Power Flow Control Solutions for a Modern Grid Using SMART Power Flow Controllers

Оглавление

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

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Power Flow Control Solutions for a Modern Grid using SMART Power Flow Controllers

Authors’ Biographies

Foreword

Nomenclature

Preface

Acknowledgments

About the Companion Website

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

1.4.1 Defining a Cost‐Effective Solution

1.4.2 Payback Time

1.4.3 Economic Analysis

1.5 Independent Active and Reactive PFCs

1.6 SMART Power Flow Controller (SPFC)

1.6.1 Example of an SPFC

1.6.2 Justification

1.6.3 Additional Information

1.7 Discussion

2 Power Flow Control Concepts

Example 2‐1

Example

Example 2‐3

Example 2‐4

2.1 Power Flow Equations for a Natural or Uncompensated Line

Example 2‐5

2.2 Power Flow Equations for a Compensated Line

2.2.1 Shunt‐Compensating Voltage

2.2.1.1 Power Flow at the Modified Sending End with a Shunt‐Compensating Voltage

Example 2‐6

2.2.1.2 Power Flow at the Receiving End with a Shunt‐Compensating Voltage

Example 2‐7

Example 2‐8

Example 2‐9

Example 2‐10

Example 2‐11

2.2.1.3 Exchanged Power by a Shunt‐Compensating Voltage

2.2.1.4 Representation of a Shunt‐Compensating Voltage as a Shunt‐Compensating Impedance

Example 2‐12

2.2.2 Series‐Compensating Voltage as an Impedance Regulator, Voltage Regulator, and Phase Angle Regulator (Asymmetric)

Example 2‐13

Example 2‐14

Example 2‐15

2.2.2.1 Power Flow at the Sending End with a Series‐Compensating Voltage

Example 2‐16

2.2.2.2 Power Flow at the Receiving End with a Series‐Compensating Voltage

Example 2‐17

Example 2‐18

Example 2‐19

2.2.2.3 Power Flow at the Modified Sending End with a Series‐Compensating Voltage

Example 2‐20

Example 2‐21

Example 2‐22

Example 2‐23

2.2.2.4 Exchanged Power by a Series‐Compensating Voltage

Example 2‐24

Example 2‐25

Example 2‐26

Example 2‐27

Example 2‐28

Example 2‐29

Example 2‐30

Example 2‐31

Example 2‐32

Example 2‐33

Example 2‐34

Example 2‐35

2.2.2.5 Additional Series‐Compensating Voltages

2.2.2.5.1 Phase Angle Regulator (Symmetric)

2.2.2.5.2 Reactance Regulator

2.2.2.6 Representation of a Series‐Compensating Voltage as a Series‐Compensating Impedance

Example 2‐36

Example 2‐37

2.2.2.6.1 Equivalent Impedance of a Voltage Regulator (VR)

Example 2‐38

2.2.2.6.2 Equivalent Impedance of a Phase Angle Regulator (Asymmetric)

Example 2‐39

2.2.2.6.3 Equivalent Impedance of a Phase Angle Regulator (Symmetric)

Example 2‐40

2.2.2.6.4 Equivalent Impedance of a Reactance Regulator

Example 2‐41

2.2.3 Comparison Between Series‐ and Shunt‐Compensating Voltages

2.3 Implementation of Power Flow Control Concepts

2.3.1 Voltage Regulation

2.3.1.1 Direct Method

2.3.1.2 Indirect Method

2.3.2 Phase Angle Regulation

2.3.2.1 Single‐core Phase Angle Regulator

2.3.2.2 Dual‐core Phase Angle Regulator

2.3.3 Series Reactance Regulation

2.3.3.1 Direct Method

2.3.3.2 Indirect Method

2.3.4 Impedance Regulation

2.3.4.1 Unified Power Flow Controller (UPFC)

2.3.4.2 Sen Transformer (ST)

2.4 Interline Power Flow Concept

2.4.1 Back‐to‐Back SSSC

2.4.2 Multiline Sen Transformer (MST)

2.4.3 Back‐to‐Back STATCOM

2.4.4 Generalized Power Flow Controller

2.5 Figure of Merits Among Various PFCs

2.5.1 VR

2.5.2 PAR (sym)

2.5.3 PAR (asym)

2.5.4 RR

2.5.5 IR

2.5.6 RPI, LI, and APR of a PFC

Example 2‐42

Example 2‐43

Example 2‐44

Example 2‐45

Example 2‐46

Example 2‐47

Example 2‐48

Example 2‐49

Example 2‐50

2.6 Comparison Between Shunt‐Compensating Reactance and Series‐Compensating Reactance

2.6.1 Shunt‐Compensating Reactance

2.6.1.1 Restoration of Voltage at the Midpoint of the Line

2.6.1.2 Restoration of Voltage at the One‐Third and Two‐Third Points of the Line

2.6.1.3 Restoration of Voltage at the One‐Fourth, Half, and Three‐Fourth Points of the Line

2.6.1.4 Restoration of Voltage at n Points of the Line

2.6.2 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

2.7.1 PAR (sym)

2.7.2 PAR (asym)

2.7.3 RR

2.7.4 IR

2.8 Sen Index of a PFC

3 Modeling Principles

3.1 The Modeling in EMTP

Code 3‐1 EMTP template datafile (TEMPLATE.DAT)

3.1.1 A Single‐Generator/Single‐Line Model

Code 3‐2 EMTP test datafile (TEST.DAT)

3.1.2 A Two‐Generator/Single‐Line Model

Code 3‐3 EMTP datafile for a two‐generator/single‐line power system network (301NTWK1.DAT)

Code 3‐4 EMTP $INCLUDE file for inputs from node voltages and line currents (302MEAS1.SWT)

Code 3‐5 EMTP $INCLUDE file for normalizing the measured voltages and currents (303PTCT.SCL)

Code 3‐6 EMTP $INCLUDE file for implementing an ideal PLL (304IPLL.PLL)

Code 3‐7 EMTP $INCLUDE file for computing the line resistance (305LINER.CMP)

Code 3‐8 Representation of shorts between VS and BUS01 nodes and between BUS01 and BUS02 nodes

Code 3‐9 EMTP $INCLUDE file for implementing the source impedance and the line impedance (306NTWK1.BRN)

Code 3‐10 EMTP $INCLUDE file for measuring the branch currents (307MEAS2.SWT)

Code 3‐11 EMTP $INCLUDE file for the source voltages and the receiving‐end voltages (308NTWK1.SRC)

Code 3‐12 EMTP datafile for a two‐generator/single‐line faulted power system network (309NTWK2.DAT)

3.2 Vector Phase‐Locked Loop (VPLL)

Code 3‐13 EMTP $INCLUDE file for a Vector Phase‐Locked Loop (310VPLL.PLL)

Code 3‐14 EMTP $INCLUDE file for implementing the source impedance and the line impedance (311NTWK2.BRN)

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

Code 3‐15 EMTP datafile for an independent PFC (Shunt‐Series), integrated in a two‐generator/single‐line power system network (312PQPFC.DAT)

Code 3‐16 EMTP $INCLUDE file for a three‐phase series‐coupling transformer (315TRAN2.TRN) with a leakage impedance

Code 3‐17 EMTP $INCLUDE file for user's input (313PQPFC.USR)

Code 3‐18 EMTP $INCLUDE file for P‐Q power flow control, using the mathematical model of a PFC in a Shunt‐Series configuration (314PQPFC.CON)

4 Transformer‐Based Power Flow Controllers

4.1 Voltage‐Regulating Transformer (VRT)

4.1.1 Voltage Regulating Transformer (Shunt‐Series Configuration)

Code 4-1 EMTP datafile for mathematical model of ST, operating as a VRT in a Shunt‐Series configuration, integrated in a two‐generator/single‐line power system network (401PQPFC.DAT)

Code 4‐2 EMTP $INCLUDE file for a three‐phase, series‐coupling transformer (402TRAN2.TRN) without any leakage impedance

Code 4‐3 EMTP datafile for the mathematical model of the ST, operating as a VRT in a Shunt‐Series configuration, integrated in a two‐generator/single‐line power system network (403PQPFC.DAT). The series‐compensating voltage magnitude (Vs′s) is a multiplier of the sending‐end voltage magnitude (Vs)

Code 4‐4 EMTP $INCLUDE file for user's input (404PQPFC.USR)

Code 4‐5 EMTP datafile for an ideal VRT (Shunt‐Series configuration), integrated in a two‐generator/single‐line power system network (405IDLAT.DAT)

Code 4‐6 EMTP $INCLUDE file for an ideal three‐phase VRT in a Shunt‐Series configuration for increasing 15% line voltage (406IDLAT.TRN)

Code 4‐7 EMTP $INCLUDE file for an ideal three‐phase VRT in a Shunt‐Series configuration for decreasing 15% line voltage (406IDLAT.TRN)

4.1.2 Two‐Winding Transformer

Code 4‐8 EMTP datafile for an ideal VRT (Shunt‐Shunt configuration), integrated in a two‐generator/single‐line power system network (407IDLTT.DAT)

Code 4‐9 EMTP $INCLUDE file for an ideal three‐phase VRT in a Shunt‐Shunt configuration for increasing 15% line voltage (408IDLTT.TRN)

Code 4‐10 EMTP $INCLUDE file for an ideal three‐phase VRT in a Shunt‐Shunt configuration for decreasing 15% line voltage (408IDLTT.TRN)

4.2 Phase Angle Regulator (PAR)

4.2.1 PAR (Asymmetric)

Code 4‐11 EMTP $INCLUDE file for user's input (404PQPFC.USR)

Code 4‐12 EMTP datafile for a PAR (asym), integrated in a two‐generator/single‐line power system network (409PAR1.DAT)

Code 4‐13 EMTP $INCLUDE file for an ideal single‐core PAR (asym) for decreasing power flow (410PAR1D.TRN)

Code 4‐14 EMTP $INCLUDE file for an ideal single‐core PAR (asym) for increasing power flow (410PAR1I.TRN)

4.2.2 PAR (Symmetric)

Code 4‐15 EMTP datafile for a PAR (sym), integrated in a two‐generator/single‐line power system network (411PAR2.DAT)

Code 4‐16 EMTP $INCLUDE file for an ideal single‐core PAR (sym) for decreasing power flow (412PAR2D.TRN)

Code 4‐17 EMTP $INCLUDE file for an ideal single‐core PAR (sym) for increasing power flow (412PAR2I.TRN)

5 Mechanically‐Switched Voltage Regulators and Power Flow Controllers

5.1 Shunt Compensation

5.1.1 Mechanically‐Switched Capacitor (MSC)

Code 5‐1 EMTP datafile for a shunt‐compensating, mechanically‐switched capacitor, integrated in a two‐generator/single‐line power system network (501SHREA.DAT)

Code 5‐2 EMTP $INCLUDE file for user's input (502SHREA.USR)

Code 5‐3 EMTP $INCLUDE file for calculation of exchanged power by a shunt compensator (503SHREA.CON)

Code 5‐4 EMTP $INCLUDE file for implementing a three‐phase, shunt‐compensating capacitor (504SHRE1.BRN)

Code 5‐5 EMTP datafile for a shunt‐compensating, mechanically‐switched capacitor with a series bypass reactor, integrated in a two‐generator/single‐line power system network (505SHREA.DAT)

Code 5‐6 EMTP $INCLUDE file for user's input (506SHREA.USR)

Code 5‐7 EMTP $INCLUDE file for implementing a three‐phase, shunt‐compensating capacitor with a series bypass reactor (507SHRE2.BRN)

5.1.2 Mechanically‐Switched Reactor (MSR)

Code 5‐8 EMTP $INCLUDE file for implementing a three‐phase, shunt‐compensating reactor (508SHRE3.BRN)

5.2 Series Compensation

5.2.1 Mechanically‐Switched Reactor (MSR)

Code 5‐9 EMTP datafile for series‐compensating, mechanically‐switched reactors, integrated in a two‐generator/single‐line power system network (509SEREA.DAT)

Code 5‐10 EMTP $INCLUDE file for user's input (510SEREA.USR)

Code 5‐11 EMTP $INCLUDE file for calculation of exchanged‐power by a series‐compensator (511SEREA.CON)

Code 5‐12 EMTP $INCLUDE file for implementing three‐phase, series‐compensating reactors (512SERE1.BRN)

5.2.2 Mechanically‐Switched Capacitor (MSC) with a Reactor

Code 5‐13 EMTP datafile for a series‐compensating, mechanically‐switched capacitor with a reactor, integrated in a two‐generator/single‐line power system network (513SEREA.DAT)

Code 5‐14 EMTP $INCLUDE file for implementing a three‐phase series‐connected capacitor with a reactor (514SERE2.BRN)

5.2.3 Series Reactance Emulator

Code 5‐15 EMTP datafile for a series‐compensating reactor, integrated in a two‐generator/single‐line power system network (515PQPFC.DAT)

Code 5‐16 EMTP $INCLUDE file for user's input (516PQPFC.USR)

6 Sen Transformer

6.1 Existing Solutions

6.1.1 Voltage Regulation

6.1.2 Phase Angle Regulation

6.2 Desired Solution

6.2.1 ST as a New Voltage Regulator

6.2.2 ST as an Independent PFC

6.2.3 Control of ST

6.2.3.1 Impedance Emulation

6.2.3.2 Resistance Emulation

6.2.3.3 Reactance Emulation

6.2.3.4 Closed‐Loop Power Flow Control

6.2.3.5 Open‐Loop Power Flow Control

6.2.4 Simulation of ST Integrated in a Two‐Generator/One‐Line Power System Network

Code 6‐1 EMTP datafile for an ST integrated in a two‐bus network (601IDLST.DAT)

Code 6‐2 EMTP $INCLUDE file for an ST with an operating point, pu and β = 0° (602IDLST.TRN)

Code 6‐3 EMTP $INCLUDE file for an ST with an operating point, pu and β = 60.0° (ST4060P0.TRN)

6.2.5 Simulation of ST Integrated in a Three‐Generator/Four‐Line Power System Network

Code 6‐4 EMTP datafile for an ST integrated in a three‐generator/four‐line power system network (603IDLST.DAT)

Code 6‐5 EMTP $INCLUDE file for implementing four‐line branches (604NTWK4.BRN)

Code 6‐6 EMTP $INCLUDE file for implementing three‐generator sources (605NTWK4.SRC)

6.2.6 Testing of ST

Code 6‐7 EMTP datafile for an ST integrated in a one‐generator/one‐line power system network (606IDLST.DAT)

Code 6‐8 EMTP datafile for an ST integrated in a one‐generator/one‐line power system network (607IDLST.DAT)

6.2.7 Limited‐Angle Operation of ST

6.2.8 ST Using LTCs with Lower Current Rating

6.2.9 ST with a Two‐Core Design

6.3 Comparison Among the VRT, PAR, UPFC, and ST

6.3.1 Power Flow Enhancement

6.3.2 Speed of Operation

6.3.3 Losses

6.3.4 Switch Rating

6.3.5 Magnetic Circuit Design

6.3.6 Optimization of Transformer Rating

6.3.7 Harmonic Injection into the Power System Network

6.3.8 Operation During Line Faults

6.4 Multiline Sen Transformer

6.4.1 Basic Differences Between the MST and BTB‐SSSC

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

Appendix A Miscellaneous. A.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.5.1 Conversion of a Variable Containing Positive‐, Negative‐, and Zero‐Sequence Components into d‐q Frame

A.5.2 Calculation of Instantaneous Power into d‐q Frame

A.5.3 Calculation of Instantaneous Power into d‐q Frame for a Three‐Phase, Three‐Wire System

A.6 Fourier Analysis

A.7 Adams‐Bashforth Numerical Integration Formula

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.2.1 Shunt‐Compensating Voltage

B.2.1.1 Power Flow at the Modified Sending End with a Shunt‐Compensating Voltage

B.2.1.2 Power Flow at the Receiving End with a Shunt‐Compensating Voltage

B.2.1.3 Exchanged Power by a Shunt‐Compensating Voltage

B.2.1.4 Representation of a Shunt‐Compensating Voltage as a Shunt‐Compensating Impedance

B.2.2 Series‐Compensating Voltage as an Impedance Regulator, Voltage Regulator, and Phase Angle Regulator (Asymmetric)

B.2.2.1 Power Flow at the Sending End with a Series‐Compensating Voltage

B.2.2.2 Power Flow at the Receiving End with a Series‐Compensating Voltage

B.2.2.3 Power Flow at the Modified Sending End with a Series‐Compensating Voltage

B.2.2.4 Exchanged Power by a Series‐Compensating Voltage

B.2.2.5 Additional Series‐Compensating Voltages

B.2.2.5.1 Phase Angle Regulator (Symmetric)

B.2.2.5.2 Reactance Regulator

B.2.2.6 Representation of a Series‐Compensating Voltage as a Series‐Compensating Impedance

B.2.2.6.1 Equivalent Impedance of a Voltage Regulator (VR)

B.2.2.6.2 Equivalent Impedance of a Phase Angle Regulator (Asymmetric)

B.2.2.6.3 Equivalent Impedance of a Phase Angle Regulator (Symmetric)

B.2.2.6.4 Equivalent Impedance of a Reactance Regulator

B.2.2.7 RPI, LI, and APR of a PFC

B.3 Descriptions of the Examples in Chapter 2

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

References

Further Reading. Books

General

STATCOM

SSSC

UPFC

IPFC

ST

Index. a

b

c

d

e

f

g

h

i

k

l

m

n

p

r

s

t

u

v

z

Books in the IEEE Press Series on Power and Engineering

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