Transmission line modeling for the purpose of analog power flow computation of large scale power ...

153 Pages·2005·4.16 MB·English

by  St. Leger

Transmission Line Modeling for the Purpose of Analog Power Flow Computation of
Large Scale Power Systems
A Thesis
Submitted to the Faculty
of
Drexel University
by
Aaron St. Leger
in partial fulfillment of the
requirements for the degree
of
Master of Science in Electrical Engineering
July 2005
ii
© Copyright 2005
Aaron St. Leger. All Rights Reserved
iii
ACKNOWLEDGMENTS

I would like to acknowledge and thank my advisor, Dr. Chikaodinaka Nwankpa,
for all his help and guidance in the research and the development of this thesis. I also
thank him for the opportunity to study and conduct research in the Center of Electric
Power Engineering (CEPE). The facilities, faculty and students in CEPE all contribute to
an environment that is very conducive to learning and conducting research. I am ever
grateful for the opportunity to be a part of this organization.

I would also like to thank Dr. Miu, Dr. Halpin and Dr. Nagvajara for serving on
my thesis committee. I am appreciative for their expertise, participation in my graduate
studies and their time dedicated to reviewing and commenting on this work.

Finally I would like to express gratitude to Jeffrey Yakaski, Anthony Deese,
Qingyan Liu and Michael Olaleye for their help and participation in the PowerGrid
research project. Their valuable work has assisted me in my research efforts and made
much of the work in this thesis possible.
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TABLE OF CONTENTS
LIST OF TABLES............................................................................................................vii
LIST OF FIGURES............................................................................................................x
ABSTRACT.....................................................................................................................xiv
1 INTRODUCTION......................................................................................................1
1.1 OVERVIEW.......................................................................................................1
1.2 BACKGROUND................................................................................................4
1.3 MOTIVATION...................................................................................................8
1.4 PROBLEM STATEMENT...............................................................................10
1.5 ORGANIZATION OF THESIS.......................................................................11
2 DESIGN AND BENCHMARKING ENVIRONMENT..........................................12
2.1 OVERVIEW.....................................................................................................12
2.2 PSPICE.............................................................................................................12
2.3 POWERWORLD..............................................................................................15
2.4 HARDWARE...................................................................................................17
3 POWER TRANSMISSION LINE MODELING.....................................................19
3.1 OVERVIEW OF TRANSMISSION LINE MODELING................................19
3.2 DISTRIBUTED TRANSMISSION LINE PARAMETERS............................20
3.3 LUMPED TRANSMISSION LINE PARAMETERS......................................24
3.4 LUMPED PARAMETER TRANSMISSION LINE MODELS.......................27
4 ANALOG EMULATION OF A POWER SYSTEM...............................................33
4.1 INTRODUCTION............................................................................................33
4.2 ANALOG POWER SYSTEM DC EMULATION METHODOLOGY..........34
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4.3 POWER SYSTEM EMULATION COMPONENTS.......................................40
4.3.1 GENERATORS........................................................................................40
4.3.2 TRANSMISSION LINES.........................................................................43
4.3.3 LOADS.....................................................................................................55
5 METHODOLOGY AND DEVELOPMENT OF ANALOG TRANSMISSION LINE
BULDING BLOCKS........................................................................................................57
5.1 INTRODUCTION............................................................................................57
5.2 CHARACTERIZATION OF OPERATIONAL TRANSCONDUCTANCE
AMPLIFIER (OTA)......................................................................................................58
5.3 POSITIVE OTA VARIABLE RESISTOR......................................................65
5.3.1 SIMULATION RESULTS.......................................................................71
5.3.2 HARDWARE RESULTS.........................................................................77
5.4 NEGATIVE OTA VARIABLE RESISTOR....................................................81
5.4.1 SIMULATION RESULTS.......................................................................83
5.4.2 HARDWARE RESULTS.........................................................................87
6 VERIFICATION OF ANALOG LINE MODELS...................................................90
6.1 OVERVIEW.....................................................................................................90
6.2 PARAMETER SCALING................................................................................91
6.3 PROTOTYPE NETWORK MODULE............................................................92
6.4 NETWORK MODULE TESTING...................................................................95
6.4.1 LOSSLESS LINE MODEL......................................................................98
6.4.2 LOSSY LINE MODEL.............................................................................98
6.4.3 PI LINE MODEL....................................................................................102
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6.5 NETWORK AND LOAD EMULATOR TESTING......................................106
7 CONCLUSIONS AND FUTURE WORK.............................................................109
7.1 CONCLUSIONS.............................................................................................109
7.2 SUMMARY OF RESEARCH CONTRIBUTIONS.......................................110
7.3 FUTURE WORK............................................................................................111
LIST OF REFERENCES................................................................................................112
APPENDIX A: EXAMPLES OF COMMERCIAL ANALOG COMPUTERS............115
APPENDIX B: EMULATION RESULTS FOR 3 BUS LOSSLESS TRANSMISSION
LINE NETWORK..........................................................................................................118
APPENDIX C: EMULATION RESULTS FOR 3 BUS LOSSY TRANSMISSION LINE
NETWORK.....................................................................................................................125
APPENDIX D: PSPICE SIMULATION OF THREE BUS POWER SYSTEM
EMULATION WITH PI LINE MODELS.....................................................................127
APPENDIX E: EMULATION RESULTS FOR NETWORK AND LOAD MODULE133
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LIST OF TABLES
Table 1: Cost of System Downtime in Different Industries...............................................9
Table 2: Details on Lumped Line Models........................................................................32
Table 3: Simulation Details for Lossy Network...............................................................99
Table 4: Emulation Parameters for Lossy Transmission Lines......................................100
Table 5: Emulation Bus Voltages for Lossy Transmission Line Test............................101
Table 6: Emulated Line Currents for Lossy 3 Bus Network..........................................101
Table 7: Offset Corrected Emulation Line Currents.......................................................101
Table 8: Error Analysis on Emulation Results for 3 Bus Lossy Network......................102
Table 9: Power System Parameters for Pi Line HW Test...............................................103
Table 10: Pi Line Emulation Parameters........................................................................104
Table 11: Emulation Parameters for Pi Transmission Line............................................104
Table 12: Emulated Line Currents for Pi Transmission Line.........................................104
Table 13: Ybus and Emulation Current Injections.........................................................105
Table 14: Emulation Error for Pi Transmission Line HW Test......................................105
Table 15: PowerWorld Parameters and Results..............................................................107
Table 16: Emulation Parameters and Results.................................................................107
Table 17: Error Analysis on Emulation with Network and Load Modules....................107
Table 18: Simulation Results for Lossless Network.......................................................119
Table 19: Scaling Factors for Lossless Network Testing...............................................119
Table 20: Emulation Parameters for Lossless Transmission Lines................................119
Table 21: Emulation Bus Voltages for Lossless Transmission Line Test......................119
Table 22: Emulated Line Currents for Lossless 3 Bus Network....................................120
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Table 23: Emulated Current Injections for Lossless 3 Bus Network..............................120
Table 24: Error Analysis on Emulation Results for 3 Bus Lossless Network................120
Table 25: Simulation Results for Lossless Network.......................................................121
Table 26: Emulation Bus Voltages for Lossless Transmission Line Test......................122
Table 27: Emulated Line Currents for Lossless 3 Bus Network....................................122
Table 28: Emulated Current Injections for Lossless 3 Bus Network..............................122
Table 29: Error Analysis on Emulation Results for 3 Bus Lossless Network................122
Table 30: Simulation Results for Lossless Network.......................................................123
Table 31: Emulation Bus Voltages for Lossless Transmission Line Test......................124
Table 32: Emulated Line Currents for Lossless 3 Bus Network....................................124
Table 33: Emulated Current Injections for Lossless 3 Bus Network..............................124
Table 34: Error Analysis on Emulation Results for 3 Bus Lossless Network................124
Table 35: Simulation Results for Lossy Network...........................................................126
Table 36: Emulated Line Currents for Lossy 3 Bus Network........................................126
Table 37: Offset Corrected Emulation Results for Lossy 3 Bus Network......................126
Table 38: Error Analysis on Emulation Results for 3 Bus Lossy Network....................126
Table 39: Power World Simulation Results for Three Bus System with Pi Lines.........127
Table 40: Emulation Scaling Factors..............................................................................127
Table 41: DC Emulation Network Parameters...............................................................128
Table 42: Emulation Line Configuration for Pi Transmission Lines.............................128
Table 43: Error Analysis on Emulation Results for 3 Bus Pi Line Network..................128
Table 44: PowerWorld Parameters and Results..............................................................134
Table 45: Emulation Parameters and Results.................................................................134
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Table 46: Error Analysis on Emulation with Network and Load Modules....................134
Table 47: PowerWorld Parameters and Results..............................................................135
Table 48: Emulation Parameters and Results.................................................................136
Table 49: Error Analysis on Emulation with Network and Load Modules....................136
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LIST OF FIGURES
Figure 1: PSoC Development Process................................................................................3
Figure 2: Analog Transmission Line Model Control Panel................................................6
Figure 3: PSpice Electrical Schematic with Voltage and Current Probes........................14
Figure 4: PSpice Plot of Probed Signals vs. Bias Current................................................14
Figure 5: PowerWorld One Line Diagram of a 6 Bus Power System..............................16
Figure 6: PowerWorld Transmission Line Options..........................................................17
Figure 7: Analog Emulation Hardware Test Setup...........................................................18
Figure 8: Distributed Parameter Transmission Line Model.............................................21
Figure 9: Lumped Parameter Π-Equivalent Transmission Line.......................................25
Figure 10: Long Transmission Line Model......................................................................28
Figure 11: Medium Length Transmission Line Model.....................................................29
Figure 12: Short Lossy Transmission Line Model...........................................................30
Figure 13: Short Lossless Transmission Line Model.......................................................31
Figure 14: Power System Emulation Network.................................................................35
Figure 15: Polar and Rectangular Coordinate Comparison..............................................36
Figure 16: Classical Generator Model..............................................................................41
Figure 17: Analog Generator Module for DC Emulation.................................................43
Figure 18: Resistor Networks for a Short Lossless Transmission Line............................45
Figure 19: Resistor Networks for a Short Lossy Transmission Line................................46
Figure 20: Resistor Networks for a Medium Length Transmission Line.........................48
Figure 21: Resistor Networks for a Long Transmission Line Model...............................49
Figure 22: Single Line Diagram of a Three Bus Power System.......................................50