Updating preconditioner for iterative method in time domain simulation of power systems

K. Wang, W. Xue, H.X. Lin, S. Xu, W. Zheng

    Research output: Contribution to journalArticleScientificpeer-review

    Abstract

    The numerical solution of the differential-algebraic equations (DAEs) involved in time domain simulation (TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems. The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems. The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS. As an improvement of dishonest preconditioner (DP) strategy, updating preconditioner strategy (UP) is introduced to the field of TDS for the first time. The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices. In order to make the linear system sequence in TDS suitable for UP strategy, a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating. The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China. Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%–61% the iteration count of the GMRES when compared with the DP method in all test cases. Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.
    Original languageEnglish
    Pages (from-to)1024-1034
    Number of pages11
    JournalJournal Sci China Techn. Sci.
    Volume54
    Issue number4
    Publication statusPublished - 2011

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    Iterative methods
    Linear systems
    Differential equations
    Experiments

    Cite this

    Wang, K., Xue, W., Lin, H. X., Xu, S., & Zheng, W. (2011). Updating preconditioner for iterative method in time domain simulation of power systems. Journal Sci China Techn. Sci., 54(4), 1024-1034.
    Wang, K. ; Xue, W. ; Lin, H.X. ; Xu, S. ; Zheng, W. / Updating preconditioner for iterative method in time domain simulation of power systems. In: Journal Sci China Techn. Sci. 2011 ; Vol. 54, No. 4. pp. 1024-1034.
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    title = "Updating preconditioner for iterative method in time domain simulation of power systems",
    abstract = "The numerical solution of the differential-algebraic equations (DAEs) involved in time domain simulation (TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems. The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems. The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS. As an improvement of dishonest preconditioner (DP) strategy, updating preconditioner strategy (UP) is introduced to the field of TDS for the first time. The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices. In order to make the linear system sequence in TDS suitable for UP strategy, a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating. The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China. Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9{\%}–61{\%} the iteration count of the GMRES when compared with the DP method in all test cases. Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.",
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    Wang, K, Xue, W, Lin, HX, Xu, S & Zheng, W 2011, 'Updating preconditioner for iterative method in time domain simulation of power systems', Journal Sci China Techn. Sci., vol. 54, no. 4, pp. 1024-1034.

    Updating preconditioner for iterative method in time domain simulation of power systems. / Wang, K.; Xue, W.; Lin, H.X.; Xu, S.; Zheng, W.

    In: Journal Sci China Techn. Sci., Vol. 54, No. 4, 2011, p. 1024-1034.

    Research output: Contribution to journalArticleScientificpeer-review

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    AU - Wang, K.

    AU - Xue, W.

    AU - Lin, H.X.

    AU - Xu, S.

    AU - Zheng, W.

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    N2 - The numerical solution of the differential-algebraic equations (DAEs) involved in time domain simulation (TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems. The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems. The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS. As an improvement of dishonest preconditioner (DP) strategy, updating preconditioner strategy (UP) is introduced to the field of TDS for the first time. The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices. In order to make the linear system sequence in TDS suitable for UP strategy, a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating. The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China. Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%–61% the iteration count of the GMRES when compared with the DP method in all test cases. Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.

    AB - The numerical solution of the differential-algebraic equations (DAEs) involved in time domain simulation (TDS) of power systems requires the solution of a sequence of large scale and sparse linear systems. The use of iterative methods such as the Krylov subspace method is imperative for the solution of these large and sparse linear systems. The motivation of the present work is to develop a new algorithm to efficiently precondition the whole sequence of linear systems involved in TDS. As an improvement of dishonest preconditioner (DP) strategy, updating preconditioner strategy (UP) is introduced to the field of TDS for the first time. The idea of updating preconditioner strategy is based on the fact that the matrices in sequence of the linearized systems are continuous and there is only a slight difference between two consecutive matrices. In order to make the linear system sequence in TDS suitable for UP strategy, a matrix transformation is applied to form a new linear sequence with a good shape for preconditioner updating. The algorithm proposed in this paper has been tested with 4 cases from real-life power systems in China. Results show that the proposed UP algorithm efficiently preconditions the sequence of linear systems and reduces 9%–61% the iteration count of the GMRES when compared with the DP method in all test cases. Numerical experiments also show the effectiveness of UP when combined with simple preconditioner reconstruction strategies.

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