A Memory-Efficient Parallelizable Method for Computation of Thévenin Equivalents used in Real-Time Stability Assessment

Christina Hildebrandt Lüthje Jørgensen*, Jakob Glarbo Møller, Stefan Sommer, Hjörtur Jóhannsson

*Corresponding author for this work

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Abstract

This paper introduces a factor-solve method, which efficiently computes Thevenin equivalents for all buses in the power system. A range of real-time stability assessment methods rely on Thevenin equivalents, and it is therefore essential that these can be determined fast and efficiently. The factor-solve method has runtime for computing Thevenin voltage that scales linearly with system size resulting in runtime of only a few milliseconds even for systems with several thousand buses. The computations only need the sparse admittance matrix for the power system and a sparse factorization resulting in low memory requirements, and furthermore Thevenin impedances can be determined in parallel. The factor-solve method is compared to a reference method, which uses coefficients for super-position to determine the Thevenin equivalents. The reference method is shown to have dissatisfying runtime and complexity. The factorsolve method is tested, parallelized and analysed, which shows a considerable speed-up in computations of Thevenin equivalents enabling them to be computed in real-time.
Original languageEnglish
JournalI E E E Transactions on Power Systems
Volume34
Issue number4
Pages (from-to)2675-2684
Number of pages9
ISSN0885-8950
DOIs
Publication statusPublished - 2019

Keywords

  • Algorithms
  • Power system analysis computing
  • Real-time assessment
  • Thevenin equivalent

Cite this

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title = "A Memory-Efficient Parallelizable Method for Computation of Th{\'e}venin Equivalents used in Real-Time Stability Assessment",
abstract = "This paper introduces a factor-solve method, which efficiently computes Thevenin equivalents for all buses in the power system. A range of real-time stability assessment methods rely on Thevenin equivalents, and it is therefore essential that these can be determined fast and efficiently. The factor-solve method has runtime for computing Thevenin voltage that scales linearly with system size resulting in runtime of only a few milliseconds even for systems with several thousand buses. The computations only need the sparse admittance matrix for the power system and a sparse factorization resulting in low memory requirements, and furthermore Thevenin impedances can be determined in parallel. The factor-solve method is compared to a reference method, which uses coefficients for super-position to determine the Thevenin equivalents. The reference method is shown to have dissatisfying runtime and complexity. The factorsolve method is tested, parallelized and analysed, which shows a considerable speed-up in computations of Thevenin equivalents enabling them to be computed in real-time.",
keywords = "Algorithms, Power system analysis computing, Real-time assessment, Thevenin equivalent",
author = "J{\o}rgensen, {Christina Hildebrandt L{\"u}thje} and M{\o}ller, {Jakob Glarbo} and Stefan Sommer and Hj{\"o}rtur J{\'o}hannsson",
year = "2019",
doi = "10.1109/TPWRS.2019.2900560",
language = "English",
volume = "34",
pages = "2675--2684",
journal = "I E E E Transactions on Power Systems",
issn = "0885-8950",
publisher = "Institute of Electrical and Electronics Engineers",
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TY - JOUR

T1 - A Memory-Efficient Parallelizable Method for Computation of Thévenin Equivalents used in Real-Time Stability Assessment

AU - Jørgensen, Christina Hildebrandt Lüthje

AU - Møller, Jakob Glarbo

AU - Sommer, Stefan

AU - Jóhannsson, Hjörtur

PY - 2019

Y1 - 2019

N2 - This paper introduces a factor-solve method, which efficiently computes Thevenin equivalents for all buses in the power system. A range of real-time stability assessment methods rely on Thevenin equivalents, and it is therefore essential that these can be determined fast and efficiently. The factor-solve method has runtime for computing Thevenin voltage that scales linearly with system size resulting in runtime of only a few milliseconds even for systems with several thousand buses. The computations only need the sparse admittance matrix for the power system and a sparse factorization resulting in low memory requirements, and furthermore Thevenin impedances can be determined in parallel. The factor-solve method is compared to a reference method, which uses coefficients for super-position to determine the Thevenin equivalents. The reference method is shown to have dissatisfying runtime and complexity. The factorsolve method is tested, parallelized and analysed, which shows a considerable speed-up in computations of Thevenin equivalents enabling them to be computed in real-time.

AB - This paper introduces a factor-solve method, which efficiently computes Thevenin equivalents for all buses in the power system. A range of real-time stability assessment methods rely on Thevenin equivalents, and it is therefore essential that these can be determined fast and efficiently. The factor-solve method has runtime for computing Thevenin voltage that scales linearly with system size resulting in runtime of only a few milliseconds even for systems with several thousand buses. The computations only need the sparse admittance matrix for the power system and a sparse factorization resulting in low memory requirements, and furthermore Thevenin impedances can be determined in parallel. The factor-solve method is compared to a reference method, which uses coefficients for super-position to determine the Thevenin equivalents. The reference method is shown to have dissatisfying runtime and complexity. The factorsolve method is tested, parallelized and analysed, which shows a considerable speed-up in computations of Thevenin equivalents enabling them to be computed in real-time.

KW - Algorithms

KW - Power system analysis computing

KW - Real-time assessment

KW - Thevenin equivalent

U2 - 10.1109/TPWRS.2019.2900560

DO - 10.1109/TPWRS.2019.2900560

M3 - Journal article

VL - 34

SP - 2675

EP - 2684

JO - I E E E Transactions on Power Systems

JF - I E E E Transactions on Power Systems

SN - 0885-8950

IS - 4

ER -