Graph Theory Applications to Deregulated Power Systems

62 Pages·2021·2.137 MB·English

by  Ricardo Moreno Chuquen, Harold R. Chamorro

SPRINGER BRIEFS IN
ELECTRICAL AND COMPUTER ENGINEERING
Ricardo Moreno Chuquen
Harold R. Chamorro
Graph Theory
Applications
to Deregulated
Power Systems
SpringerBriefs in Electrical and Computer
Engineering
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Ricardo Moreno Chuquen Harold R. Chamorro
(cid:129)
Graph Theory Applications
to Deregulated Power
Systems
123
Ricardo MorenoChuquen Harold R.Chamorro
Universidad Autónoma deOccidente KULeuven
Cali,Colombia Leuven,Belgium
ISSN 2191-8112 ISSN 2191-8120 (electronic)
SpringerBriefs inElectrical andComputer Engineering
ISBN978-3-030-57588-5 ISBN978-3-030-57589-2 (eBook)
https://doi.org/10.1007/978-3-030-57589-2
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Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scope and Contribution of This Book . . . . . . . . . . . . . . . . . . . . . 3
1.3 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Topological Characterization of Power Systems
Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3 Identification of Multiple Subnetworks. . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Identification of Two Subnetworks . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Algebraic Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Identification of K-Subnetworks . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.4 Illustrative Examples: the IEEE 118-Bus System . . . . . . . . . . . . . 15
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 Network Robustness for Power Systems . . . . . . . . . . . . . . . . . . . . . . 19
4.1 Quantification of the Network Robustness . . . . . . . . . . . . . . . . . . 20
4.2 Illustrative Examples: 68-Bus and 118-Bus IEEE Test
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.3 Concluding Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Security Strategies Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1 Hierarchical Islanding of Power System as a Security
Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2 Illustrating the Hierarchical Islanding Procedures . . . . . . . . . . . . . 31
5.2.1 A Medium Size Network Example . . . . . . . . . . . . . . . . . . 31
5.2.2 A Large Size Network Example . . . . . . . . . . . . . . . . . . . . 32
5.2.3 Concluding Remarks About Hierarchical
Islanding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
v
vi Contents
5.3 Quantification of Grid-Impactive Events . . . . . . . . . . . . . . . . . . . 37
5.3.1 Identification of Critical Transmission Lines . . . . . . . . . . . 37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6 Cyber Physical Systems Security for the Smart Grid . . . . . . . . . . . . 43
6.1 Energy Management Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.2 Cyber Physical Systems Security for the Smart Grid. . . . . . . . . . . 44
6.3 Network Topology Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.4 Electricity Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.5 Transmission Automation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.6 Defense Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
6.7 Concluding Remarks and Future Work . . . . . . . . . . . . . . . . . . . . 47
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
7 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.1 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
Appendix A... .... .... .... ..... .... .... .... .... .... ..... .... 55
Appendix B... .... .... .... ..... .... .... .... .... .... ..... .... 57
List of Figures
Fig. 1.1 Graph example.. .... ..... .... .... .... .... .... ..... .. 2
Fig. 1.2 Graph example.. .... ..... .... .... .... .... .... ..... .. 2
Fig. 2.1 Topological characterization of the 68-bus system .... ..... .. 7
Fig. 2.2 Topological characterization of the IEEE 118-bus test
system. .... .... .... ..... .... .... .... .... .... ..... .. 7
Fig. 3.1 Ten Islands identified for the graph model of IEEE 118-bus
test system . .... .... ..... .... .... .... .... .... ..... .. 15
Fig. 3.2 Ten Islands identified for the IEEE 118-bus test system..... .. 15
Fig. 4.1 Fully connected 5-bus network... .... .... .... .... ..... .. 22
Fig. 4.2 5-bus network with a robustness index of 81%... .... ..... .. 22
Fig. 4.3 5-bus network with a robustness of 46% ... .... .... ..... .. 22
Fig. 4.4 68-bus test system.... ..... .... .... .... .... .... ..... .. 23
Fig. 4.5 IEEE 118-bus system and four subnetwork . .... .... ..... .. 24
Fig. 5.1 General algorithm to develop Hierarchical Islanding... ..... .. 30
Fig. 5.2 68-bus system... .... ..... .... .... .... .... .... ..... .. 31
Fig. 5.3 Separation of 68-bus test system into two Islands. .... ..... .. 32
Fig. 5.4 Second request to divide the Island 1 into two Islands. ..... .. 33
Fig. 5.5 Second request to divide the Island 2 into two Islands. ..... .. 33
Fig. 5.6 118-bus test system... ..... .... .... .... .... .... ..... .. 34
Fig. 5.7 Separation of the 118-bus test system into two Islands. ..... .. 34
Fig. 5.8 Separation of the Island 1 into two Islands.. .... .... ..... .. 35
Fig. 5.9 Separation of the Island 2 into two Islands.. .... .... ..... .. 36
Fig. 5.10 Critical transmission lines connecting NETS and NYPS
in 68-bus system. .... ..... .... .... .... .... .... ..... .. 38
Fig. 5.11 Five Islands identified for the IEEE 118-bus test system .... .. 38
Fig. 5.12 Two subnetworks in the IEEE 39-bus system.... .... ..... .. 39
Fig. 5.13 LODFs of all lines when the lines are tripped out .... ..... .. 40
vii
List of Tables
Table 3.1 Tie transmission lines for the IEEE 118-bus system .. ..... .. 16
Table 4.1 Robustness index for EEE 118-buses system.... .... ..... .. 25
Table 5.1 Robustness index for EEE 118-buses system.... .... ..... .. 28
Table 5.2 Two subnetworks for the 68-bus system ... .... .... ..... .. 32
Table 5.3 Division of 118-bus system into two Islands.... .... ..... .. 35
Table 5.4 Buses belonging to the Islands 3 and 4 for the 118-bus
system .... .... .... ..... .... .... .... .... .... ..... .. 36
Table 5.5 Buses belonging to the Islands 5 and 6 for the 118-bus
system .... .... .... ..... .... .... .... .... .... ..... .. 36
Table 5.6 LODFs for the 118-bus system .. .... .... .... .... ..... .. 39
ix
Chapter 1
Introduction
Abstract Inthischapter,wedescribethesettingfortheproblemsofinterestforthe
workpresentedinthisbook.Wefirstintroducethebackgroundandthemotivation
of our research. Then, we present the scope of this report and highlight the major
contributionsifthiswork.Weendwithanoutlinethecontentsoftheremainderof
thischapter.
1.1 BackgroundandMotivation
Networksarepresentinalmosteveryaspectofourlife.Theworldsurroundingus
is full of networks. Social networks consist of relationships among social entities
(i.e.,friends,colleagues,relatives,etc.).Relationshipsamongfirms,vendors,manu-
facturers,andproducersofrawmaterialrepresenteconomicnetworks.Ontheother
hand, technological networks such as the Internet, the computer data network that
representstheinteractionamongcomputersconnectedbyphysicaldataconnections.
TheWorldWideWebnetwork,associatedwiththeInternet,consistsofwebpages
connected by “hyperlinks”. Also, Communication networks consist of telephones
and mobiles phones. The focus of this book is on the power system networks that
have evolved into the largest and most complex system of the technological age.
Additionally, transportation system constitutes important networks i.e., cities and
countries areconnected by road or airlinenetworks.Mostrecently, networks have
becomeimportantinbiology,inconcretetostudythreefields;thefirstoneisrelated
withbiochemicalnetworks,suchasmetabolicnetworks,protein-proteininteraction
networks,andgeneticregulatorynetworks.Ametabolicnetworkisarepresentation
ofthechemicalreactionsthatfuelcellsandorganism.Thesecondone,it’stheappli-
cationofnetworkstogaininsightintoneuralnetworksthatconsistoftheinteraction
amongneurons,ecologicalnetworksarethethirdfieldofstudyinwhicharestudied
theinteractionamongspeciesi.e.,predator-preyrelationships.
Thestudyofnetworkshadalonghistoryinmathematicsandthesciences.Specif-
ically,graphtheoryhasbeenthemathematicallanguagefordescribingtheproperties
ofnetworks.Graphtheoryisrootedintheeighteencenturywhenthemathematician
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SpringerBriefsinElectricalandComputerEngineering,
https://doi.org/10.1007/978-3-030-57589-2_1