SVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models

Authors

  • Mahtab Uddin Institute of Natural Sciences, United International University, Dhaka-1212, Bangladesh
  • M. Monir Uddin Department of Mathematics and Physics, North South University, Dhaka-1229, Bangladesh
  • M. A. Hakim Khan Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh
  • M. Tanzim Hossain Department of Electrical and Computer Engineering, North South University, Dhaka-1229, Bangladesh

DOI:

https://doi.org/10.38032/jea.2021.03.002

Keywords:

Singular Value Decomposition, Krylov Subspace, Alternative Direction Implicit, Riccati Equation, ℌ2 -norm, Optimal Feedback Stabilization

Abstract

We propose an efficient sparsity-preserving reduced-order modelling approach for index-1 descriptor systems extracted from large-scale power system models through two-sided projection techniques. The projectors are configured by utilizing Gramian based singular value decomposition (SVD) and Krylov subspace-based reduced-order modelling. The left projector is attained from the observability Gramian of the system by the low-rank alternating direction implicit (LR-ADI) technique and the right projector is attained by the iterative rational Krylov algorithm (IRKA). The classical LR-ADI technique is not suitable for solving Riccati equations and it demands high computation time for convergence. Besides, in most of the cases, reduced-order models achieved by the basic IRKA are not stable and the Riccati equations connected to them have no finite solution. Moreover, the conventional LR-ADI and IRKA approach not preserves the sparse form of the index-1 descriptor systems, which is an essential requirement for feasible simulations. To overcome those drawbacks, the fitting of LR-ADI and IRKA based projectors from left and right sides, respectively, desired reduced-order systems attained. So that, finite solution of low-rank Riccati equations, and corresponding feedback matrix can be executed. Using the mechanism of inverse projection, the Riccati-based optimal feedback matrix can be computed to stabilize the unstable power system models. The proposed approach will maintain minimized ℌ2 -norm of the error system for reduced-order models of the target models.

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Published

20-08-2021 — Updated on 25-09-2021

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How to Cite

Uddin, M., Uddin, M. M. ., Khan, M. A. H. ., & Hossain, M. T. . (2021). SVD-Krylov based Sparsity-preserving Techniques for Riccati-based Feedback Stabilization of Unstable Power System Models. Journal of Engineering Advancements, 2(03), 125–131. https://doi.org/10.38032/jea.2021.03.002 (Original work published August 20, 2021)

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Research Articles