Towards Faster Solution of Large Power Flow Problems

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

doi:10.1109/tpwrs.2013.2252631

Cited by 24 publications

(13 citation statements)

References 39 publications

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“…Also shown in Table 1 is the maximum number of hierarchy levels for each of the networks. Note that we do not use the small-angle approximation in (18), but use the exact angle update.…”

Section: Smoothingmentioning

confidence: 99%

“…While multigrid is not the only class of methods with this feature (e.g., see [36] for graph Laplacian linear solvers), achieving algorithmic scalability typically requires the use of some coarse problem hierarchy. With the exception of the AMG preconditioner in [18], the solvers in the above papers do not make use of a hierarchy of coarse problems. Recently, [28] also proposed the use of multigrid in the time domain for dynamic power grid simulations.…”

mentioning

confidence: 99%

“…The nonlinear algebraic multigrid framework and methods developed in this paper do not use algebraic multigrid to solve the Jacobian of a Newton--Raphson iterate as in [18]. Rather, it builds a multigrid hierarchy for the power flow problem directly.…”

mentioning

confidence: 99%

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A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Ponce¹,

Bindel²,

Vassilevski³

2018

SIAM J. Sci. Comput.

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Multigrid is a highly scalable class of methods most often used for solving large linear systems. In this paper we develop a nonlinear algebraic multigrid framework for the power flow equations, a complex quadratic system of the form diag(\bfitv)Y \bfitv = \bfits , where Y is approximately a complex scalar rotation of a real graph Laplacian. This is a standard problem that needs to be solved repeatedly during power grid simulations. A key difference between our multigrid framework and typical multigrid approaches is the use of a novel multiplicative coarse-grid correction to enable a dynamic multigrid hierarchy. We also develop a new type of smoother that allows one to coarsen together the different types of nodes that appear in power grid simulations. In developing a specific multigrid method, one must make a number of choices that can significantly affect the method's performance, such as how to construct the restriction and interpolation operators, what smoother to use, and how aggressively to coarsen. In this paper, we make simple but reasonable choices that result in a scalable and robust power flow solver. Experiments demonstrate this scalability and show that it is significantly more robust to poor initial guesses than current state-of-the-art solvers.

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“…Also shown in Table 1 is the maximum number of hierarchy levels for each of the networks. Note that we do not use the small-angle approximation in (18), but use the exact angle update.…”

Section: Smoothingmentioning

confidence: 99%

mentioning

confidence: 99%

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A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Ponce¹,

Bindel²,

Vassilevski³

2018

SIAM J. Sci. Comput.

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“…Since the computation of eigenvalues and eigenvectors is usually the most challenging and time-consuming part of the analysis, investigations on methods capable of handling matrices with multiple and clustered eigenvalues can be worthy and timely. Despite that Krylov methods have already been tested for iterative solution of linear systems in power flow (Poma et al 2017;Idema et al 2013;Pessanha et al 2011), and time domain (Pessanha et al 2013), a modest interest in such methods for small-signal stability problems emerged in the last decade with promising results (Chabane and Hellal 2014;Chung and Dai 2013;Li et al 2006).…”

Section: Introductionmentioning

confidence: 99%

Augmented Block Householder Arnoldi Method Applied in Small-Signal Stability Analysis of Power Systems

Rezende

Pessanha

2020

J Control Autom Electr Syst

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Iterative methods built on Krylov subspaces have been little explored to date for the computation of eigenvalues and eigenvectors in small-signal stability analysis. Such computation is challenging and computationally expensive for matrices with a certain number of multiple and clustered eigenvalues, conditions that can be found in many dynamic state Jacobian matrices. The present paper aims to contribute with a block algorithm to perform small-signal stability analysis with this particular type of matrix, built on the Augmented Block Householder Arnoldi (ABHA) method. The advantages of using a block method lie on the fact that the searching subspace for approximate solutions is the sum of every Krylov subspace, and therefore, the solution is expected to converge in less iterations than an unblock method. The efficiency and robustness of the proposal are examined through numerical simulations using three power systems and two other methods: the conventional Arnoldi (unblock) and QR decomposition. The results indicate that the proposed numerical algorithm is more robust than the other two for handling dynamic state Jacobian matrices having a certain number of multiple and clustered eigenvalues.

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“…Although Krylov-subspace methods are not still of widespread usage in the Power Systems community, as is for the PDE-simulation researchers, their use has gained increasing attention, as well as the emerging GPU computing [26] [27].…”

Section: State Of the Artmentioning

confidence: 99%

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

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Towards Faster Solution of Large Power Flow Problems

Cited by 24 publications

References 39 publications

A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Augmented Block Householder Arnoldi Method Applied in Small-Signal Stability Analysis of Power Systems

Computação paralela em GPU para resolução de sistemas de equações algébricas resultantes da aplicação do método de elementos finitos em eletromagnetismo.

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