Evaluation of Factorization Methods for Thévenin Equivalent Computations in Real-Time Stability Assessment

Christina Hildebrandt, Bahtiyar Can Karatas, Jakob Glarbo Muller, Hjortur Johannsson

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Thevenin equivalents are used by a range of power system stability indicators, such as the L-index for voltage stability and the aperiodic small signal rotor angle stability indicator. This paper investigates the effect of using different factorization methods for computing coefficients for wide-area Thevenin equivalents. Direct and incomplete factorization methods are compared with respect to runtime, accuracy and amount of fill-in. The paper introduces a proof that the block triangular form of bus admittance matrices will have no non-zero entries in the off-diagonal. KLU factorization is found to perform almost twice as fast as the standard LU factorization with no cost of accuracy. It is, however, shown that the largest computational workload is associated with dense matrix multiplications. An incomplete method reduces the fill-in of coefficient matrices at the cost of accuracy in Thevenin voltages. It is shown, that inaccuracies are amplified as the L-index approaches the stability limit.
Original languageEnglish
Title of host publicationProceedings of 2018 Power Systems Computation Conference
Number of pages7
Publication date2018
Pages7 pp.
ISBN (Print)9781910963104
Publication statusPublished - 2018
Event20th Power Systems Computation Conference - O’Brien Centre for Science at University College Dublin, Dublin, Ireland
Duration: 11 Jun 201815 Jun 2018
Conference number: 20


Conference20th Power Systems Computation Conference
LocationO’Brien Centre for Science at University College Dublin
Internet address


  • Power system analysis computing
  • Real-time assessment
  • Thevenin equivalent
  • Wide-area monitoring
  • Power system stability indicators


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