Augmented Block Householder Arnoldi Method Applied in Small-Signal Stability Analysis of Power Systems
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Augmented Block Householder Arnoldi Method Applied in Small-Signal Stability Analysis of Power Systems Lucas Bertoldo Rezende1
· José Eduardo Onoda Pessanha1
Received: 8 March 2020 / Revised: 28 July 2020 / Accepted: 8 September 2020 © Brazilian Society for Automatics--SBA 2020
Abstract 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. Keywords Krylov subspace · Small-signal stability · Eigenvalues · Computational efficiency
1 Introduction Small-signal stability problem is usually associated with insufficient damping of oscillations, and it is formulated in such a way that the disturbances are considered sufficiently small that linearization of the system’s equations is acceptable for purposes of analysis (Kundur et al. 2004; Kundur 1994). In this case, two types of investigations are possible: (a) multimachine linearized analysis that computes the eigenvalues and also finds those machines that contribute to a particular eigenvalue—both local and interarea oscillations can be studied, and (b) a single-machine This work was partially supported by the Coordination for the Improvement of Higher Education Personnel (CAPES foundation–Ministry of Education—Brazil) 88,882.445751/2019–01.
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Lucas Bertoldo Rezende [email protected] José Eduardo Onoda Pessanha [email protected]
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Group of Advanced Studies in Power Systems Dynamics and Control - GASPDC, Department of Electrical Engineering, Federal University of Maranhão - UFMA, Av. dos Portugueses, 1966 - Vila Bacanga, São Luís, MA 65080-805, Brazil
infinite-bus system scenario that investigates only local oscillations (Kundur 1994). However, in order to supply and reach more customers within a reliable and continuous service, power systems around the world are continuously increasing in terms of dimension, controllability challenges and complexity, besides operating in stressed conditions (high load levels). As a
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