Scalable Newton-Krylov Solver for Very Large Power Flow Problems

Idema, Reijer; Lahaye, Domenico; Vuik, C.; Sluis, L. van der

doi:10.1109/tpwrs.2011.2165860

Cited by 35 publications

(49 citation statements)

References 30 publications

(32 reference statements)

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“…The linear Jacobian systems are solved using GMRES [9], with a high quality ILU factorization of the Jacobian as preconditioner. For more information on the test case and solution method see [6].…”

Section: Numerical Experimentsmentioning

confidence: 99%

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On the Convergence of Inexact Newton Methods

Idema

Lahaye

Vuik

2014

Lecture Notes in Computational Science and Engineering

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Section: Numerical Experimentsmentioning

confidence: 99%

“…Power flow computations in power systems, which lead to systems of non-linear equations, are no different. In our research towards improving power flow computations we have used the inexact Newton method, where an iterative linear solver is used for the linear systems [5,6].…”

Section: Introductionmentioning

confidence: 99%

On the Convergence of Inexact Newton Methods

Idema

Lahaye

Vuik

2014

Lecture Notes in Computational Science and Engineering

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“…In [6] we showed that the LU factorization-which is used by both these traditional methods-is not viable for very large power flow problems. As an alternative, we proposed the use of Newton-Krylov methods: inexact Newton methods that incorporate Krylov methods to solve the linear problems.…”

Section: The Power Flow Problemmentioning

confidence: 99%

“…In this paper we propose the use of Newton-Krylov power flow methods, and analyze a multitude of preconditioning techniques to optimize performance. The good results of incomplete LU factorizations [6] are explained, and extended with incomplete Cholesky factorizations. Further, inner-outer Krylov methods are investigated, with proper attention to the accuracy of the inner solves.…”

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confidence: 97%

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Towards Faster Solution of Large Power Flow Problems

Idema

Papaefthymiou

Lahaye

et al. 2013

IEEE Trans. Power Syst.

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Monitoring a PGD solver for parametric power flow problems with goal‐oriented error assessment

García-Blanco

Borzacchiello

Chinesta

et al. 2017

Numerical Meth Engineering

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This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft

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Scalable Newton-Krylov Solver for Very Large Power Flow Problems

Cited by 35 publications

References 30 publications

On the Convergence of Inexact Newton Methods

On the Convergence of Inexact Newton Methods

Towards Faster Solution of Large Power Flow Problems

Monitoring a PGD solver for parametric power flow problems with goal‐oriented error assessment

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