed in Chapter 4 is adapted for BtB-STATCOM operation. The power circuit, pulse generating circuits, and BtB-STATCOM control scheme is verified through different simulation scenarios in PSCAD. Conventional PI controllers are robust and yet practically applicable to voltage magnitude and real power transfer control owing to their simplicity. THD levels of the two converters comply with the regulations even the switching is made at low frequency. This study can easily be extended to VSC-HVDC transmission with DC transmission line models. With back-to-back converters, it is also possible to supply controlled real power transfer in micro grid applications. 5.6. Summary In this chapter, quasi multi-pulse VSC is adapted for the three-types of multiconverter FACTS devices. Power circuit, gating pulse generation circuits, and 2angle control method for the quasi multi-pulse VSC, mentioned in Chapter 4, are also verified for different control actions together with different disturbance scenarios in one sense. If no further performance is required in terms of power quality, eight sixpulse converters operating together for VSC configuration can be used without the need for any AC filters, since measured THD levels always lie below IEEE-519 standard. Independent control of voltage magnitude and phase angle of the converters without high frequency PWM methods makes use of separate control functions for real and reactive power possible. Although the concerned FACTS devices have many possible operating modes, it is anticipated that the shunt converter is operated in automatic voltage-control mode (GUPFC, BtB-STATCOM) and the series converter (GUPFC, IPFC) is operated in automatic power-flow control mode. The bottleneck of finding a lot of suitable parameters for many controllers that should operate together in stable and robust is overcome by simultaneously tuning of these parameters using simplex method. This solution is practically applied for the controllers of GUPFC and IPFC when different cost functions are defined. A novel 144 5. DYNAMIC MODELING STUDIES A. Mete VURAL HFPI controller for IPFC is designed to decouple the control loops of real and reactive power flows that can be generalized to any series converter of the multiconverter FACTS device. The simulation results prove superior dynamic performance when compared with the simplex optimized PI controller both without/with analytically computed feed-forward decoupling gains. 145 5. DYNAMIC MODELING STUDIES A. Mete VURAL 146 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 6. TRANSIENT STABILITY STUDIES 6.1. Introduction Transient stability is “the ability of the power system to maintain synchronism when subjected to a severe transient disturbance such as faults on transmission facilities, loss of generation, or loss of a large load” (Kundur, 1994). Conventionally, electromechanical oscillations, either being local mode (1-2.5 Hz) or inter-area mode (0.1-0.8 Hz), occur due to the natural dynamic behavior of synchronous machines when the system is subjected to faults and may lead to total or partial power interruption if not damped out effectively. On the other hand, integration of large wind farms with electrical network is inevitable due to growing electrical demand and environmental reasons which leads to interconnected operation of synchronous generators and wind turbine driven generators (Chen et al., 2009), (Kaldellis et al., 2011). The use of induction machines in wind generation is widely accepted as a generator of choice due to their simple structure and cost (Junyent-Ferre et al., 2010), (Li et al., 2011). On one hand, wind farms employing induction generators consume reactive power which produces low voltage profile and dynamic instability observed following after faults (Chompoo-inwai et al., 2005), (Sentil-Kumar et al., 2011). On the other hand, the integration not only requires stable operation of synchronous generators, but also induction generators should operate stable without disturbing demand side. This situation comes into prominence since the induction generator’s behavior during a fault is very different from that of a synchronous generator. Rotor speed instability of the induction generator is seen when it is subjected to a nearby fault. In this situation, the rotor may accelerate and reach higher steady-state speed (Samuelsson et al., 2005). Self-excited double cage induction generators (SEDCIG) which energize the wind farm is considered due to following two reasons (Li et al., 2011): (i) Although, doubly fed induction generator (DFIG) has gained remarkable attention currently, SEDCIGs are still operated in many grid-connected wind turbines, (ii) the transient 147 6. TRANSIENT STABILITY STUDIES A. Mete VURAL behavior of DFIG is similar to SEDCIG when the crowbar system of the DFIG protects the converter under grid fault by bypassing the rotor circuit over the crowbar impedance. Combining two completely different machine stability concerns mentioned above, stability of the power systems connected with the wind farm is enhanced by GUPFC, with the following simultaneous control tasks which are proposed for the first time: i) oscillation damping of wind farm integrated power system by a selftuning fuzzy damping controller (STFDC), ii) multi-line real and reactive power flow control, iii) AC bus voltage control. STFDC proposed in this chapter is further adapted for IPFC for damping inter-area mode of oscillations of a power system consisting of several conventional synchronous generators. Finally, the performances of the PI controllers proposed for BtB-STATCOM in the last chapter is investigated in terms of oscillation damping and hence to improve transient stability of the power systems in this chapter. 6.2. Literature Survey on Transient Stability Studies A literature survey is carried out here for transient stability studies of GUPFC, IPFC, and BtB-STATCOM. In spite of intensive research work on UPFC related transient stability studies, very few papers are available about GUPFC. An average model of GUPFC is integrated into Phillips-Heffron model of a multimachine system to investigate the impact of GUPFC on power system oscillation damping (Lubis et al., 2012). Another GUPFC’s average model is embedded into user-defined model of PSASP software to investigate the effect of GUPFC on stability of China’s Sichuan Power Grid (Sun et al., 2003). IPFC based transient stability studies generally uses IPFC’s average model included in Phillips-Heffron model of single-machine infinite-bus (SMIB) system rather than using converter-level model (Kazemi et al., 2006), (Parimi et al., 2008), (Banaei et al., 2009a), (Veeramalla et al., 2010), (Parimi et al., 2010a), (Belwanshi et al., 2011). In average model based approaches, some IPFC studies are extended for multi-machine systems (Parimi et al., 2010b), (Parimi et al., 2011), (Shan et al., 148 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 2011). On the other hand, IPFC is fuzzy and/or neural network controlled to improve stability based on average modeling approach (Mishra et al., 2002), (Parimi et al., 2010a), (Belwanshi et al., 2011), (Banaei et al., 2011). Different from those, transient stability of a multi-machine system is improved by IPFC using derived energy function for IPFC which is developed from an average model (Azbe et al., 2009). Three-phase model of IPFC is derived using switching functions for a twelve-pulse VSC based IPFC for SSR studies (Padiyar et al., 2007). A non-linear control scheme for BtB-STATCOM is developed using an average modeling approach (Lee et al., 2011). The stability studies are conducted on Phillips-Heffron model of SMIB system which includes the average model of two BtB VSCs (Banaei et al., 2009b). A supplementary control for VSC based BtB link in damping SSR of series capacitive compensated transmission system is studied using an average model of each VSC (Faried et al., 2009). According to literature review results, transient stability studies of GUPFC, IPFC, and BtB-STATCOM generally rely on average models included into PhillipsHeffron SMIB system or multi-machine systems, rather than using converter-level models. This chapter is aimed to investigate these FACTS devices on transient stability enhancement using converter-level modeling approach, together with a novel damping control scheme. 6.3. Transient Stability Improvement Using GUPFC 6.3.1. Dynamic Equations for Power Generation 6.3.1.1. Wind Model The wind can be modeled with the following equation that properly includes spatial effects of the wind behavior such as gusting, ramp changes, and background noise (Anderson et al., 1983), VW = VWB + VWG + VWR + VWN (6.1) 149 6. TRANSIENT STABILITY STUDIES A. Mete VURAL where VW is the wind speed, VWB is the base or mean wind speed which is always assumed to be present where the wind generator is required to be in service. VWG is the gust wind component, VWR is the ramp wind component, and VWN is the noise wind component. In this chapter, only transient fault simulations are considered where the simulated events last up to only 12.5 s. Moreover, the wind farm considered here is aggregations of many single wind turbines in which wind speed variations can cancel each other (Sorensen et al., 2002), (Jauch et al., 2007), (Erlich et al., 2007). That’s why natural wind variations (VWG,VWR,VWN) are not taken into account. VWB is set to 14 m/s allowing all turbines to produce rated power (Jauch et al., 2007), (Kusiak et al., 2010). 6.3.1.2. Blade Dynamics The mechanical system mainly consists of blade and shaft which transforms wind kinetic energy into rotational motion. Shaft dynamics are not presented in this research which is characterized by blade speed, hub speed, gear box speed, and the generator mechanical speed (Anderson et al., 1983). The available wind power is assumed to be captured by horizontal axis wind turbine with three blades. The blade dynamics are represented by the following functions (Anderson et al., 1983), γ = VW wB Cp = 1 (γ − 0.022 β p 2 − 5.6)e −0.17γ 2 PW = 1 ρAC p VW 3 2 (6.2) where wB is the blade angular velocity, γ is the tip speed ratio, βp is the blade pitch angle, Cp is the dimensionless power coefficient, ρ is air density, and A is blade impact area. PW is the resultant mechanical power which is extracted from the wind. 150 6. TRANSIENT STABILITY STUDIES 6.3.1.3. A. Mete VURAL Self-excited Double Cage Induction Generator Self-excited double cage induction generator (SEDCIG) can be modeled by the following equations for its one phase while saturation effects are ignored (Levi, 1997). Underlined variables denote space vectors in the arbitrary rotating reference frame with a speed of wa. v s = R s i s + d ϕ s / dt + jwa ϕ s 0 = R r1 i r1 + d ϕ r1 / dt + j ( w a − w)ϕ r1 + Rc (i r1 + i r 2 ) 0 = R r 2 i r 2 + d ϕ r 2 / dt + j ( wa − w)ϕ r 2 + Rc (i r1 + i r 2 ) ϕ s = L s i s + Lm (ir1 + ir 2) ϕ r1 = Lr1 i r1 + Lm i s + L12 i r 2 ϕ r 2 = Lr 2 i r 2 + Lm i s + L12 ir1 TE = (3 / 2) Pϕ s × is TE − TL = ( J / P)dw / dt (6.3) where v, i, φ respectively describes voltage, current, and flux linkage. Subscripts r and s stands for rotor and stator, respectively. Subscripts 1 and 2 represent the rotor winding numbers, respectively. R describes resistance and RC is common end-ring resistance between the two cages in the SEDCIG. L represents inductance and Lm is the mutual leakage inductance between stator and the two rotor windings. L12 is the mutual leakage inductance between the two rotor windings, w is the rotation speed and P is the number of pole pairs. TE and TL stand for electrical torque and load torque, respectively. J is the inertia of the machine. 6.3.1.4. Salient-Pole Synchronous Generator The unsaturated dq model of the salient-pole synchronous generator (SG) can be approximated by the following functions (Teng et al., 2010). 151 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Stator equations: Vq = − Ra iq + e ′q′ − X d′′ i d Vd = − Ra i d + e d′′ − X q′′i q Td′′0 Td′ 0 Tq′′0 Tq′0 de q′′ = e ′q − e q′′ − ( X d′ − X d′′ )i d dt de ′q = V f − e q′ − dt de d′′ X d − X d′ (e ′q − e ′q′ ) X d′ − X d′′ = e ′d − e ′d′ − ( X q′ − X q′′ )iq dt de d′ = −e d′ − dt X q − X q′ X q′ − X q′′ (e d′ − e d′′ ) T ′ = e ′d′ i d + e ′q′ i q + ( X q′′ + X d′′ )i d i q (6.4) Rotor equation: M d 2δ dt 2 +D dδ = TM − TE dt (6.5) V, i, X respectively describes voltage, current, and reactance. Subscripts d and q stand for direct and quadrature axis, respectively. Subscript 0 means open circuit and Ra describes armature resistance. T defines time constant. Vf and e is the excitation winding voltage and internal generated voltage, respectively. Superscripts ' and '' respectively denote transient and sub-transient modes. M and D describe inertia constant and damping coefficient, respectively. TE is electrical torque which is opposing the mechanical torque, TM. δ is the torque angle of the machine. 6.3.2. Power System Configuration Time domain simulation studies are carried out on wind farm integrated power system installed with GUPFC, which is shown in Figure 6.1. The system is kept as simple as possible and grid data are inspired from IEEE first benchmark model (IEEE, 1997). Series converters VSC2 and VSC3 are inserted into Lines 2 and 1, respectively. Shunt converter (VSC1) is connected to Bus 1. 152 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Figure 6.1. Power system configuration embedded with GUPFC 153 6. TRANSIENT STABILITY STUDIES A. Mete VURAL The wind farm is rated at 50 MVA and comprised of 20 SEDCIGs operating coherently, each driven by a horizontal axis three-blade wind turbine. 320 μF capacitor for each phase is installed at wind farm bus for unity power factor operation. AC grid power generation side is the aggregated model of 5 parallel hydro-governed SGs with solid-state exciters, rated at 120 MVA each. 100 MVA, 154 kV, and 60 Hz are chosen as base values and start-up transients of the generators are not taken into account since the faults are considered soon after the system comes to steady-state. Wind farm integrated power system, GUPFC with three quasi multipulse VSCs, and control blocks are modeled in PSCAD while fuzzy interfaces are designed in MATLAB fuzzy logic toolbox. PSCAD is interfaced with MATLAB through a custom written interface in PSCAD that exchanges data with MATLAB continuously at every solution time step of 100 µs, shown in Figure 6.2. Each VSC of GUPFC is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 60 Hz, 8.33 MVA, 20/2/1.154 kV with a leakage reactance of j0.025 pu. Each single-phase transformer of summing and magnetic interface is rated at 60 Hz, 16.67 MVA, 137.92/38 kV, j0.1 pu for shunt VSC. For series VSC, the rating is modified as 23.42/23.42 kV, j0.1 pu. Each single-phase transformer of series coupling magnetic interface is rated at 60 Hz, 33.33 MVA, 104.13/40 kV, j0.01 pu. Figure 6.2. PSCAD-MATLAB interface 154 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 6.3.3. Damping Control Scheme of GUPFC The self-tuning scheme for PI type fuzzy controllers is originally proposed by the authors (Mudi et al., 1999) and later applied to TCSC to improve the stability of multi-machine power systems (Hameed et al., 2008). STFDC is designed with altered fuzzy inputs for GUPFC. The performance is further improved by optimizing scaling gains using simplex optimization method. Damping control scheme of the GUPFC is based on the modification of real power flow control loop shown in Figures 5.3c or 5.3e. All other control loops of GUPFC in Figure 5.3 are applied without any alteration in this section. Real power flow controllers shown in Figures 5.3c or 5.3e can be expressed alternatively as in equation (6.6) where s is Laplace operator, Kp and Ti are proportional gain and integral time constant of the PI controller, respectively. ΔP=(Pref-P) stands for real power flow error and VseiQ is the q-axis voltage component of series converter-i of GUPFC in which damping control function is added. VseiQ = ( K p + 1 / Ti s )∆P (6.6) In case of damping mode, error at sample-k is simply modified as in equation (6.7) by an auxiliary damping signal based on the speed error of SG (Δw=wref - w), e(k ) = ∆P + K w ∆w (6.7) where Kw is the damping gain. Since aggregated synchronous machine model is used, w and wref represents the speed at sample-k, and base speed of all parallel operating generators, respectively. As opposed to one of the originally proposed fuzzy inputs in the paper (Mudi et al., 1999), control system is made insensitive to noise in the error measurement using error-integral instead of error-derivative which lessen control signal oscillations highly observed in simulation cases. In this case, the error-integral at sample-k can be computed as 155 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Σe(k ) = Σe(k − 1) + e(k ) (6.8) It is important to note that the series converter of the GUPFC, where STFDC is not utilized, controls real power flow on Line-1 using equation (6.6) with auxiliary damping signal, as shown in Figure 6.1. STFDC is the alternative of this control mode and constructed from a fuzzy damping controller (FDC) and a fuzzified gain tuner (FGT), as shown in Figure 6.1. 6.3.3.1. Fuzzy Damping Controller (FDC) In FDC scheme, the signals e and Σe in equations (6.7) and (6.8) are respectively multiplied by gains (a1, a2), which needs to be optimized. Crisp values are then mapped to their equivalent fuzzy values by the membership functions of knowledge base in Figure 6.3. Membership functions for eO and ΣeO are symmetrical triangles (except the two at both ends) which have equal 50% base overlap, divides the domain [-1,1] into 7 equal regions. The term sets of eO and ΣeO contain the same linguistic expressions for the magnitude part of the linguistic values and characterizes rule matrix-1 in Figure 6.3, which contains 49 rules. The cell defined by the intersection of the first row and the first column represents a rule such as, {“If ΣeO is P1 and eO is N2 then ΔVq is N1”}. The antecedents are evaluated by applying “min” operator and the output fuzzy set is truncated by applying “min” implication operator. The fuzzy sets are aggregated into a single fuzzy set by “max” operator that should be later dezuffied to resolve a single real number for each output variable. Centroid defuzzification method is applied to get incremental change in series converter voltage as in equation (6.9): ∆Vq (k ) = ∑i49=1 bi ∫ µ (i) (6.9) 49 ∑ ∫ µ (i ) i =1 156 6. TRANSIENT STABILITY STUDIES A. Mete VURAL where µ(i) and bi are the output membership function and the center of output membership function of the consequent of rule i, respectively. Finally, at sample-k, q-axis component of the series converter voltage for oscillation damping (as well as for dynamic real power flow control) is calculated in equation (6.10) where β is the gain factor at sample-k which is decided by FGT. Vq (k ) = Vq (k − 1) + a 3 β ∆Vq (k ) (6.10) Figure 6.3. Membership functions and fuzzy rules for STFDC 6.3.3.2. Fuzzified Gain Tuner (FGT) In STFDC scheme, FDC performance is further enhanced by FGT which computes the gain factor β by a self-tuning mechanism independent from FDC itself. So, two fuzzy modules (FDC and FGT) operate concurrently to generate Vq signal reference for the series converter. The value of β is not fixed and modified at each sample-k according to the following relation, β (k ) = f (eo (k ), Σeo (k ) ) (6.11) 157 6. TRANSIENT STABILITY STUDIES A. Mete VURAL where f denotes a non-linear mapping function, described by rule matrix-2 with 49 rules in Figure 6.2 and associated by the FGT scheme whose structure is exactly the same for its fuzzy operators and input membership functions with those of FDC. Universe of discourse for β lies in the domain [0,1] and is obtained by shifting and scaling (add 1 and multiply with 0.5) input membership functions of FDC along the horizontal axis. Rule matrix-2 is designed to improve the damping performance of GUPFC under large disturbances such as three-phase short circuit on transmission lines. For instance, after a fault occurs, error may be small-positive (P1) but errorintegral can be sufficiently large (P3). In this case, β should be big enough (VB) to increase converter voltage. Under such a situation, the rule is {“If ΣeO is P3 and eO is P1 then β is VB”}. The control surfaces of the proposed STFDC are shown in Figure 6.4. (a) FDC Figure 6.4. Control surfaces of the proposed STFDC 6.3.3.3. (b) FGT Tuning of Scaling Factors The scaling factors (a1, a2,) are used to normalize input variables of the FDC. {eO=a1e; ΣeO=a2Σe}. Similarly, FDC output variable (ΔVq) is first multiplied by a3 then tuned by FGT adaptively. Commonly, there is no well-defined method for selection of scaling factors (Mudi et al., 1999). In this research, these parameters are optimized by simplex method. The cost function is based on integral time absolute error (ITAE) and given in equation (6.12) where t is the simulation time, t0 is the fault time. T is the total simulation time for case 1 in the next section. PSCAD 158 6. TRANSIENT STABILITY STUDIES A. Mete VURAL configuration for this task is shown in Figure 6.5. The convergence performance of cost function in simplex method is shown in Figure 6.6. The value of f is minimized from 0.0720 to 0.0114 in 51 iterations for a tolerance of 1.0E-6 when only FDC is executed while FGT is deactivated. The optimized parameters are listed in Table 6.1. T ( ) f (a1 , a 2 , a 3 ) = ∫ t ⋅ wref − w ⋅ dt t =t0 (6.12) Figure 6.5. PSCAD implementation of simplex method Figure 6.6. Convergence performance of cost function in simplex method 159 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Table 6.1. Optimization results of scaling factors scaling factors a1 a2 a3 initial guess 0.001 0.001 0.001 converged result 0.7369 0.3253 0.8221 6.3.4. Simulation Studies The stability concern is first evaluated for three-phase and single-phase faults without GUPFC in the power network and then with GUPFC. The dynamic simulations investigate the impact of faults (i) on the stability of synchronous/induction generators, (ii) on GUPFC performance when controlling real and reactive power flows as well as AC bus voltage. PSCAD and MATLAB are used simultaneously for simulating transient behavior of the models. The parameters of PI controllers, shown in Figure 6.1, are given in Appendix C. The capacitance of DC link is C=0.2 F. The performance of STFDC is examined for different disturbance conditions which lead to local mode of oscillations in conjunction with the following dynamic control tasks of the GUPFC: • Line-2 real power flow (PL2) using either FDC or STFDC by VSC2 • Line-2 reactive power flow (QL2) by VSC2 • Line-1 real power flow (PL1) by VSC3 • Line-1 reactive power flow (QL1) by VSC3 • Bus 1 voltage (V1) by VSC1 • DC link voltage (E) by VSC1 6.3.4.1. Case 1: Three-phase to Ground Fault A three-phase to ground fault of 120 ms duration is applied to Line-3 near Bus 1 at 8.5s. Pre-disturbance operating conditions are; PL1ref=1.75 pu, PL2ref=0.5 pu, QL1ref=QL2ref=0.0 pu, Eref=2.0 kV, and V1ref=1.0 pu. To have a quantitative comparison, the ITAE values between 8.5 s and 12.5 s are calculated for different 160 6. TRANSIENT STABILITY STUDIES A. Mete VURAL control schemes. Although, STFDC is only activated for VSC2 and Line-2 reactive power flow and Line-1 real and reactive power flows are controlled by simple PI controllers, it is found that STFDC indirectly smoothens the variations of simulated waveforms against fault and shows better performance than FDC in general. As evidence by response curves depicted in Figure 6.7a, STFDC performance is superior to FDC on SEDCIG rotor speed damping, being also better than that of PI controller. In Figure 6.7b, STFDC responses better than FDC and PI controller in damping SG oscillations with reduced undershoot/overshoot and less settling time. As the consequence of the fault, real and reactive power flow variations of Line-1, presented in Figures 6.7c and 6.7d, and those of Line-2 presented in Figures 6.7e and 6.7f are minimized better by STFDC with less undershoot/overshoot compared with the FDC. DC link voltage excursions of GUPFC for different damping control schemes are depicted in Figure 6.7g and it is found that among the two control schemes, the ITAE index is smaller for STFDC. In Figure 6.7h, PI controller settles Bus 1 voltage to its controlled value of 1.0 pu with a smaller ITAE value in case of STFDC. Effect of employing STFDC with optimized gains improves transient responses of both SEDCIG speed and IG speed. This situation is illustrated on Figures 6.7i and 6.7j, respectively. Voltage and current signals of the quasi multi-pulse converters after the fault are presented in Figure 6.8. In more detail, simulated phase shift angles of converters M and N and one selected GTO voltage are shown in Figure 6.9. (a) Transient response of SEDCIG speed under different control modes 161 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Transient response of SG speed under different control modes (c) Variation of Line-1 real power flow under different control modes (d) Variation of Line-1 reactive power flow under different control modes 162 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (e) Variation of Line-2 real power flow under different control modes (f) Variation of Line-2 reactive power flow under different control modes (g) DC link voltage excursions of GUPFC under different control modes 163 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (h) Variation of Bus 1 voltage under different control modes (i) Effect of optimized gains on transient response of SEDCIG speed (j) Effect of optimized gains on transient response of SG speed Figure 6.7. Simulated STFDC performance against three-phase fault 164 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Figure 6.8. Simulated voltage and current waveforms of GUPFC converters Figure 6.9. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage 6.3.4.2. Case 2: Three-phase Fault with Longer Duration The same fault is applied as in case 1 to Line-3 with an increased duration of 160 ms. Pre-disturbance operating conditions are changed as; PL1ref=0.8 pu, PL2ref=1.5 pu, QL1ref=QL2ref=0.0 pu, Eref=2.0 kV, and V1ref=1.0 pu. As shown in Figure 6.10a, longer fault results in a speed increase of SEDCIGs without GUPFC (steadystate speed is 1.483 pu which is not shown), making wind farm unstable in its 165 6. TRANSIENT STABILITY STUDIES A. Mete VURAL operation (Samuelsson et al., 2005). STFDC damps speed fluctuation of SEDCIG slightly better than FDC or PI controller with less overshoot characteristics. On the other hand, Figure 6.10b shows that STFDC exhibits good damping response to SG speed oscillations as compared with the FDC or PI controller with less settling time and less undershoot characteristics. It is observed that for both case1 and case2, SEDCIGs and SGs get stabilized and regain their original speed after fault clearance. The variations of real and reactive power flows of Line-1 shown in Figures 6.10c and 6.10d and the variation of reactive power flow of Line-2 in Figure 6.10f are indirectly improved by appointing STFDC generally with better control characteristics than FDC. When a comparison between Figures 6.10c and 6.10e is made particularly, STFDC holds better real power flow of Line-2 in its reference value than that of Line-1. Since STFDC commands the series converter which is inserted into Line-2, while only PI controller is activated for the series converter inserted into Line-1. DC voltage excursions of GUPFC depicted in Figure 6.10g are practically the same in case of both FDC and STFDC. Figure 6.10h shows that the Bus 1 voltage settles down to 0.7 pu and comes to 1.0 pu steadily, practically the same response for both FDC and STFDC, but with improved ITAE index in case of STFDC. Real and reactive power fluctuations of the wind farm and AC grid under two control modes are shown in Figure 6.11. STFDC mitigates these fluctuations effectively which overcomes the instability of PI controller. In particular, Figure 6.11b shows that without STFDC, the reactive power demand of the wind farm is very high due to the fault, which reduces substantially once the STFDC is activated instead of PI controller. 166 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (a) Transient response of SEDCIG speed under different control modes (b) Transient response of SG speed under different control modes (c) Variation of Line-1 real power flow under different control modes 167 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (d) Variation of Line-1 reactive power flow under different control modes (e) Variation of Line-2 real power flow under different control modes (f) Variation of Line-2 reactive power flow under different control modes 168 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (g) DC voltage excursions of GUPFC under different control modes (h) Variation of Bus 1 voltage under different control modes Figure 6.10. Simulated STFDC performance against longer three-phase fault (a) Real power output of the wind farm following three-phase fault 169 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Reactive power output of the wind farm following three-phase fault (c) Real power output of the SGs following three-phase fault (d) Reactive power output of the SGs following three-phase fault Figure 6.11. Power fluctuations following three-phase fault 170 6. TRANSIENT STABILITY STUDIES 6.3.4.3. A. Mete VURAL Case 3: Single-phase to Ground Fault The system is subjected to phase-A to ground fault on Line-3 near Bus 1 for a duration of 265 ms at 8.5 s. Pre-disturbance operating conditions are changed as; PL1ref=1.0 pu PL2ref=0.75 pu, QL1ref=QL2ref=0.0 pu, Eref=2.0 kV, V1ref=1.0 pu. Figures 6.12a and 6.12b shows the transient fluctuations of the SEDCIG speed and SG speed, respectively and provide a comparison between different control schemes. Besides, rise time and settling time of FDC and STFDC is practically the same for both generators, STFDC gives lower undershoot in case of SEDCIG and quantitative comparison shows better STFDC results for oscillation damping of SG speed. The waveforms in Figures 6.12c-f indicate that STFDC is again found to be superior to FDC in general when controlling real and reactive power flows of the lines after the fault both with reduced overshoot/undershoot characteristics and with smaller ITAE indices. Although undershoot in case of STFDC exceeds the undershoot in case of FDC by approximately 4.5% in Figure 6.12e, the steady-state error is more effectively minimized by STFDC and a minimum ITAE index is reached. DC voltage regulation of the GUPFC is satisfactory in Figure 6.12g and STFDC reduces DC voltage fluctuations significantly better than FDC. Figure 6.12h shows Bus 1 voltage variations following single-phase to ground fault. The AC voltage controller is again satisfactory like in previous case studies and gives practically the same response in case of FDC and STFDC with a better ITAE index than that of FDC. (a) Transient response of SEDCIG speed without GUPFC and with GUPFC 171 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Transient response of SG speed without GUPFC and with GUPFC (c) Variation of Line-1 real power flow under different control modes (d) Variation of Line-1 reactive power flow under different control modes 172 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (e) Variation of Line-2 real power flow under different control modes (f) Variation of Line-2 reactive power flow under different control modes (g) DC voltage excursions of GUPFC under different control modes 173 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (h) Variation of Bus 1 voltage following single-phase fault Figure 6.12. Simulated STFDC performance against single-phase to ground fault 6.3.4.4. THD Content Table 6.2 summarizes voltage distortions at Buses 1 and 2 as a measure of THD. Records of the simulated cases taken at 12.5 s show that THD values are within acceptable limits when STFDC is activated (IEEE, 1993). Consequently, filtering is not required even GTOs are switching at fundamental system frequency. THD V2(L-L) 1.26 % 1.25 % THD V1(L-L) THD V2(L-L) 1.53 % 1.29 % Case 3 THD V1(L-L) Case 2 Case 1 Table 6.2. THD values of power system bus voltages THD V1(L-L THD V2(L-L) 1.48 % 1.27 % 6.3.5. Discussion The newly proposed damping controller is robust to change in fault type and fault duration as well as robust to changing operating conditions of the power system. Better damping characteristics for local mode of oscillations of SG are achieved by GUPFC equipped with STFDC. Furthermore, STFDC can control SEDCIG speed better than FDC in case of a fault although SEDCIG speed signal is 174 6. TRANSIENT STABILITY STUDIES A. Mete VURAL not measured in the proposed damping control scheme. The successful operation of the shunt and series converters of the GUPFC is proven by maintaining constant DC link voltage and after faults GUPFC shows stable operation and able to restore real and reactive power flows of the transmission lines to their regulated values with significantly less variations in case of STFDC. This situation can claim longer transient fault duration that the system can withstand. It is also noted that shunt reactive power support of GUPFC improves voltage profile of the wind farm bus during transient conditions. 6.4. Transient Stability Improvement Using IPFC It is demonstrated in the previous section that, STFDC exhibits superior dynamic performance than classical PI controller with supplementary damping signal or a fixed fuzzy damping scheme in damping local mode of oscillations of SG and improves SEDCIG speed stability. In this section, STFDC, originally proposed for GUPFC, is adapted for IPFC to damp out inter-area mode of oscillations in a multimachine power system having many SGs, spread out two remote areas. 6.4.1. Power System Configuration Two-Area System shown in Figure 6.13 is used to illustrate an interconnected system of two remote areas without an infinite bus. Both areas are represented by aggregate machines which are connected together via double transmission line intertie. Following a large disturbance, such as short circuit, the system exhibits inter-area mode of oscillations where the two machines in each area act as single unit and swing coherently against the network at the other end of the line. Series converters VSC1 and VSC2 of the IPFC are positioned on Line-1 and Line-2, respectively by means of series coupling interfaces, tr1 and tr2. Using switches, sw1, sw2, and sw3, IPFC can also be operated as SSSC, required for the simulation cases. 10, 5, and 8 aggregated SGs, rated 120 MVA each, are operated in parallel to produce 1200 MVA (G1), 600 MVA (G2), and 960 MVA (G3) output, respectively. 175 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Figure 6.13. Two-Area System embedded with IPFC and its control scheme 176 6. TRANSIENT STABILITY STUDIES A. Mete VURAL All generators are driven by hydro-governors with solid-state exciters. Transmission line data of the system are given in Appendix B. 20 μF capacitor for each phase is installed at Bus 1 to boost bus voltage in steady-state operation. 100 MVA and 154 kV are chosen as base values and the start-up transients of the generators are not taken into account since the faults are considered soon after the system comes to steady-state. Two-Area System and IPFC having two quasi multipulse VSCs, and control blocks are modeled in PSCAD while fuzzy interfaces are designed in MATLAB fuzzy logic toolbox. PSCAD is interfaced with MATLAB through the custom written interface in PSCAD that exchanges data with MATLAB continuously at every solution time step of 100 µs, shown in Figure 6.14. On the contrary of GUPFC based transient stability studies in previous section, error derivative is adapted, instead of error integral as one of the inputs for STFDC since this configuration gives better results. Each VSC of IPFC is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 60 Hz, 8.33 MVA, 10/1/0.5774 kV with a leakage reactance of j0.1 pu. Each single-phase transformer of summing and magnetic interface is rated at 60 Hz, 16.67 MVA, 23.42/23.42 kV, j0.1 pu. Each single-phase transformer of series coupling magnetic interface is rated at 50 Hz, 33.33 MVA, 23.42/9.0 kV, j0.01 pu. Figure 6.14. PSCAD-MATLAB interface 177 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 6.4.2. Tuning of Scaling Factors The scaling factors (a1, a2, and a3) in STFDC configuration for GUPFC should be re-optimized using simplex method to normalize input and output variables of the STFDC, since a different type of multi-converter FACTS device is embedded into a different power system. The cost function is based on ITAEs of different measured generator speeds given in equation (6.13) where w1, w2, and w3 are the speeds of G1, G2, and G3 in Figure 6.13, respectively. For IPFC, the value of f is minimized from 0.2078 to 0.0399 in 97 iterations for a tolerance of 1.0E-6 as shown in Figure 6.15a. Similarly, for SSSC, the value of f is minimized from 0.2452 to 0.2221 in 60 iterations for a tolerance of 1.0E-6 as shown in Figure 6.15b. Simplex method is run when only FDC is executed while FGT is deactivated for both FACTS devices. The optimized parameters are listed in Table 6.3. f (a1 , a2 , a3 ) = ∫ (t ⋅ w1 − w2 + t ⋅ w1 − w3 )⋅ dt T (6.13) t =t0 6.4.3. Simulation Studies The stability of the Two-Area System is investigated without and with IPFC having STFDC by applying different types of faults with different durations. Moreover the damping feature of IPFC is compared with that of SSSC for all cases under the same control scheme. The impact of faults is also investigated on the performances of control loops of IPFC which is shown in Figure 6.13. PSCAD having a solution time step of 100 μs and MATLAB are communicated on-line for simulating transient behavior of the models. The chosen parameters of the PI controllers for the IPFC are given in Appendix C. The capacitance of DC link is C=0.2 F. Steady-state uncontrolled real power flows of the intertie are 0.975 pu for each transmission line. IPFC is activated for both Lines 1-2 when switch sw1 and sw3 are opened and sw2 is closed. SSSC is activated on Line-2 when switch sw2 and sw3 are opened and sw1 is closed. The performance of STFDC for both IPFC and 178 6. TRANSIENT STABILITY STUDIES A. Mete VURAL SSSC is examined individually for the same disturbance conditions applied to TwoArea System which lead to inter-area mode of oscillations in conjunction with the following dynamic control tasks of the IPFC and SSSC: • Line-1 real power flow by VSC1 of IPFC • Line-2 real power flow by VSC2 of IPFC • DC link voltage by VSC2 of IPFC • Line-2 real power flow by VSC2 (or SSSC) • DC link voltage by VSC2 (or SSSC) (a) for IPFC (b) for SSSC Figure 6.15. Cost function minimization for both FACTS devices a1 0.1 0.6 a2 0.1 0.6 179 a3 0.1 3.67 SSSC scaling factors initial guess converged result IPFC Table 6.3. Optimization results of scaling factors a1 0.1 0.75 a2 0.1 0.45 a3 0.1 4.60 6. TRANSIENT STABILITY STUDIES 6.4.3.1. A. Mete VURAL Case 1: Three-phase to Ground Fault Before applying disturbance, the reference values of tie-line flows, PLine-1 and PLine-2 are respectively set to 1.1 pu and 1.2 pu at the real power flow controllers of IPFC while the DC link voltage is regulated at 1.4 kV. The same reference value of PLine-2 is set for SSSC’s real power flow controller. Then a three-phase to ground fault near Bus 1 on Line-1 with 140 ms duration is applied at t=2.0 s. As shown in Figures 6.16a and 6.16b, the angle oscillations of generators G2 and G3 with respect to generator G1 are cumulative and lead to unstable operation when no FACTS device is activated. SSSC having only VSC2 exhibits weakly damped inter-area modes at approximately 0.50 Hz for both G2 and G3 with respect to G1. On the other hand, IPFC, having both VSC1 and VSC2, effectively damps out the oscillations caused by this severe disturbance in relatively short duration. Comparing the responses of IPFC to the SSSC compensation scheme in Figures 6.16c and 6.16d, the positive contribution of the proposed STFDC adapted for IPFC is clear when controlling intertie real power flows caused by inter-area oscillations. Figure 6.16e shows that the time responses of the DC link voltage of both SSSC and IPFC are practically the same which is highly required for proper VSC operation. Figure 6.16f shows reactive power flow fluctuations on Line-1 caused by three-phase disturbance when reactive power flow control function of IPFC is disabled to make a fair comparison to SSSC. Figures 6.16g and 6.16h show that STFDC equipped IPFC better improves bus voltage profiles of the intertie with smoother responses following three-phase fault when compared with STFDC equipped SSSC. Figures 6.17 and 6.18 shows some selected time domain signals of the two VSCs of IPFC which reveal stable converter operation. 6.4.3.2. Case 2: Two-phase to Ground Fault The system is disturbed by a two-phase (phases B and C) to ground fault near Bus 1 on Line-1 for 160 ms duration at t=2.0 s, while keeping the same predisturbance steady-state operating conditions as in case 1. The system is unstable 180 6. TRANSIENT STABILITY STUDIES A. Mete VURAL when there is no compensation is applied. Figures 6.19a and 6.19b show the responses of the generators G2 and G3 with respect to generator G1 when SSSC with STFDC are applied and when IPFC with STFDC are applied. The comparative timedomain results show that the stabilizing function of IPFC for inter-area oscillations is superior to those of SSSC even STFDC is adapted individually to both FACTS devices by optimizing its scaling factors. IPFC with STFDC easily stops the real power oscillations both on Lines 1 and 2 and forces them to their steady-state controlled values as shown in Figures 6.19c and 6.19d. When a particular comparison between Figures 6.16c and 6.19c is made, SSSC weakly suppresses power oscillation in case of two-phase to ground fault due to longer duration of fault. DC link voltage controllers of both SSSC and that of IPFC gives practically the same response to the short circuit as shown in Figure 6.19e. Figure 6.19f shows reactive power flow fluctuations on Line-1 when IPFC and SSSC are operated separately when reactive power flow control function of IPFC is disabled. Accordingly, as in case 1 the fluctuations are less as in case of IPFC when compared with SSSC. Figures 6.19g and 6.19h show that STFDC equipped IPFC better improves bus voltage profiles of the intertie with smoother responses following two-phase fault when compared with STFDC equipped SSSC. (a) Generator G2 rotor angle measured with respect to generator G1 rotor angle 181 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Generator G3 rotor angle measured with respect to generator G1 rotor angle (c) Variation of Line-2 real power flow following three-phase fault (d) Variation of Line-1 real power flow following three-phase fault 182 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (e) DC link voltage excursions of two FACTS devices following three-phase fault (f) Variation of Line-1 reactive power flow following three-phase fault (g) Variation of Bus 1 voltage following three-phase fault 183 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (h) Variation of Bus 2 voltage following three-phase fault Figure 6.16. Simulated STFDC performance following three-phase fault Figure 6.17. Simulated voltage and current waveforms of IPFC converters Figure 6.18. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage 184 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (a) Generator G2 rotor angle measured with respect to generator G1 rotor angle (b) Generator G3 rotor angle measured with respect to generator G1 rotor angle (c) Variation of Line-2 real power flow following two-phase fault 185 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (d) Variation of Line-1 real power flow following two-phase fault (e) DC link voltage excursions of two FACTS devices following two-phase fault (f) Variation of Line-1 reactive power flow following two-phase fault 186 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (g) Variation of Bus 1 voltage following two-phase fault (h) Variation of Bus 2 voltage following two-phase fault Figure 6.19. Simulated STFDC performance against two-phase fault 6.4.3.3. Case 3: Single-phase to Ground Fault The system is disturbed by a single-phase (phase C) to ground fault near Bus 1 on Line-1 for 200 ms duration at t=2.0 s, while keeping the same pre-disturbance steady-state operating conditions as in case 1. This relatively longer fault makes the multi-machine system operation unstable as large cumulative oscillations are observed both in time responses of generators’ relative angles and real power flows of intertie without any compensation scheme. In detail, Figures 6.20a and 6.20b 187 6. TRANSIENT STABILITY STUDIES A. Mete VURAL shows that IPFC with STFDC robustly stabilizes the inter-area mode of oscillations while SSSC with STFDC shows a poor suppressing function. Figures 6.20c and 6.20d show that IPFC endowed with the proposed STFDC eliminates the oscillations of the real power transmission of Line-2, between the two areas, and resumes the real power transmission to its controlled level before the fault. Figure 6.20e indicates that the DC link voltage controllers of both SSSC and that of IPFC gives practically the same response to the short circuit as in previous fault cases. Figure 6.20f shows reactive power flow fluctuations on Line-1 when IPFC and SSSC are operated separately when reactive power flow control function of IPFC is disabled as in previous fault scenarios. It is shown that the reactive power fluctuations are practically the same for two FACTS devices. Figures 6.20g and 6.20h show that STFDC equipped IPFC better improves bus voltage profiles of the intertie with smoother responses following single-phase fault when compared with STFDC equipped SSSC. (a) Generator G2 rotor angle measured with respect to generator G1 rotor angle 188 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Generator G3 rotor angle measured with respect to generator G1 rotor angle (c) Variation of Line-2 real power flow following single-phase fault (d) Variation of Line-1 real power flow following single-phase fault 189 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (e) DC link voltage excursions of two FACTS devices following single-phase fault (f) Variation of Line-1 reactive power flow following single-phase fault (g) Variation of Bus 1 voltage following single-phase fault 190 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (h) Variation of Bus 2 voltage following single-phase fault Figure 6.20. Simulated STFDC performance against single-phase fault 6.4.3.4. THD Content Table 6.4 summarizes voltage distortions of the intertie buses, namely Buses 1 and 2, as a measure of THD. Records of the simulated cases taken at 12.5 s show that THD values are within acceptable limits when STFDC is activated in both control loops of IPFC and SSSC (IEEE, 1993). Consequently, filtering is not required for the two FACTS devices even GTOs are switched at fundamental system frequency. Case 2 Case 3 IPFC Case 1 THD for V1(L-L) 0.29 % THD for V1(L-L) 0.25 % THD for V1(L-L) 0.12 % THD for V2(L-L) 0.18 % THD for V2(L-L) 0.15 % THD for V2(L-L) 0.10 % 191 SSSC Table 6.4. THD values of power system bus voltages THD for V1(L-L) 0.20 % THD for V1(L-L) 0.20 % THD for V1(L-L) 0.12 % THD for V2(L-L) 0.12 % THD for V2(L-L) 0.12 % THD for V2(L-L) 0.08 % 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 6.4.4. Discussion The originally proposed STFDC for one of the series converters of the GUPFC is adapted for one of the IPFC’s converters and SSSC by changing one of the inputs of the fuzzy interface and re-optimizing the scaling factors of the STFDC. STFDC is robust to change in fault-type and fault duration while damping inter-area mode of oscillations in Two-Area System. IPFC equipped with STFDC mitigates better angle oscillations of the generators than SSSC equipped with STFDC. Moreover, IPFC can control line real power flows of the intertie better than SSSC in case of faults. These results show that IPFC shows superior control characteristics, owing to the fact that IPFC has more control degrees of freedom than SSSC. Although there is no voltage control function is included either to IPFC or SSSC operations, both are able to make voltages of the intertie buses less oscillatory in case of severe faults. Successful operations of the IPFC and SSSC are proven by maintaining constant DC link voltage under fault scenarios. 6.5. Transient Stability Improvement using BtB-STATCOM 6.5.1. Power System Configuration To investigate BtB-STATCOM behavior under large disturbances, the SMIB system shown in Figure 6.21 is simulated for the study purpose when fault scenarios in different case studies are separately applied. Shunt converters VSC1 and VSC2 of the BtB-STATCOM are positioned at Buses 1 and 2, respectively by means of shunt coupling interfaces, tr1 and tr2. It is aimed to provide controlled real power transfer from 120 MVA rated SG to the infinite bus, while regulating neighboring bus voltages by means of BtB-STATCOM. The control schemes of the two converters are also depicted in Figure 6.21. SG is driven by hydro-governor with solid-state exciter. Simulated system has two 50 km transmission lines having data identical to the line positioned between Buses 1 and 4 in Section 6.4 with base values of 100 MVA, 154 kV, and 60 Hz. 192 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Figure 6.21. Power system configuration embedded with BtB-STATCOM 193 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Power system and BtB-STATCOM having two quasi multi-pulse VSCs, and control blocks are simulated in PSCAD with a solution time step of 100 µs. Each VSC of BtB-STATCOM is rated at 100 MVA. Each single-phase three-winding transformer in twelve-pulse converter unit is rated at 60 Hz, 8.33 MVA, 20/2/1.1548 kV with a leakage reactance of j0.1 pu. Each single-phase transformer of summing and magnetic interface is rated at 60 Hz, 16.67 MVA, 137.92/38 kV, j0.1 pu. 6.5.2. Simulation Studies The stability of the SMIB system is investigated without and with BtBSTATCOM having the PI control schemes shown in Figure 6.21 by applying different types of faults with different durations. The damping ability of BtBSTATCOM is evaluated for all cases with this respect. The impact of faults is also investigated on the performances of control loops of BtB-STATCOM. PSCAD having a solution time step of 100 μs is used for simulating transient behavior of the SMIB system embedded with BtB STATCOM. The chosen parameters of the PI controllers for BtB-STATCOM are given in Appendix C. The capacitance of DC link is C=0.2 F. Using switches sw1 and sw2, BtB-STATCOM can be bypassed with a line, required for the simulation cases. For instance, when sw1 is closed while sw2 is opened, BtB-STATCOM is bypassed by a short line. When sw1 is opened while sw2 is closed, BtB-STATCOM is in operation alternatively. The following dynamic control tasks of the BtB-STATCOM are examined for different disturbance conditions: • Bus-1 voltage control by VSC1 of BtB-STATCOM • Bus-2 voltage control by VSC2 of BtB-STATCOM • DC link voltage by VSC2 of BtB-STATCOM • Real power transfer control by VSC1 of BtB-STATCOM 194 6. TRANSIENT STABILITY STUDIES 6.5.2.1. A. Mete VURAL Case 1: Three-phase to Ground Fault at Generator Bus Three-phase to ground fault at 30.0 s for a duration of 120 ms is applied near Bus 1 in Figure 6.21. Simulated waveforms of the SMIB system embedded with BtB-STATCOM following this severe disturbance are presented in Figure 6.22. Figure 6.22a shows that SG speed under the fault decreasingly oscillates for about 15 s when BtB-STATCOM is deactivated, but returns to its steady-state value with a slight drop when BtB-STATCOM is in operation. The 0.0015 pu steady-state speed difference is due to different demanded real power from SG in two different cases. The nominal value of the real power exchange from Bus 1 to Bus 2 is around 0.45 pu (45 MW) when a short line connects these two buses. Following fault, real power exchange oscillates for a duration of around 8 s as shown in Figure 6.22b. With the inclusion of BtB-STATCOM which ties neighboring buses, the oscillation is almost damped out with a steady-state increase of real power exchange to 0.8 pu (80 MW). Figure 6.22c shows that the DC link voltage of the BtB-STATCOM decreases for a short time when the fault occurs at Bus 1 and restored to its controlled value immediately, not affecting the operation of BtB-STATCOM. Reactive power demand of SG in Figure 6.22d is temporarily increased under the fault, but it restores immediately without losing stability when the fault is cleared. Figures 6.22e and 6.22f depicts that the dynamic voltage support within the study system is effectively provided by BtB-STATCOM at two neighboring buses under the three-phase fault. Figure 6.23 shows the traces of simulated voltage and current waveforms of BtBSTATCOM converters following three-phase fault. Figure 6.24 shows the traces of simulated phase shift angles (ɸM and ɸN) and selected GTO’s anode-to-cathode voltages of BtB-STATCOM converters following three-phase fault. 195 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (a) Transient response of SG speed following three-phase fault (b) Transient response of SG real power output following three-phase fault (c) DC link voltage excursions of BtB-STATCOM following three-phase fault 196 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (d) Variation of SG reactive power output following three-phase fault (e) Variation of Bus 1 voltage following three-phase fault (f) Variation of Bus 2 voltage following three-phase fault Figure 6.22. Simulated BtB-STATCOM performance in case 1 197 6. TRANSIENT STABILITY STUDIES A. Mete VURAL Figure 6.23. Simulated voltage and current waveforms of the converters Figure 6.24. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage 6.5.2.2. Case 2: Three-phase to Ground Fault at Infinite Bus In this case, a relatively longer three-phase to ground fault is applied near Bus 2 (infinite bus) in Figure 6.21. The fault is lasted for 160 ms. Simulated waveforms of the power system configuration embedded with BtB-STATCOM following the disturbance are presented in Figure 6.25. The speed oscillations of the SG like the one in previous case study are observed in Figure 6.25a when BtB-STATCOM is deactivated. The oscillation duration is relatively shorter than that of previous case 198 6. TRANSIENT STABILITY STUDIES A. Mete VURAL since there is short line between SG and the fault location. When BtB-STATCOM is activated, SG speed oscillation is better damped out when compared with the previous case study. Moreover the slight drop in speed is not observed following three-phase fault. This is due to the fact that the fault is occurred near a stiff bus and BtB-STATCOM isolates the disturbance from SG with its converters. The same steady-state speed difference of the SG (0.0015 pu) is observed like the one in previous case study, due to the same loading condition of the SG as expected. In Figure 6.25b, the maximum overshoot of the controlled SG real power output (0.8 pu) is significantly reduced in this case with a better response of the BtB-STATCOM to the fault. The DC link voltage fall in Figure 6.25c is unavoidable. However, as soon as the fault is cleared, DC link voltage restores to its reference without affecting BtB-STATCOM operation. Reactive power demand of the SG in Figure 6.25d restores immediately to its pre-fault value as soon as the fault is cleared. A less undershoot shows up than that of previous case due to the fault isolation feature of the BtB-STATCOM. Figures 6.25e and 6.25f depicts that the dynamic voltage support within the study system is effectively provided by BtB-STATCOM at two neighboring buses under the three-phase fault. In detail, the drop in Bus 2 voltage is not avoided. However the voltage is controlled with less overshoot when BtBSTATCOM is activated. (a) Transient response of SG speed following three-phase fault 199 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (b) Transient response of SG real power output following three-phase fault (c) DC link voltage excursions of BtB-STATCOM following three-phase fault (d) Variation of SG reactive power output following three-phase fault 200 6. TRANSIENT STABILITY STUDIES A. Mete VURAL (e) Variation of Bus 1 voltage following three-phase fault (f) Variation of Bus 2 voltage following three-phase fault Figure 6.25. Simulated BtB-STATCOM performance in case 2 6.5.2.3. THD Content Voltage distortions at Buses 1 and 2 as a measure of THD are listed in Table 6.5. Records of the simulated cases show that THD values are within acceptable limits when BtB-STATCOM is in operation (IEEE, 1993). Even GTOs are switched at fundamental system frequency, filtering is not required due to low THD content. 201 6. TRANSIENT STABILITY STUDIES A. Mete VURAL THD V1(L-L) 1.38 % THD V2(L-L) 1.36 % Case 2 Case 1 Table 6.5. THD values of power system bus voltages THD V1(L-L) THD V2(L-L) 1.37 % 1.36 % 6.5.3. Discussion It is shown that BtB-STATCOM, although not utilized primarily for enhancing power system stability, can also be used to damp out generator speed oscillations effectively even with simple PI controllers without any speed signal measurement. DC power transmission among the two VSCs enables both controlled real power exchange from one bus to another and improving power system stability with the feature of isolating the fault from the rest of the power system in case of a fault. As it can be seen the oscillations in the DC link are hardly noticeable. The internal simulated signals of BtB-STATCOM show that the stable operation can be achieved both in steady- and transient states in case of a severe disturbance while providing reactive power to the neighboring buses for voltage control. Near-full rate of the converters are achieved by setting the reference value of the real power exchange among the two VSCs to relatively a large value of 0.8 pu. 6.6. Summary In this chapter, strong control capability of the GUPFC with regulating multiline flows and bus voltage is extended with an optimized self-tuned fuzzy control scheme for oscillation damping in a wind farm integrated power system. It is shown both graphically and quantitatively that the proposed damping scheme is robust in its performance over a range of disturbance conditions and does not only improves transient stability of induction/synchronous generators but also assists indirectly to other GUPFC control functions which are tightly interacted with each other. The proposed control scheme is model independent since the design is based on instantaneous system states rather than system parameters. With the inclusion of quasi-multi pulse converters switching at 60 Hz into the grid, harmonic content 202 6. TRANSIENT STABILITY STUDIES A. Mete VURAL complies with the regulations. Hence, no filter is required for harmonic reduction at the line side of the GUPFC converters. Multi-line power flow control function of IPFC is extended with the optimized self-tuned fuzzy control scheme, originally proposed for GUPFC, to robustly mitigate inter-area mode of oscillations of a multi-machine power system having two remote areas which are tied by double transmission circuit. The performance of the damping scheme is verified graphically using time domain instantaneous responses of the system states to various faults. As also shown in GUPFC based transient stability studies, the proposed damping scheme assists indirectly to the other real power flow control loop of the IPFC where damping scheme is not utilized. The robustness of the proposed fuzzy damping scheme is further verified by adapting it to the real power flow control loop of SSSC, which yield particular performance comparison between IPFC and SSSC. The quasi-multi pulse converters of the FACTS devices do not disturb power quality in terms of harmonic content, which complies with the regulations. Hence, no filter is required at the line side of the converters. Multi-control function of BtB-STATCOM is examined without any damping control scheme for improving power system stability considering various faults with different locations and durations. The obtained results confirm that the real power transfer controller of PI type of BtB-STATCOM can provide adequate damping of generator speed oscillations owing to the segmentation of the power system with the DC link of BtB-STATCOM. At the same time, it is ensured that all BtB-STATCOM control loops are working truly without losing stability under different fault scenarios. Voltage profiles of the neighboring buses are also improved with fast and independent reactive power support of BtB-STATCOM converters in both steadyand transient states. 203 6. TRANSIENT STABILITY STUDIES A. Mete VURAL 204 7. CONCLUSIONS AND FUTURE WORK 7. A. Mete VURAL CONCLUSIONS AND FUTURE WORK Now, more than ever, electrical power systems should be engineered in a flexible and controllable fashion in response to ongoing expansion and growth of the electrical power demand as well as increasing competitiveness and strict regulations of transactions between electric power companies. To achieve both operational flexibility and reliability, the existing transmission network should be utilized more efficient under the fact that there are many obstacles to build new ones. Flexible Alternating Current Transmission Systems (FACTS) are the power electronics based high power equipment with advanced control techniques that can provide solutions to new operating challenges of modern power systems. As the price of power semiconductor devices are getting low with increasing voltage/current ratings, FACTS devices are seen to be principal for the reliable and secure operation of evolving electrical power systems and the number of FACTS device installations will increase in the world. Although, the practical application of the multi-converter FACTS devices is still in its infancy, multi-converter FACTS devices are promising as multiple and fast response compensators for the modern power systems in near future. For the multi-converter FACTS devices to be included in transmission system plans, there must be appropriate models for all the analyses that are normally performed. Simulation has long been recognized as an important and necessary procedure for the development, design, and testing phases of FACTS devices. Recent advances in both computing hardware, and sophisticated power system component modeling techniques have significantly increased the applications of digital simulation of the power system industry embedded with advanced compensators, such as FACTS devices. In this thesis, both 50 Hz and 60 Hz systems are addressed for the investigation of potential FACTS device applications. Moreover, PSCAD is interfaced to MATLAB through a custom written interface so that PSCAD is able to execute one or more fuzzy inference systems which is/are not available in PSCAD master library. 205 7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL In the work reported in this thesis, a review of the state of the art is introduced based on the simplified power circuit configuration and operating characteristics of the first and the second generation of FACTS devices ranging from single- to multiconverter topologies. Power flow (load flow) analysis is an important tool for power system planning in which the transmission constraints can also be determined in a given network. Power flow solution gives information about the magnitude and phase angle of the voltage at each bus as well as real and reactive power flows in each line for given generation, load, and transmission network data of a power system. In this context, the steady-state models of the GUPFC, IPFC, and BtB-STATCOM are proposed and designed in PSCAD environment even PSCAD is primarily aimed to simulate transient responses of the power system components. Developed models are verified in various multi-bus power systems to demonstrate the capability of steadystate controls of the real and reactive power flows on transmission lines as well as to regulate system bus voltage. Steady-state models of STATCOM, SSSC, and UPFC are also developed. Particular performance comparison is made between the aforementioned FACTS devices. The advantage of this approach is fast, modular and requiring no programming effort to include power injections and their derivatives with respect to the state variables power system, such as bus voltages and their respective phase angles, at the suitable locations of the Jacobian matrix and mismatch vector. It is concluded that as long as the operational and control constraints are satisfied, theoretically there is no limit in the number of VSCs which are employed for building up the FACTS device. The method can suffer from long computation time and may require high CPU computing power with large memory if many multi-converter FACTS devices are embedded into relatively large power systems having many buses. In this thesis, eight two-level force-commutated converters are joined together using magnetic interfaces to realize quasi multi-pulse converter operation for multi-converter FACTS device applications. The quasi multi-pulse converter is the building block of converter-level modeling studies of the multi-converter FACTS devices. Appropriate adjustment of individual phase-shifted angles of the two groups 206 7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL of series converters makes it possible to independently control the amplitude and the phase of the AC voltage of the quasi multi-pulse converter. The quasi multi-pulse converter based GUPFC, IPFC, and BtB-STACOM are successfully modeled in PSCAD, including a detailed representation of the simulation design parameters. The presented time-domain simulation results verify adequate operations of the GUPFC, IPFC, and BtB-STATCOM separately, as well as demonstrating the successful operations of the designed controllers. The proposed converter-level models of the multi-converter FACTS devices can be directly implemented in any software package that has a graphical interface. The models are independent of the type of the control schemes applied for any multi-converter FACTS device. The simplex optimization method and fuzzy logic techniques are used in designing controllers of the multi-converter FACTS devices for various control purposes. In the simplex optimization method, the cost function is minimized to optimize single- and multi-controllers of the concerned multi-converter FACTS device. Fuzzy logic theory is used to design two novel controllers for IPFC and GUPFC, which are examined through time domain simulations of various case studies applied in a variety of power systems. The first novel controller is based on the combination of a conventional PI controller and a Mamdani-type fuzzy inference system for the quasi multi-pulse IPFC, designed for high performance decoupling action between controlled real and reactive power flows of a transmission line. In general this control scheme can be employed in any series converter of the multiconverter FACTS device, for instance UPFC or GUPFC to relieve inherent real and reactive power flow coaction. On the contrary of analytically decoupled gain design, the proposed control scheme is robust and does not rely on system mathematical model. Consequently it adapts itself to parameter variations in the power system and performs better. There is also an option to activate fuzzy component only when a change in either real or reactive power flow command occurs. Such coordination can yield improved rise time and settling time for start-up transients in simulation environment. Low frequency generator oscillations are commonly experienced due to severe disturbances in the form of either local mode or inter-area mode of 207 7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL oscillations in some parts or between parts of the interconnected power systems. Local modes of oscillations take place as the synchronous generator swing with respect to its reference speed or against the other generators in a certain area. On the other hand, inter-area modes of oscillations occur as the synchronous generator swing against each other which are remotely located with each other. The frequency range of these oscillations is ranging from 0.1 to 2.5 Hz and may lead to total or partial power interruption if not damped out effectively. The second novel controller is based on self-tuned fuzzy damping scheme and successfully implemented in GUPFC and IPFC configurations to suppress oscillation damping and hence improve the transient stability of the power system, even interconnected with wind farm. The damping control strategy is based on the fuzzified manipulation of the q-component of the series converter voltage vector in response to the change in both error and its integral/derivative. The self-tuning mechanism enables the damping controller to cope with different operating points since the output of the controller is tuned on-line. Extensive digital simulations in PSCAD are carried out to examine the damping action of the proposed controller under various system conditions. These include changes in power flow levels, change of fault type together with its location and duration. The speed and rotor angle deviations of the synchronous generators are damped out quickly than a system without either GUPFC or IPFC. In this sense, the controller performance is proven in terms of robustness and the presented time-domain simulations validate the proposed control design. A brief comparison of the IPFC and SSSC is given in terms of providing stability to a disturbed power system. It is concluded that for parallel transmission lines, installing IPFC with two VSCs seems to be a better solution option to damp inter-area mode of oscillations, as an alternative to SSSC. It is shown that for BtB-STATCOM, conventional PI controllers are not only adequate for steady-state power system parameter control but also suitable for oscillation damping to enhance power system stability. Back-to-back operation of high power converters enable load transfer between two interconnected grids, without having to disconnect and then reconnecting it to the other system using mechanical switches. 208 7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL The controllers designed in this work are general and can be applied to other FACTS devices easily. The results and discussions presented in this thesis will provide valuable information to electric power utilities/companies in the near future that are engaged in the planning and operation of the FACTS devices in Turkey where mostly few STATCOM installations are reported. This thesis reveals the potential usage and benefits of GUPFC, IPFC, and BtB-STATCOM applications for intelligent control of future grids having distributed energy resources, with emphasis on high power applications of converters with low THD. Further research can be carried out in the following paragraphs: • This thesis is focused on the performance evaluation of the multi-converter FACTS devices operating individually. As a future work, the interaction and the coordination of different types of single- and/or multi-converter FACTS devices, spread out in large power systems, can be studied in steady- and/or transient states. • The benefits of the integration of energy storage systems to the multiconverter FACTS devices can provide extra dynamic real power capabilities to enhance stability and reliability of the transmission and distribution systems. In this regard, potential application characteristics can be investigated. • Distribution static synchronous compensator (D-STATCOM) is well addressed as voltage controller or power factor controller in distribution networks. Similarly, the concept of GUPFC and IPFC can be shifted from transmission level to distribution level for real-time control of multisystem parameters simultaneously and independently in micro grid applications including renewable energy sources such as solar and/or wind energy. • Based on the experience gained from this work and the simulation results accomplished, practical applications of GUPFC, IPFC, or BtB-STATCOM operations can be implemented and investigated by designing their scaled laboratory prototypes operating in low or medium voltage levels. 209 7. CONCLUSIONS AND FUTURE WORK 210 A. 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Modelling of the interline power flow controller and the generalised unified power flow controller in Newton power flow, IEE Proceedings, Generation, Transmission and Distribution, vol. 150, no. 3, pp. 268- 274. 225 226 CIRRICULUM VITAE Education: PhD Electrical and Electronics Engineering Msc Electrical and Electronics Engineering Bsc Electrical and Electronics Engineering Çukurova University 2009-….. University of Gaziantep and University of Strathclyde (as visitor scholar in 2000) University of Gaziantep 1999-2001 Work Experience: Hasan Kalyoncu University, Electrical and Electronics Engineering Department Atılım University, Electrical and Electronics Engineering Department Wuppertal University, Automation and Control Engineering Department,Germany Gaziantep University, Electrical and Electronics Engineering Department Full-time instructor Full-time instructor Research assistant Research assistant 1995-1999 July-2011 / present Sept-2008 / June-2011 Nov-2004 / Mar-2007 Aug-1999 / Nov-2004 Research Interests: • • • Modeling and control of FACTS devices Computational intelligence applications to FACTS device control Power system simulation Professional Activities: • Refereeing International Journal of Electrical Power and Energy Systems IET Generation, Transmission & Distribution Turkish Journal of Electrical Engineering & Computer Sciences Journal of Electrical and Electronics Engineering Research World Journal of Modeling and Simulation Journals of Zhejiang University-Science-C (Computers & Electronics) Ain Shams Engineering Journal • IEEE student member since 1999 • EMO member since 1999 227 Given Courses: EE 451 - Power System Analysis EE 452 - High Voltage Techniques EE 450 - Electrical Machinery and Drives EEE 101 - Introduction to Electrical and Electronics Engineering EEE 120 - Introduction to MATLAB EEE 201/202 - Circuit Analysis I-II EE 203 - Digital Circuits and Systems EE 403 - Communication Networks EE 491/492 - Design Project I-II MATH 151 - Calculus I Publications: • Journals (SCI-E) VURAL A.M., BAYINDIR K.Ç., 2012. Transient stability enhancement of the power system interconnected with wind farm using generalized unified power flow controller with simplex optimized self-tuning fuzzy damping scheme, International Review of Electrical Engineering, vol. 7, no. 4, pp. 5091-5107. VURAL A.M., BAYINDIR K.Ç., 2012. A hybrid fuzzy-PI control scheme for a quasi multi-pulse interline power flow controller including PQ decoupling feature, Journal of Power Electronics, vol. 12, no. 5, pp. 787-799. VURAL A.M., BAYINDIR K.Ç., 2011. Two-level quasi multi-pulse voltage source converter based generalized unified power flow controller, International Review of Electrical Engineering, vol. 6, no. 5, pp. 2622-2637. VURAL A.M., TÜMAY M., 2007. Mathematical modeling and analysis of a unified power flow controller: A comparison of two approaches in power flow studies and effects of UPFC location, International Journal of Electrical Power & Energy Systems, vol. 29, issue 8, pp. 617-629. TÜMAY M., VURAL A.M., LO K.L., 2004. The effect of unified power flow controller (UPFC) location in power systems, International Journal of Electrical Power & Energy Systems, vol. 26, issue 8, pp. 561-569. VURAL A.M., TÜMAY M., 2004. Analysis and modeling of unified power flow controller: Modification of Newton-Raphson algorithm and user-defined 228 modeling approach for power flow studies, Arabian Journal for Science and Engineering, vol. 29, no: 2B, pp. 135-153. TÜMAY M., VURAL A.M., LO K.L., 2005. Simulation of unified power flow controller by using modified power injection model, Iranian Journal of Science and Technology, vol. 29, pp. 49-64. • Journals VURAL A.M., BAYINDIR K.Ç., 2011. Quasi multi-pulse back-to-back static synchronous compensator employing line frequency switching 2-level GTO inverters, World Academy of Science, Engineering and Technology, issue 60, pp. 1863-1874. VURAL A.M., BAYINDIR K.Ç., 2011. Simplex optimized twelve-pulse STATCOM control system and LC filter, European Journal of Scientific Research vol. 64, issue 3, 2011. TÜMAY M., EKER İ., AKSOY H.F., VURAL A.M., ÜNVER M.U., 2002. Dynamic performances of adjustable Speed AC drives part I: Dynamic modelling and implementation of PWM-fed synchronous and asynchronous machines, Information Technology Journal, vol.1, no. 2, pp. 98-105. TÜMAY M., EKER İ., AKSOY H.F., VURAL A.M., ÜNVER M.U., 2002. Dynamic performances of adjustable speed AC drives part II: Control and simulation of AC machines, Information Technology Journal, vol. 1, no. 2, pp. 106-117. • International Conferences VURAL A.M., BAYINDIR K.Ç., 2012. Converter level modeling and control of quasi multi-pulse static synchronous series compensator, IEEE Symposium on Electrical and Electronics Engineering, EEESYM’2012, pp. 698-702. VURAL A.M., BAYINDIR K.Ç., 2012. Understanding the steady-state modeling and analysis of power systems embedded with VSC-based FACTS devices, IEEE EnergyTech2012. 229 VURAL A.M., BAYINDIR K.Ç., 2010. Optimization of parameter set for STATCOM control system, IEEE PES, Transmission and Distribution Conference and Exposition, pp. 1-6. VURAL A.M., TÜMAY M., 2003. Steady state analysis of unified power flow controller: Mathematical modeling and simulation studies, IEEE Powertech Conference, vol. 4. EKER İ., VURAL A.M., 2003. Experimental on-line identification of a three-mass mechanical system, IEEE Conference on Control Applications, vol. 1, pp. 6065. VURAL A.M., TÜMAY M., 2003. Power flow analysis of power system embedded with UPFC using Psasp program, International Conference on Electrical and Electronics Engineering, ELECO’2003, pp.22-26. EKER İ., VURAL A.M., SÜSLÜOĞLU B., 2003. Experimental identification of an electromechanical system running in open-loop conditions, International Conference on Electrical and Electronics Engineering, ELECO’2003, pp. 284-288. VURAL A.M., TÜMAY M., 2001. UPFC for controlling power flow in power systems, International Conference on Electrical and Electronics Engineering, ELECO’2001, pp. 1-4. VURAL A.M., EKER İ., 2004. Parameter identification of a permanent magnet DC motor: An experimental approach, International Conference on Electrical Machines, ICEM’2004, paper no. 104. • National Conferences VURAL A.M., BAYINDIR K.Ç., TÜMAY M., 2009. 12 darbeli bir STATCOM için denetleyici ve filtre parametrelerinin simplex yöntemi ile optimizasyonu, 13. Elektrik, Elektronik, Bilgisayar, Biyomedikal Mühendisliği Ulusal Kongresi, ODTÜ, Ankara. VURAL A.M., TÜMAY M., 2003. Gelişmiş güç akış denetleyicileri ile donatılmış güç sistemlerinin Newton-Raphson metodu ile analizi, 10. Ulusal Elektrik-Elektronik-Bilgisayar Mühendisliği Kongresi, İstanbul, pp. 63-66. 230 VURAL A.M., EKER İ., SÜSLÜOĞLU B., 2003. Doğal mıknatıslı bir DC motorun deneysel olarak tanılaması, 10. Ulusal Elektrik-Elektronik-Bilgisayar Mühendisliği Kongresi, İstanbul, pp. 122-125. VURAL A.M., EKER İ., 2003. Least squares on-line identification of a dc motor, Mühendislik Bilimleri Genç Araştırmacılar 1. Kongresi, İstanbul, pp. 183190. VURAL A.M., TÜMAY M., MA T.T., 2001. Güç sistemlerindeki güç akışının UPFC ile kontrolü, 9. Ulusal Elektrik-Elektronik-Bilgisayar Mühendisliği Kongresi, Bursa, pp. 196-199. 231 232 APPENDIX 233 APPENDIX A: Converter Design Data for Power Flow Studies A1. WSCC 3-Machine 9-Bus System and IEEE 14-Bus System • Shunt/Series Converters Component name : Three-phase voltage source model 2 Base frequency : 60 Hz Maximum voltage : 30 kV (line-to-line rms) Voltage ramp up time : 0.05 s • Shunt Coupling Magnetic Interface Component name : Three-phase two-winding transformer (x1) Base power : 100 MVA Base frequency : 60 Hz Winding voltage : 330 kV / 30 kV (Y/Δ) () Leakage reactance : 0.01 pu • Series Coupling Magnetic Interface Component name Base power Base frequency Winding voltage Leakage reactance : Single-phase two-winding transformer (x3) : 33.3333 MVA : 60 Hz : 15.4 kV / 90 kV (line-to-line rms) : 0.001 pu A2. 3-Machine 7-Bus System • Shunt Converter Component name : Three-phase voltage source model 2 Base frequency : 50 Hz Maximum voltage : 30 kV (line-to-line rms) Voltage ramp up time : 0.05 s • Shunt Coupling Magnetic Interface Component name Base power Base frequency Winding voltage Leakage reactance : Three-phase two-winding transformer (x1) : 100 MVA : 50 Hz : 170 kV / 30 kV (Y/Δ) (line-to-line rms) : 0.01 pu 234 APPENDIX B: Test Systems Data B1. WSCC 3-Machine 9-Bus System (230 kV, 60 Hz, 100 MVA base) Generation Data: Generator No: 1 2 3 Location Bus 1 Bus 2 Bus 3 Voltage: 16.5 kV 18.0 kV 13.8 kV Transformer No: 1 2 3 Location Bus 1-Bus 4 Bus 2-Bus 7 Bus 3-Bus 9 Real MW Swing Bus 163 85 Transformer Data: Tap: 16.5 / 230 kV 18.0 / 230 kV 13.8 / 230 kV X (pu) 0.0576 0.0625 0.0586 Load Data: Load No: 1 2 3 Location Bus 5 Bus 6 Bus 8 Real MW 125 90 100 Reactive MVAR 50 30 35 Line Data: Line No: 1 2 3 4 5 6 Location: Bus 4-Bus 5 Bus 4-Bus 6 Bus 5-Bus 8 Bus 6-Bus 9 Bus 7-Bus 8 Bus 8-Bus 9 R (pu) 0.01000 0.01700 0.03200 0.03900 0.00850 0.01190 235 X (pu) 0.08500 0.09200 0.16100 0.17000 0.07200 0.10080 B/2 (pu) 0.04400 0.03950 0.07650 0.08950 0.03725 0.05225 B2. IEEE 14-Bus System (230 kV, 60 Hz, 100 MVA base) Generation and Load Data: Bus No: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Bus Generation: Real Reactive MW MVAR 232.4 -16.9 40.0 42.4 0.0 23.4 0.0 0.0 0.0 0.0 0.0 12.2 0.0 0.0 0.0 17.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Real MW 0.0 21.7 94.2 47.8 7.6 11.2 0.0 0.0 29.5 9.0 3.5 6.1 13.5 14.9 Bus Load: Reactive MVAR 0.0 12.7 19.0 -3.9 1.6 7.5 0.0 0.0 16.6 5.8 1.8 1.6 5.8 5.0 Line Data: Line No: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Location: Bus 1-Bus 2 Bus 2-Bus 3 Bus 2-Bus 4 Bus 1-Bus 5 Bus 2-Bus 5 Bus 3-Bus 4 Bus 4-Bus 5 Bus 7-Bus 8 Bus 7-Bus 9 Bus 9-Bus 10 Bus 6-Bus 11 Bus 6-Bus 12 Bus 6-Bus 13 Bus 9-Bus 14 Bus 10-Bus 11 Bus 12-Bus 13 Bus 13-Bus 14 R (pu) 0.01938 0.04699 0.05811 0.05403 0.05695 0.06701 0.01335 0.00000 0.00000 0.03181 0.09498 0.12291 0.06615 0.12711 0.08205 0.22092 0.17093 X (pu) 0.05917 0.19797 0.17632 0.22304 0.17388 0.17103 0.04211 0.17615 0.11001 0.08450 0.19890 0.25581 0.13027 0.27038 0.19207 0.19988 0.34802 B/2 (pu) 0.02640 0.02190 0.01870 0.02460 0.01700 0.01730 0.00640 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 Transformer Data: Transformer No: 1 2 3 Location: Bus 4-Bus 7 Bus 4-Bus 9 Bus 5-Bus 6 Tap: 0.978 0.969 0.932 X (pu) 0.20912 0.55618 0.25202 • Condenser is connected at Bus 8 to regulate bus voltage at 1.09 pu • Shunt capacitance of 2.6465 µF is connected at Bus 9 236 B3. 3-Machine 7-Bus System (154 kV, 50 Hz, 100 MVA base) Generation and Load Data: Bus No: 1 2 3 4 5 6 7 Bus Generation: Real Reactive MW MVAR 317.8 369.4 50.0 0.0 0.0 0.0 50.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Real MW 0.0 200 0.0 200 0.0 0.0 0.0 Bus Load: Reactive MVAR 0.0 150 0.0 150 0.0 0.0 0.0 Line Data: Line No: 1 2 3 4 5 6 7 8 9 Location: Bus 1-Bus 2 Bus 1-Bus 5 Bus 1-Bus 4 Bus 2-Bus 3 Bus 2-Bus 3 Bus 3-Bus 4 Bus 3-Bus 4 Bus 2-Bus 6 Bus 4-Bus 7 R (pu) 0.0075 0.00000 0.00476 0.00527 0.00527 0.00527 0.00527 0.00000 0.00000 X (pu) 0.1324 0.00099 0.08390 0.09276 0.09276 0.09276 0.09276 0.00020 0.00020 B/2 (pu) 0.04340 0.00000 0.02750 0.03030 0.03030 0.03030 0.03030 0.00000 0.00000 B4. 4-Machine 4-Bus System (154 kV, 50 Hz, 100 MVA base) G1 and G3 terminal voltage is 1.0 pu with a phase shift of 0.0º. G2 and G4 terminal voltage is 0.974 pu with a phase shift of 10.0º. Series inductive reactances of all generators are 0.0265 pu. Each transmission line is identical having resistance=0.01938 pu, inductive reactance=0.05917 pu, susceptance =0.0528 pu. B5. Wind Farm Integrated Power System (154 kV, 60 Hz, 100 MVA) Wind turbine parameters: 2.5 MVA, rated angular mechanical speed= 20 Hz, ρ = 1.225 kg/m3, A= 5026 m2 with a rotor radius of 40 m, gear box efficiency = 97 %, gear ratio (machine/turbine) = 55. SEDCIG parameters: 2.5 MVA, 0.86 pf lagging (without fixed capacitors), VLL=13.8 kV, base angular frequency=60 Hz, Rs = 0.066 pu, Rr1= 0.298 pu, Rr2=0.018 pu, Ls = 0.046 pu, Lm = 3.86 pu, Lr1=0.122 pu, Lr2 = 0.105 pu, J=2H=3.40 237 s, mechanical damping = 0.01 pu. 20 SEDCIGs are operated in parallel to give 50 MVA output. SG parameters: 120 MVA, VLL=13.8 kV, base angular frequency=60 Hz, pf= 0.9957, H = 3.117 s, mechanical windage and friction loss = 0.04 pu, iron loss = 300 pu, Ra = 0.0025 pu (armature time constant, Ta = 0.278 s), Xd = 1.014 pu, X'd = 0.314 pu, T'd0 = 6.55 s, X''d = 0.280 pu, T''d0 = 0.039 s, Xq = 0.770 pu, X''q = 0.375 pu T''q0 = 0.071 s, potier reactance Xp = 0.163 pu, air gap factor = 1.0, number of Q-axis damper windings = 1. IEEE type 2 hydro governor and turbine parameters: for controller: real pole gain = 0.88, proportional gain = 3.7, integral gain = 0.44, real pole time constant = 0.02 s, Turbine lead time constant = 0.01 s, turbine lag time constant =0.01 s, governor time constant =0.05 s, inverse gate velocity limit =4.8 s/pu, gate velocity time constant =0.1 s, permanent droop gain =0.08, gate position control rate limit = 0.22 pu/s, temporary droop gain = 0.0, temporary droop time constant = 0.01 s, conversion constant = 0.895, time constant for smoothing = 0.02 s. IEEE type SCRX solid state exciter parameters: VLN = 7967 V, line current=5020 A, rectifier smoothing time constant = 0.02 s, controller lead/lag time constant = 1.5/1.0 s, exciter time constant = 0.02 s, exciter gain = 100 pu, min/max field voltage = -+5 pu, reverse resistance = 15 KΩ. B6. Two-Area System (154 kV, 60 Hz, 100 MVA) Line Data Line No: 1 2 3 4 Location: Bus 1-Bus 4 Bus 1-Bus 6 Bus 1-Bus 2 Bus 1-Bus 2 R (Ω/m) 0.178159E-4 0.178159E-4 0.178159E-4 0.178159E-4 X (Ω/m) 0.31388E-3 0.31388E-3 0.31388E-3 0.31388E-3 238 B (MΩ/m) 273.5448 273.5448 273.5448 273.5448 Length (m) 50E3 100E3 350E3 350E3 APPENDIX C: PI Controller Parameters • Power Flow Studies (Chapter 3) WSCC 3-Machine 9-Bus System Proportional gain-Kp, integral time constant -τi STATCOM (Figure 3.4a) Voltage regulator : 0.001, 0.008 Real power balance regulator : 0.1, 0.0004 SSSC (Figure 3.4b) Voltage regulator : 0.001, 0.008 Real power balance regulator : 0.1, 0.0004 UPFC (Figure 3.4c) Shunt VSC Voltage regulator : 0.001, 0.008 Real power balance regulator : 0.1, 0.0004 Series VSC Series reactive power regulator : 0.1, 0.008 IPFC (Figure 3.4d) Series VSC-1 Voltage regulator : 0.001, 0.008 Real power balance regulator : 0.1, 0.0004 Series VSC-2 Series reactive power regulator : 0.1, 0.008 GUPFC (Figure 3.4f) Shunt VSC Voltage regulator : 0.001, 0.008 Real power balance regulator : 0.1, 0.0004 Series VSCs Series reactive power regulator-1 and 2 : 0.1, 0.008 IEEE 14-Bus System Proportional gain-Kp, integral time constant -τi UPFC (for both UPFCs) (Figure 3.4c) Shunt VSC Voltage regulator : 0.1, 0.008 Real power balance regulator : 0.002, 0.008 Series VSC 239 Real power flow regulator Reactive power flow regulator IPFC (Figure 3.4d) Series VSC-1 Reactive power flow regulator Real power balance regulator Series VSC-2 Real power flow regulator Reactive power regulator GUPFC (Figure 3.4f) Shunt VSC Voltage regulator Real power balance regulator Series VSC-1 Real power flow regulator Reactive power regulator Series VSC-2 Real power flow regulator Reactive power regulator : 0.06, 0.002 : 0.001, 0.008 : 0.001, 0.004 : 0.00008, 0.004 : 0.001, 0.008 : 0.0001, 0.002 : 0.001, 0.08 : 0.001, 0.004 : 0.001, 0.08 : 0.001, 0.04 : 0.001, 0.08 : 0.0001, 0.02 3-Machine 7-Bus System Proportional gain-Kp, integral time constant -τi STATCOM (for both STATCOMs) (Figure 3.4a) Voltage regulator : 0.05, 0.0008 Real power balance regulator : 0.002, 0.008 BtB-STATCOM (Figure 3.4e) Shunt VSC-1 Voltage regulator : 0.05, 0.0008 Real power balance regulator : 0.1, 0.0004 Shunt VSC-2 Voltage regulator : 0.05, 0.0008 Real power transfer regulator : 0.01, 0.08 • Converter-Level Modeling Studies (Chapter 5) 3-Machine 7-Bus System Proportional gain-Kp, integral time constant -τi BtB-STATCOM (Figure 5.33) Shunt VSC-1 DC link voltage controller (Figure 5.33a) : 0.8, 0.001 AC voltage controller (Figure 5.33b) : 0.1, 0.01 240 Shunt VSC-2 Real power transfer controller (Figure 5.33c): 0.8, 0.01 AC voltage controller (Figure 5.33d) : 0.8, 0.001 • Transient Stability Studies (Chapter 6) Wind Farm Integrated Power System Proportional gain-Kp, integral time constant -τi GUPFC (Figure 6.1) Shunt VSC DC link voltage controller (Figure 5.33a) : 0.8, 0.01 AC voltage controller (Figure 5.33b) : 8, 0.02 Lower Series VSC Real power flow controller : 1.0, 0.001 Reactive power controller : 1.0, 0.01 Damping gain (Kw) : 500 Upper Series VSC Real power flow controller : 1.0, 0.001 Reactive power controller : 1.0, 0.01 Damping gain (Kw) : 500 Two-Area System Proportional gain-Kp, integral time constant -τi IPFC (Figure 6.13) Lower Series VSC DC link voltage controller : 0.1, 0.001 Real power controller : 0.2, 0.001 Damping gain (Kw) : 500 Upper Series VSC Real power flow controller : 1.0, 0.001 SSSC Controllers (Figure 6.13) Series VSC DC link voltage controller : 0.1 0.001 Real power controller : 0.2, 0.001 Damping gain (Kw) : 500 SMIB System Proportional gain-Kp, integral time constant -τi BtB-STATCOM (Figure 6.21) Series VSC1 AC voltage controller : 0.8, 0.01 241 Real power transfer controller : 0.8, 0.01 Series VSC2 AC voltage controller : 0.8, 0.01 DC voltage controller : 0.1, 0.1 APPENDIX D: Derivation of Maximum Power Injections for BtB-STATCOM (Chapter 3) The following derivations are made for ensuring maximum real power transfer and maximum reactive power compensation at the same time for BtBSTATCOM. For VSC1 (loss meeting function is assigned); ( Pinj1 max 2 + Qinj1 max 2 ) ≤ 1.0 (D.1) When real power transfer from VSC1 to VSC2 Pinj1max = - 0.003 + 0.7071 = 0.7041 pu Qinj1 max = + 0.7101 pu (71.01 % capacitive compensation) When real power transfer from VSC2 to VSC1 Pinj1max = - 0.003 - 0.7071 = - 0.7101 pu Qinj1 max = + 0.7041 pu (70.41 % capacitive compensation) For VSC4; ( Pinj 2 max 2 + Qinj 2 max 2 ) ≤ 1.0 (D.2) Pinj 2 max = Qinj 2 max = 1 / 2 = 0.7071 pu Pinj 2 max = - 0.7071 pu (when real power transfer from VSC1 to VSC2) Pinj 2 max = + 0.7071 pu (when real power transfer from VSC2 to VSC1) Qinj 2 max = + 0.7071 pu (70.71 % capacitive compensation) 242 APPENDIX E: Programming Scripts • Matlab m-file to Plot Simulation Results Obtained From PSCAD % This m-file reads PSCAD "*.out" file and puts it in matrix form for Matlab % written by A. Mete VURAL % begin % reading main "*.out" file sepet = importdata('file_name_no.out'); % specify the output file name with number extension obtained by saving the channels to disk in PSCAD % reading input data t=sepet.data(:,1); % 1st column: PSCAD simulation time data_namesimcase=sepet.data(:,n); n is the column number of data in *.out file % end • Chapter 5 Fortran Script of PSCAD-MATLAB Interface #STORAGE REAL:5 IF($Enabl.GT.0.9) THEN STORF(NSTORF) = $sig_inp(1) STORF(NSTORF+1) = $sig_inp(2) STORF(NSTORF+2) = $sig_inp(3) STORF(NSTORF+3) = $sig_inp(4) CALL MLAB_INT("$Path", "$Name", "R R R R", "R R") $sig_out(1) = STORF(NSTORF+4) $sig_out(2) = STORF(NSTORF+5) END IF NSTORF = NSTORF + 6 MATLAB m-file Calling Fuzzy Decoupler (FUDE) function [E F] = skynet2(A,B,C,D) fuzdec_3b = readfis('fuzdec_3b'); [E F] = evalfis([A B C D], fuzdec_3b); Fuzzy Inference System in Matlab for FUDE [System] 243 Name='fuzdec_3b' Type='mamdani' Version=2.0 NumInputs=4 NumOutputs=2 NumRules=98 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='centroid' [Input1] Name='perrdot' Range=[-33 33] NumMFs=7 MF1='n3':'trimf',[-44 -33 -22] MF2='n2':'trimf',[-33 -22 -11] MF3='n1':'trimf',[-22 -11 0] MF4='z':'trimf',[-11 0 11] MF5='p1':'trimf',[0 11 22] MF6='p2':'trimf',[11 22 33] MF7='p3':'trimf',[22 33 44] [Input2] Name='perr' Range=[-21 21] NumMFs=7 MF1='n3':'trimf',[-28 -21 -14] MF2='n2':'trimf',[-21 -14 -7] MF3='n1':'trimf',[-14 -7 0] MF4='z':'trimf',[-7 0 7] MF5='p1':'trimf',[0 7 14] MF6='p2':'trimf',[7 14 21] MF7='p3':'trimf',[14 21 28] [Input3] Name='qerrdot' Range=[-40 40] NumMFs=7 MF1='n3':'trimf',[-53.33 -40 -26.67] MF2='n2':'trimf',[-40 -26.67 -13.33] MF3='n1':'trimf',[-26.67 -13.33 1.776e-015] MF4='z':'trimf',[-13.33 -4.441e-016 13.33] MF5='p1':'trimf',[1.776e-015 13.33 26.67] MF6='p2':'trimf',[13.33 26.67 40] MF7='p3':'trimf',[26.67 40 53.33] [Input4] Name='qerr' Range=[-35 35] NumMFs=7 MF1='n3':'trimf',[-46.67 -35 -23.33] MF2='n2':'trimf',[-35 -23.33 -11.67] MF3='n1':'trimf',[-23.33 -11.67 -1.776e-015] MF4='z':'trimf',[-11.67 1.11e-016 11.67] 244 MF5='p1':'trimf',[-1.776e-015 11.67 23.33] MF6='p2':'trimf',[11.67 23.33 35] MF7='p3':'trimf',[23.33 35 46.67] [Output1] Name='delvq' Range=[-80 80] NumMFs=7 MF1='n3':'trimf',[-106.7 -80 -53.32] MF2='n2':'trimf',[-80 -53.32 -26.64] MF3='n1':'trimf',[-53.32 -26.64 0] MF4='z':'trimf',[-26.64 0 26.68] MF5='p1':'trimf',[0 26.68 53.32] MF6='p2':'trimf',[26.68 53.32 80] MF7='p3':'trimf',[53.32 80 106.7] [Output2] Name='delvd' Range=[-400 400] NumMFs=7 MF1='n3':'trimf',[-533 -400 -266.8] MF2='n2':'trimf',[-400 -266.8 -133.3] MF3='n1':'trimf',[-266.8 -133.3 0] MF4='z':'trimf',[-133.3 0 133.3] MF5='p1':'trimf',[0 133.3 266.8] MF6='p2':'trimf',[133.3 266.8 400] MF7='p3':'trimf',[266.8 400 533] [Rules] 7 7 0 0, 7 6 0 0, 7 5 0 0, 7 4 0 0, 7 3 0 0, 7 2 0 0, 7 1 0 0, 6 7 0 0, 6 6 0 0, 6 5 0 0, 6 4 0 0, 6 3 0 0, 6 2 0 0, 6 1 0 0, 5 7 0 0, 5 6 0 0, 5 5 0 0, 5 4 0 0, 5 3 0 0, 5 2 0 0, 5 1 0 0, 4 7 0 0, 4 6 0 0, 4 5 0 0, 4 4 0 0, 4 3 0 0, 4 2 0 0, 7 7 7 6 6 5 4 7 7 6 6 5 4 3 7 6 6 5 4 3 2 6 6 5 4 3 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 245 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 7 7 7 7 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 4 4 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 6 6 5 4 7 7 6 6 5 4 3 7 6 6 5 4 3 2 6 6 5 4 3 2 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 • 1 7 6 5 4 3 2 1 7 6 5 4 3 2 1 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 6 5 4 3 2 2 1 5 4 3 2 2 1 1 4 3 2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 6 5 4 3 2 2 1 5 4 3 2 2 1 1 4 3 2 2 1 1 1 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Chapter 6 Fortran Script of PSCAD-MATLAB Interface (for GUPFC and IPFC) #STORAGE REAL:3 IF($Enabl.GT.0.9) THEN STORF(NSTORF) = $sig_inp(1) STORF(NSTORF+1) = $sig_inp(2) CALL MLAB_INT("$Path", "$Name", "R R", "R R") $sig_out(1) = STORF(NSTORF+2) $sig_out(2) = STORF(NSTORF+3) END IF NSTORF = NSTORF + 4 MATLAB m-file Calling Self-Tuning Fuzzy Damping Controller (STFDC) (for GUPFC and IPFC) function [C,D] = osc_damp1(A,B) strb1 = readfis('strb1'); strb2 = readfis('strb2'); C = evalfis([A B], strb1); D = evalfis([A B], strb2); Fuzzy Inference System in Matlab for Fuzzy Damping Controller (FDC) (for GUPFC and IPFC) [System] 246 Name='strb1' Type='mamdani' Version=2.0 NumInputs=2 NumOutputs=1 NumRules=49 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='centroid' [Input1] Name='perrdot' Range=[-1 1] NumMFs=7 MF1='n3':'trimf',[-10 -1 -0.6665] MF2='n2':'trimf',[-1 -0.6665 -0.3334] MF3='n1':'trimf',[-0.6665 -0.3334 0] MF4='z':'trimf',[-0.3334 0 0.3334] MF5='p1':'trimf',[0 0.3334 0.6665] MF6='p2':'trimf',[0.3334 0.6665 1] MF7='p3':'trimf',[0.6665 1 10] [Input2] Name='perr' Range=[-1 1] NumMFs=7 MF1='n3':'trimf',[-15 -1 -0.6666] MF2='n2':'trimf',[-1 -0.6666 -0.3332] MF3='n1':'trimf',[-0.6666 -0.3332 0] MF4='z':'trimf',[-0.3332 0 0.3332] MF5='p1':'trimf',[0 0.3332 0.6667] MF6='p2':'trimf',[0.3332 0.6667 1] MF7='p3':'trimf',[0.6667 1 15] [Output1] Name='delvq' Range=[-0.4 0.4] NumMFs=7 MF1='n3':'trimf',[-0.5336 -0.4 -0.2666] MF2='n2':'trimf',[-0.4 -0.2666 -0.1332] MF3='n1':'trimf',[-0.2666 -0.1332 0] MF4='z':'trimf',[-0.1332 0 0.1334] MF5='p1':'trimf',[0 0.1334 0.2666] MF6='p2':'trimf',[0.1334 0.2666 0.4] MF7='p3':'trimf',[0.2666 0.4 0.5336] [Rules] 7 7, 7 (1) 7 6, 7 (1) 7 5, 7 (1) 7 4, 6 (1) 7 3, 5 (1) 7 2, 5 (1) 7 1, 4 (1) : : : : : : : 1 1 1 1 1 1 1 4 4 4 3 3 3 3 247 3, 2, 1, 7, 6, 5, 4, 3 2 1 6 5 4 3 (1) (1) (1) (1) (1) (1) (1) : : : : : : : 1 1 1 1 1 1 1 6 6 6 6 6 6 6 5 5 5 5 5 5 5 4 4 4 4 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 7 6 6 6 5 4 3 7 6 5 5 4 3 2 7 6 5 4 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 3 2 1 5 4 3 2 2 2 1 4 3 3 2 1 1 1 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Fuzzy Inference System in Matlab for Fuzzified Gain Tuner (FGT) (for GUPFC and IPFC) [System] Name='strb2' Type='mamdani' Version=2.0 NumInputs=2 NumOutputs=1 NumRules=49 AndMethod='min' OrMethod='max' ImpMethod='min' AggMethod='max' DefuzzMethod='centroid' [Input1] Name='errdot' Range=[-1 1] NumMFs=7 MF1='n3':'trimf',[-10 -1 -0.6665] MF2='n2':'trimf',[-1 -0.6665 -0.3334] MF3='n1':'trimf',[-0.6665 -0.3334 0] MF4='z':'trimf',[-0.3334 0 0.3334] MF5='p1':'trimf',[0 0.3334 0.6665] MF6='p2':'trimf',[0.3334 0.6665 1] MF7='p3':'trimf',[0.6665 1 10] [Input2] Name='err' Range=[-1 1] NumMFs=7 MF1='n3':'trimf',[-15 -1 -0.6666] MF2='n2':'trimf',[-1 -0.6666 -0.3332] 248 MF3='n1':'trimf',[-0.6666 -0.3332 0] MF4='z':'trimf',[-0.3332 0 0.3332] MF5='p1':'trimf',[0 0.3332 0.6667] MF6='p2':'trimf',[0.3332 0.6667 1] MF7='p3':'trimf',[0.6667 1 15] [Output1] Name='alfa' Range=[0 1] NumMFs=7 MF1='z':'trimf',[-0.167 0 0.1668] MF2='vs':'trimf',[0 0.1668 0.3335] MF3='s':'trimf',[0.1668 0.3335 0.5] MF4='sb':'trimf',[0.3335 0.5 0.6667] MF5='mb':'trimf',[0.5 0.6667 0.8333] MF6='b':'trimf',[0.6667 0.8333 1] MF7='vb':'trimf',[0.835945502645503 1.0026455026455 1.1696455026455] [Rules] 7 7, 7 (1) 7 6, 7 (1) 7 5, 7 (1) 7 4, 6 (1) 7 3, 4 (1) 7 2, 3 (1) 7 1, 1 (1) 6 7, 7 (1) 6 6, 7 (1) 6 5, 6 (1) 6 4, 6 (1) 6 3, 5 (1) 6 2, 3 (1) 6 1, 2 (1) 5 7, 7 (1) 5 6, 5 (1) 5 5, 6 (1) 5 4, 7 (1) 5 3, 2 (1) 5 2, 3 (1) 5 1, 2 (1) 4 7, 3 (1) 4 6, 4 (1) 4 5, 5 (1) 4 4, 1 (1) : : : : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 1 1 1 1 1 1 1 249 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 5 4 3 2 3 2 7 6 5 7 2 3 5 6 6 7 7 1 3 4 6 7 7 7 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) : : : : : : : : : : : : : : : : : : : : : : : : 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1