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

Mahtab Uddin; M. Monir  Uddin; M. A. Hakim  Khan; M. Tanzim  Hossain

doi:10.38032/jea.2021.03.002

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 approaches do not preserve 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 the 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 computation time and ℌ2 -norm of the error system for reduced-order models of the target models.

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