Kalyan K. Sen - Power Flow Control Solutions for a Modern Grid Using SMART Power Flow Controllers

1 Cover

2 Series Page IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Ekram Hossain, Editor in Chief Jón Atli Benediktsson Xiaoou Li Jeffrey Reed Anjan Bose Lian Yong Diomidis Spinellis David Alan Grier Andreas Molisch Sarah Spurgeon Elya B. Joffe Saeid Nahavandi Ahmet Murat Tekalp

3 Title Page

4 Copyright Page

5 Dedication Page

6 Authors’ Biographies

7 Foreword

8 Nomenclature

9 Preface

10 Acknowledgments

11 About the Companion Website

12 1 Smart Controllers 1.1 Why is a Power Flow Controller Needed? 1.2 Traditional Power Flow Control Concepts 1.3 Modern Power Flow Control Concepts 1.4 Cost of a Solution 1.5 Independent Active and Reactive PFCs 1.6 SMART Power Flow Controller (SPFC) 1.7 Discussion

13 2 Power Flow Control Concepts 2.1 Power Flow Equations for a Natural or Uncompensated Line 2.2 Power Flow Equations for a Compensated Line 2.3 Implementation of Power Flow Control Concepts 2.4 Interline Power Flow Concept 2.5 Figure of Merits Among Various PFCs 2.6 Comparison Between Shunt‐Compensating Reactance and Series‐Compensating Reactance 2.7 Calculation of RPI , LI , and APR for a PAR (sym), a PAR (asym), a RR, and an IR in a Lossy Line 2.8 Sen Index of a PFC

14 3 Modeling Principles 3.1 The Modeling in EMTP 3.2 Vector Phase‐Locked Loop (VPLL) 3.3 Transmission Line Steady‐State Resistance Calculator 3.4 Simulation of an Independent PFC, Integrated in a Two‐Generator/Single‐Line Power System Network

15 4 Transformer‐Based Power Flow Controllers 4.1 Voltage‐Regulating Transformer (VRT) 4.2 Phase Angle Regulator (PAR)

16 5 Mechanically‐Switched Voltage Regulators and Power Flow Controllers 5.1 Shunt Compensation 5.2 Series Compensation

17 6 Sen Transformer 6.1 Existing Solutions 6.2 Desired Solution 6.3 Comparison Among the VRT, PAR, UPFC, and ST 6.4 Multiline Sen Transformer 6.5 Flexible Operation of the ST 6.6 ST with a Shunt‐Compensating Voltage 6.7 Limited Angle Operation of the ST with Shunt‐Compensating Voltages 6.8 MST with Shunt‐Compensating Voltages 6.9 Generalized Sen Transformer 6.10 Summary

18 Appendix A: MiscellaneousA.1 Three‐Phase Balanced Voltage, Current, and Power A.2 Symmetrical Components A.3 Separation of Positive‐, Negative‐, and Zero‐Sequence Components in a Multiple Frequency Composite Variable A.4 Three‐Phase Unbalanced Voltage, Current, and Power A.5 d‐q Transformation (3‐Phase System, Transformed into d‐q axes; d‐axis Is the Active Component and q‐axis Is the Reactive Component) A.6 Fourier Analysis A.7 Adams‐Bashforth Numerical Integration Formula

19 Appendix B: Power Flow Equations in a Lossy Line B.1 Power Flow Equations for a Natural or Uncompensated Line B.2 Power Flow Equations for a Compensated Line B.3 Descriptions of the Examples in Chapter 2

20 Appendix C: Modeling of the Sen Transformer in PSS ®E C.1 Sen Transformer C.2 Modeling with Two Transformers in Series C.3 Relating the Sen Transformer with the PSS ®E Model C.4 Chilean Case Study C.5 Limitations – PSS ®E Two‐Transformer Model C.6 Conclusion

21 References Further Reading

22 Index

23 Books in the IEEE Press Series on Power and Engineering

24 End User License Agreement

1 Chapter 1 Table 1‐1 Economic Analysis of ST versus UPFC over a 45‐year time period. Table 1‐2 Various features of all Shunt–Shunt and Shunt–Series configuration... Table 1‐3 Various compensators for utility applications. Table 1‐4 Features, advantages, and benefits of various solutions.

2 Chapter 2 Table 2‐1 Electrical system data. Table 2‐2 Equations for natural active and reactive power flows ( P snand Q snTable 2‐3 Equations for active and reactive power flows ( P s′and Q s′...Table 2‐4 Equations relating the active and reactive power flows ( P s′...Table 2‐5 Equations for magnitude ( V s′) and modified power angle ( δ ...Table 2‐6 Equations for magnitude ( V s′), modified power angle ( δ ′...Table 2‐7 Equations for magnitude ( V s′s) and relative phase angle ( β ...Table 2‐8 Line current for a VR and a PAR (asym).Table 2‐9 Relationships between active and reactive power flows ( P sand Q s) ...Table 2‐10 Equations for active and reactive power flows ( P sand Q s), ( P ran...Table 2‐11 Equations for magnitude ( V s′s) and relative phase angle ( β ...Table 2‐12 Equations for P s, P r, P s′, and P sewhen a VR is used.Table 2‐13 Equations relating ( P sand Q s), ( P rand Q r), ( P s′and Q s′...Table 2‐14 Equations for P s, P r, P s′, and P sewhen a PAR (asym) is used...Table 2‐15 Equations relating ( P sand Q s), ( P rand Q r), ( P s′and Q s′...Table 2‐16 Equations for active and reactive power flows ( P s′and Q s′...Table 2‐17 Equations relating the active and reactive power flows ( P s′Table 2‐18 Selected operating points of an IR and the corresponding series‐c...Table 2‐19 Selected operating points of a VR and the corresponding series‐co...Table 2‐20 Selected operating points of a PAR (asym) and the corresponding s...Table 2‐21 Selected operating points of a PAR (sym) and the corresponding se...Table 2‐22 Selected operating points of a RR and the corresponding series‐co...Table 2‐23 Series‐compensating resistance ( R se) and reactance ( X se) for an I...Table 2‐24 Series‐compensating impedance ( Z se) for an IR, a VR, a PAR (asym)...Table 2‐25 Electrical system data and base power flow data.Table 2‐26 RPI , LI , and APR of a PAR (sym) for power flow increases in three case...Table 2‐27 RPI , LI , and APR of a PAR (asym) for power flow increases in three cas...Table 2‐28 RPI , LI , and APR of a RR for power flow increases in three cases: Case...Table 2‐29 RPI , LI , and APR of an IR for power flow increases in three cases: Cas...Table 2‐30 Comparison of APR of a PAR (sym), a PAR (asym), a RR, and an IR fo...Table 2‐31 Comparison of RPI , LI , and APR of a PAR (sym), a PAR (asym), a RR,...Table 2‐32 Comparison of RPI , LI , and APR per unit of active power ( P r) trans...Table 2‐33 Figure of merits of shunt compensation with a power angle of .Table 2‐34 Figure of merits of shunt compensation with a power angle of .Table 2‐35 Figure of merits of shunt compensation with a power angle of .Table 2‐36 Figure of merits of series compensation with a power angle of .Table 2‐37 Figure of merits of series compensation with a power angle of .Table 2‐38 Figure of merits of series compensation with a power angle of .Table 2‐39 Control parameters and their effects on V s′s, β , V s′...Table 2‐40 Comparison of RPI , LI , and APR per unit of active power ( P r) trans...Table 2‐41 Comparison of SI of a PAR (sym), a PAR (asym), a RR, and an IR for...