An adaptive dynamic Implicitly Restarted Arnoldi method for the small signal stability eigen analysis of large power systems

Chabane, Yasmina; Hellal, A.

doi:10.1016/j.ijepes.2014.06.028

Cited by 11 publications

(9 citation statements)

References 9 publications

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“…In this paper, an Augmented Block Householder Arnoldi method (Baglama 2008), known by the acronym ABHA, combining the advantages of a block and an augmented routine, is adapted and tested for small-signal stability problems. It is worthy to mention that this method has already been successfully applied in different fields of science and engineering (Chabane and Hellal 2014;Baglama 2008;Bai et al 1997;Duff et al 1992; Jiang and Wu 2010), but nothing has been found in the literature for small-signal stability problems.…”

Section: The Augmented Block Householder Arnoldi Methodsmentioning

confidence: 99%

“…This parameter is used to finetune the number of augmented vectors to avoid breakdowns and near-breakdowns, therefore preventing the iterative process to stagnate. The remaining parameters, adjust, block size (blsz) and number of blocks (nbls) have been properly adjusted after several rounds of simulations computing the eigenvalues focusing on the smallest CPU time, with the aid of information provided by previous experiments (Chabane and Hellal 2014;Baglama 2008;Bai et al 1997;Duff et al 1992;Jiang and Wu 2010). It must be noted that the block size and the number of blocks are associated with the dimension of the dynamic state Jacobian matrices.…”

Section: General Informationmentioning

confidence: 99%

“…Since the method is being tested for the first time in small-signal stability, it was necessary to resort to earlier experiments (Chabane and Hellal 2014;Baglama 2008;Bai et al 1997;Duff et al 1992; Jiang and Wu 2010) for a first round of simulations. The following pieces of information have been considered: block size (blsz) ranging from 1 to 4, number of blocks (nbls) approximated by the ratio n blsz, where n is the dimension of the matrix.…”

Section: General Comments and Contributionsmentioning

confidence: 99%

“…Among the methods, the QR decomposition can be successfully adapted to arbitrary complex matrices, presenting an excellent property of rounding and convergence behaviour (Francis 1961(Francis , 1962Ma et al 2006). However, for matrices with multiple and clustered eigenvalues, the method normally needs many steps to converge and it is time and memory consuming (Chabane and Hellal 2014).…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Section: The Augmented Block Householder Arnoldi Methodsmentioning

confidence: 99%

Section: General Informationmentioning

confidence: 99%

Section: General Comments and Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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Equivalent dimensionality reduction method of doubly‐fed induction generator model and discrimination of Hopf bifurcation type

Chen

Wei

et al. 2023

Energy Science & Engineering

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The strong coupling, multivariate, and nonlinear characteristics of the mathematical model of a doubly-fed induction generator (DFIG) make it challenging to analyze the bifurcation category of the DFIG. Therefore, in this study, we developed a method for analyzing the DFIG model via topologically equivalent dimensionality reduction in the neighborhood of bifurcation values based on the central manifold theorem and realized the discrimination of the Hopf bifurcation type of the DFIG. We established a complex frequency domain model of the DFIG and then calculated the critical open-loop gain point using the root trajectory method to obtain the relationship between the critical open-loop gain point and Hopf bifurcation. Thereafter, we performed topological equivalence dimensionality reduction in the neighborhood of the DFIG bifurcation values based on the central manifold theorem. Subsequently, the Hopf bifurcation type of the system was determined using the stability index (first Lyapunov exponent) of the Hopf bifurcation. Finally, a nonlinear time-domain simulation was used to verify that the four and two-dimensional DFIGs generate a stable limit cycle by supercritical Hopf bifurcation under the tuning parameter. The results indicated that the proposed method was feasible and effective in the neighborhood of bifurcation values in the state parameter space of DFIG, which provides a theoretical basis for the control of Hopf bifurcation of the DFIG.

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A scalable method with synchronous parallelization for computing selected eigenvalues of large-scale power system model

Li,

Zhang,

Zhou

et al. 2025

Electric Power Systems Research

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An adaptive dynamic Implicitly Restarted Arnoldi method for the small signal stability eigen analysis of large power systems

Cited by 11 publications

References 9 publications

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

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

Equivalent dimensionality reduction method of doubly‐fed induction generator model and discrimination of Hopf bifurcation type

A scalable method with synchronous parallelization for computing selected eigenvalues of large-scale power system model

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