Invertibility Conditions for the Admittance Matrices of Balanced Power Systems

The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies....

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Published inIEEE transactions on power systems Vol. 38; no. 4; pp. 3841 - 3853
Main Authors Turizo, Daniel, Molzahn, Daniel K.
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Admittance
Admittance matrix
circuit analysis
Current injection
Electrical impedance
Integrated circuit modeling
Network topologies
Null space
Phasors
Power engineering
Power system stability
Symmetric matrices
Voltage
Online AccessGet full text
ISSN0885-8950
1558-0679
DOI10.1109/TPWRS.2022.3206285

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Abstract The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of invertibility . Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.
AbstractList The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of invertibility . Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.
Author Turizo, Daniel
Molzahn, Daniel K.
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Cites_doi 10.1109/TPWRS.2018.2863671
10.1109/TPWRS.2016.2569563
10.1109/59.871741
10.1109/TPWRS.2019.2900560
10.1002/nla.2235
10.1016/j.segan.2018.03.002
10.1016/j.epsr.2018.12.021
10.1016/S0024-3795(02)00572-4
10.1007/s11750-010-0161-9
10.1016/j.apenergy.2017.05.012
10.1007/978-3-642-30994-6
10.1109/TPWRS.2008.922256
10.1002/9781118878309
10.1109/TPWRS.2009.2021235
10.1137/0917055
10.1109/TPAS.1982.317142
10.1109/TPWRS.2017.2768223
10.1137/1.9780898719512
10.1109/TPWRS.2017.2728618
10.1007/978-3-662-53622-3
10.1201/b19019
10.1109/TSTE.2019.2916499
10.1007/978-1-4613-0163-9
10.1109/TPWRS.2017.2719583
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References ref13
ref12
ref15
ref14
ref31
ref30
ref11
ref10
stevenson (ref26) 1994
godsil (ref27) 2001; 207
ref2
zimmerman (ref33) 2020
ref17
ref16
ref19
ref18
(ref25) 2021
kron (ref3) 1959
anderson (ref7) 1995
ref20
ref22
ref21
low (ref23) 2022
bakshi (ref24) 2008
ref28
kundur (ref1) 1994
ref29
cormen (ref32) 2022
ref8
ref9
ref4
ref6
ref5
josz (ref34) 2016
References_xml – ident: ref21
  doi: 10.1109/TPWRS.2018.2863671
– year: 2022
  ident: ref23
  article-title: Power systems analysis: A mathematical approach. lecture notes for EE/CS/EST 135. california institute of technology
– ident: ref6
  doi: 10.1109/TPWRS.2016.2569563
– ident: ref10
  doi: 10.1109/59.871741
– ident: ref4
  doi: 10.1109/TPWRS.2019.2900560
– year: 2020
  ident: ref33
  article-title: Matpower user's manual
– year: 1994
  ident: ref1
  publication-title: Power System Stability and Control
– ident: ref16
  doi: 10.1002/nla.2235
– ident: ref11
  doi: 10.1016/j.segan.2018.03.002
– ident: ref12
  doi: 10.1016/j.epsr.2018.12.021
– ident: ref13
  doi: 10.1016/S0024-3795(02)00572-4
– ident: ref15
  doi: 10.1007/s11750-010-0161-9
– ident: ref18
  doi: 10.1016/j.apenergy.2017.05.012
– year: 1994
  ident: ref26
  publication-title: Power System Analysis
– ident: ref31
  doi: 10.1007/978-3-642-30994-6
– ident: ref17
  doi: 10.1109/TPWRS.2008.922256
– year: 1995
  ident: ref7
  publication-title: Analysis of Faulted Power Systems
– ident: ref28
  doi: 10.1002/9781118878309
– ident: ref8
  doi: 10.1109/TPWRS.2009.2021235
– ident: ref14
  doi: 10.1137/0917055
– ident: ref9
  doi: 10.1109/TPAS.1982.317142
– ident: ref5
  doi: 10.1109/TPWRS.2017.2768223
– year: 2022
  ident: ref32
  publication-title: Introduction to Algorithms
– ident: ref29
  doi: 10.1137/1.9780898719512
– ident: ref22
  doi: 10.1109/TPWRS.2017.2728618
– ident: ref30
  doi: 10.1007/978-3-662-53622-3
– year: 2016
  ident: ref34
  article-title: AC power flow data in MATPOWER and QCQP format: ITesla, RTE snapshots, and PEGASE
– year: 2008
  ident: ref24
  article-title: Electrical networks
– ident: ref2
  doi: 10.1201/b19019
– year: 1959
  ident: ref3
  publication-title: Tensors for Circuits
– ident: ref19
  doi: 10.1109/TSTE.2019.2916499
– volume: 207
  year: 2001
  ident: ref27
  publication-title: Algebraic Graph Theory
  doi: 10.1007/978-1-4613-0163-9
– year: 2021
  ident: ref25
  article-title: The power grid library for benchmarking AC optimal power flow algorithms (20.07)
– ident: ref20
  doi: 10.1109/TPWRS.2017.2719583
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Snippet The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors....
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SubjectTerms Admittance
Admittance matrix
circuit analysis
Current injection
Electrical impedance
Integrated circuit modeling
Network topologies
Null space
Phasors
Power engineering
Power system stability
Symmetric matrices
Voltage
Title Invertibility Conditions for the Admittance Matrices of Balanced Power Systems
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